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Book summary
Mathematics Handbook for Science and Engineering is a comprehensive handbook for scientists, engineers, teachers and students at universities. The book presents in a lucid and accessible form classical areas of mathematics like algebra, geometry and analysis and also areas of current interest like discrete mathematics, probability, statistics, optimization and numerical analysis. It concentrates on definitions, results, formulas, graphs and tables and emphasizes concepts and methods with applications in technology and science.For the fifth edition the chapter on Optimization has been enlarged and the chapters on Probability Theory and Statstics have been carefully revised. TOCFundamentals, Discrete Mathematics.- Algebra.- Geometry and Trigometry.- Linear Algebra.- The Elementary Functions.- Differential Calculus One Variable.- Integral Calculus.- Sequences and Series.- Ordinary Differential Equations ODE.- Multidimensional Calculus.- Vector Analysis.- Orthogonal Series and Special Functions.- Transforms.- Complex Analysis.- Optimization.- Numerical Analysis.- Probability Theory.- Statistics.- Miscellaneous.- Glossary of Functions.- Glossary of Symbols. [via] |
: Hi, my son is taking algebra II. He really struggled with alg.I and his tutor said it is because he does not have a solid grounding in the basics, for example, squaring numbers, multiplying numbers of opposite signs, automatic recall of facts, tips and tricks, etc. In our school system, EVERYONE has to take algebra in high school, unless they are in special ed. Can someone recommend a workbook that I can have him work in daily to pound some basics into his head? : Thank you.
******************************* The basic book you want should be on "pre algaebra". You can goto some book-store and find work-book on that subject. |
Materials
Instructional Plan
This lesson develops conceptual understanding of linear programming by walking students through the process of linear programming. Along the way, students are asked to explain what is happening and why, which allows them to internalize the procedural skill necessary to solve linear programming problems.
The basis of this lesson is the Dirt Bike Dilemma activity sheet. Before attempting to use this material in class, be sure to look over the activity sheet and solve the problems on your own.
In particular, you should notice that the activity sheet requires the use of TI Graphing Calculators. If you intend to use this lesson with a different type of calculator or with a spreadsheet program, you will need to modify the activity packet before copying and distributing it to students.
To be prepared for this lesson, you will need to copy the DRTBK program into your calculator. Right click on the DRTBK Program and choose "Save Target As…" Then, save the file to your computer desktop.
Double click on the TI ConnectTM icon.
Attach the TI‑83 plus or TI‑84 plus graphing calculator to the computer using the TI GRAPHLINKTM cable. (This USB cable comes with the calculator.)
Click on Data Explorer or TI Group Explorer.
Drag the DRTBK icon from the desk top into the TI Data file.
Click on DRTBK.8xp to highlight it.
Select Actions from the tool bar.
Select Send to TI Device.
The computer should show the file being transferred to the calculator.
You will also need a program called Transformation on your calculator. It may already be there. You can determine if the Transformation program is installed by pressing the APPS button and scrolling through the alphabetical list of applications. If Transformation is not listed, you will need to install the program. The Transformation Graphing Application can be downloaded from the TI Web site. As before, download the program to your computer, and transfer it to your calculator using a TI GRAPHLINKTM cable and TI ConnectTM software.
Each student will need a TI‑83+ or TI‑84+ graphing calculator containing the DRTBK program and the Transformation Graphing application. If these programs are not installed, take some time at the beginning of class to have students download these programs to their calculators. In addition, each student will need a copy of the Dirt Bike Dilemma activity sheet. Each team will also need some colored pencils and a deck of the Dirt Bike Cards.
Divide the class into teams of three students. One member of the team should be given all of the Wheel cards; this team member is responsible for completing Question 1 on the activity sheet. Similarly, another team member should be given all of the Exhaust Pipe cards and complete Question 2, and the last team member should receive all of the Seat cards and complete Question 3.
This lesson is designed to guide students to discover and consolidate the concepts associated with solving linear programming problems. Your role as teacher is to assess their understanding and provide assistance if they encounter difficulties. Move from one team to another, listening to the discussions. Encourage students to work cooperatively; try to refrain from answering individual student questions, especially those that can be answered by the team.
Read the problem out loud to your students. Ask a student to describe the problem in his or her own words.
The first part of the lesson (Questions 1‑3) asks the students to work independently. Basically, Questions 1 3 deal with the same concepts. Each team member is asked to complete a table and graph, relating the number of Rovers that can be assembled given the number of Riders that have been assembled, based on the number of wheels, exhaust pipes, or seats. The purpose of these questions is to help the student visualize the problem and to come up with the constraints for the linear programming problem that they will solve.
Randomly ask different teams to explain how they arrived at their responses, especially to Questions 7, 9, 10, 12, 13, and 14. If you are not satisfied with their response, ask some probing questions, such as the following:
What happens if I select a point outside the feasible region?
Can the corner points also tell me the combination that will give the minimum profit?
Continue to question until you feel that they are making a connection. Visit each group at least once.
Bring the class together after most teams have completed Question 10. Go through the steps with the class of how to set up and use the DRTBK program. (The procedure for using this program is found in Question 11 on the activity sheet.) Also, go through the first three steps of using the Transformation Graphing Apps. (These steps are found in Question 12 on the activity sheet.) When completing the table in Question 11, tell your students if the maximum value occurs more than once, they should write down both combinations.
When all teams have completed Questions 1 through 13, have a whole‑class discussion. Use the questions from the Questions For Students section.
On the board or overhead projector, list all of the responses to Question 14, "List five major steps required to solve a linear programming problem?" After all responses have been collected, allow the class to narrow the list down to the five major steps.
Allow the class to complete Question 14 on the activity sheet. This can be done with the time remaining in class or as a homework assignment. If used as a homework assignment, the solution should be discussed the next day.
Questions for Students
What is a feasible region?
[The feasible region is the region formed by the intersection of all of the constraints.]
What is an objective function?
[An objective function is function for which you are trying to find the minimum or maximum value.]
Why must the corner points of the feasible region produce the maximum or minimum value of the objective function?
[The corner points of the feasible region produces the maximum or minimum value of the objective function because as the y‑intercept of the objective function line increases (or decreases), the last point it encounters as it leaves the feasible region is one of the corner points.]
Are there times when no unique point will minimize or maximize an objective function? If so, when? If not, why not?
[There are times when there is no unique point that will minimize or maximize an objective function. This occurs when the objective function lines are parallel to one of the sides of the feasible region. Therefore, as the y‑intercept of the objective function line increases (or decreases), the last object it encounter is a line segment and not a single point. In this case, there will be multiple points that yield the maximum (or minimum) value.]
What are the five major steps necessary for solving linear programming problems?
[The five major steps for solving a linear programming problem are:
Determine the inequalities that represent the constraints.
Graph the feasible region.
Determine the corner points of the feasible region.
Determine the objective function.
Substitute the coordinates of the corner points into the objective function to determine which yields the maximum (or minimum) value.
Note that student lists may appear differently, but they should contain these same basic ideas.]
Assessment Options
Students can play the Clue Cards Game as an assessment activity. As students work, circulate and assess their ability to solve linear programming problems.
Make one copy of the clue cards for each team. Copying each set (Dog Food, Painting, and Four Wheelers) onto a different color of card stock can help manage the collection of cards when teams are finished. Cut each sheet into four clue cards. Each team receives three sets of four clues cards. Place a set of cards for each team in an envelope. Each set of four cards contains the information for one linear programming problem.
Copy the game board to a transparency sheet, and place it on the overhead projector. Assign a colored chip or marker to each team. As each team correctly solves a set of clues, move their colored chip to the next level.
The class should be divided into teams of four students.
Each team should have an envelope containing three sets of clue cards, scratch paper, pencils, graph paper, a ruler, and a graphing calculator (optional).
To begin, open the envelope and find the Dog Food clue cards. Give one card to each member of each team.
Students may only look at the clue on the card they received. They may not look at anyone else's. Each students should read their clue to their team members. Cooperatively, they should solve the problem.
When a team thinks that they have arrived at the solution to a problem, they should raise their hands. They should not say the answer aloud.
If a team's solution is correct, direct them to go to the set of clue cards for Paintings. Then, move their playing piece to the next level, and award the team five points. If the team's solution is not correct, ask them to look over their work and try again.
Students should continue this process until they have found the solution to all three sets of clues.
A correct solution to Dog Food is worth five points. A correct solution to Paintings is worth ten points, and a correct solution to Four Wheelers is worth fifteen points. The first team to find the solutions to all three sets of clues wins an additional twenty points. The second team wins an additional ten points, and the third team wins an additional five points.
Teacher Reflection
Was students' level of enthusiasm/involvement high or low? Explain why |
Mathematics for 11+ is an
educational software package aimed at testing and
evaluating the mathematics skills of primary school
students in the Caribbean who are about to take the
secondary school entrance examination.
English for 11+ is aimed at testing and
evaluating the English skills of primary school
students in the Caribbean who are about to take the
secondary school entrance examination.
We offer the Home Edition
for home use which is installed on a single computer.
An unlimited number of users can use the program on that
computer by setting up multiple user accounts.
The School
Edition is used in schools with a client/server
environment. The server side of the application will be installed on a
central server and there is no limit to the number
of simultaneous users. The client side is
installed on each machine that students will use to run
the program. |
Mathematics
Mathematics
The Mathematics Department offers a broad, in-depth curriculum for exploring all aspects of mathematics – including quantities, changes, abstraction, structure and space – through small, engaging classroom settings. Within the department there is a great sense of discovery and collaboration as students and faculty are active in research, journal publication, conference presentations, mathematics competitions and many have received distinguished awards and recognition.
Research
is an integral part of the program and is incorporated into coursework as well as ongoing, unique research solutions outside of the classroom. In addition to collaborative research projects with faculty, students are highly active in the Math Club where they have the opportunity to discuss mathematics, solve problems and participate in social activities. A dedicated tutoring facility, great professor accessibility and the encouragement of open discussions in the classroom all contribute to a nurturing and supportive learning environment that lends a deep exploration of mathematics. Graduates are poised to excel in graduate programs and have become highly successful alumni who are skilled educators, actuaries, engineers, financial mathematicians and more.
Wally Sizer, Mathematics, had a paper "Period two solutions to some systems of rational difference equations" published in the book "Differential and Difference Equations with Applications," edited by Sandra Pinelas, Michel Chipot, and Zuzana Dusla, and published by Springer Verlag.
MSUM Math Club is holding the "Pie The Professor" fundraising event Wednesday, April 24 from 12-4 p.m.. It will be on the campus mall on the north side of MacLean Hall. Come throw cream pies at volunteered math professors. Slices of pie will also be for sale. |
A First Course in Mathematical Modeling, 4th Edition
ISBN10: 0-495-01159-2
ISBN13: 978-0-495-01159-0
AUTHORS: Giordano/Fox/Horton/Weir
Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 4th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your progressive development and confidence in mathematics and modeling |
Offering
10+ subjects, including algebra 1 algebra 1
"Mathematician and Programmer" Logic and syntax. The logic of programming is something... |
Real-World Problem Solving
The GED Mathematics Test concentrates on real-world problem solving. For about half of the items, it uses graphic-based material, such as charts, tables, graphs, and diagrams. Students can expect to see most problems presented in a practical context that may address more than one concept. The GED Mathematics Test also measures analytical and reasoning skills.
Think for a moment about the steps that you use to solve any problem, not just a math problem. When solving a problem, you probably:
Sort through the information.
Pull together the information that you need.
Discard unnecessary information.
Put the information together in a manner that works for you.
Decide on the best approach for solving the problem.
Solve the problem using that approach.
If the approach you selected worked, then you have solved your problem. If it didn't work, then you go back to the drawing board to see if there is another approach that you can use.
The same thing works in math. Students must learn how to analyze, approach, and solve problems if they are to be successful on the GED Mathematics Test. |
Apart from understanding the statements of
abstract theorems (see Formulating mathematics), you should
become used to proving them rigorously. The most
important theorems will be proved in books and
lectures, but you may be asked to reproduce the proofs
in examinations. Moreover, you will frequently be set
problems which require you to prove abstract statements
which you have not seen before. In all cases, the aim
will be to write out accurate and efficient proofs.
There are three basic skills concerning proofs: |
Textbook: Colin Adams and Robert Franzosa,
Introduction to Topology: Pure and
Applied, Prentice Hall. ISBN-13:
978-0131848696. There is a list of corrections and clarifications to the book on-line.
Course Philosophy
Topology is concerned with geometrical properties that are
preserved under continuous deformations of objects. These properties are
determined only by positioning of points with respect to each other and not by
the distances between them (topology's maiden name is Analysis Situs, which means analysis of
place). One of the first problems that could be called topological is the
Euler's Koenigsberg bridges problem. Topology may
become very abstract; in this course the emphasis will be on the geometric and
visual underpinnings of topological concepts and results, and on mathematical
rigor. One of the goals of the course is helping students to refine their capacities of reading
abstract mathematical texts and develop a basic view of topology and its
applicationsHomework: There will be
weekly homework assignments that will be collected and graded. As a rule,
homework assignments will be due on Tuesday.
Tests:
There will be two tests and a final.
Grading:
Homework 35%, Tests 40%, Final 25%
Tentative Course Outline
I expect to cover the core material of the first seven
chapters of the textbook. The really interesting stuff starts after the core chapters;
beyond the basics I plan to discuss one of the three topics listed at the
bottom the list of the key topics:
1.Topological
spaces, bases.
2.Interior,
closure, and boundary.
3.Subspaces,
product spaces, quotient spaces.
4.Continuity
and homeomorphisms.
5.Metric
spaces.
6.Connected
spaces.
7.Compactness
through coverings and limit points; compactifications.
8.Homotopy
and degree of mappings; the Brouwer fixed point
theorem.
9.Knots.
10.Classification
of surfaces (any surface is a spheres with handles), Euler characteristic.
If you have any preferences as to which topics out of the
last three on the list to consider in the course, please email me.
Student Learning Outcomes
This
is a list from the Digital Measures course profile.
-The students will refine their capacities of reading
abstract mathematical texts and develop facilities to write brief mathematical
proofs.
-The students will develop a broad view of basic
topology and of some applications.
-The students will develop understanding of basic
structure and properties of topological spaces.
-The students will learn some fundamental properties
of continuous mappings of topological spaces.
-The students will be exposed to some important
classes of spaces, such as compact and connected ones.
Statement of Academic
Integrity
The Rensselaer Handbook of Student Rights and
Responsibilities define various forms of Academic Dishonesty and you should
make yourself familiar with these. In this class, all assignments that are
turned in for a grade must represent the student's own work. In cases where
help was received, or teamwork was allowed, a notation on the assignment should
indicate your collaboration. Submission of any assignment that is in violation
of this policy may result in a penalty of a grade of F. If you have any
question concerning this policy before submitting an assignment, please ask for
clarification.
Homework Assignments
Assignment #1, due September 7 One of the problems in the first assignment (Problem
1.34) was incorrect in the first printing of the Textbook. I was not aware of
this because in the 2nd printing that I have the error was
corrected. My apologies
Topics for Presentations in
Class:
1.The Alexander Horned Sphere (pp.
339-340 of the textbook)
3.The Ham-Sandwich Theorem
4.Turning the sphere S2
inside-out
Please let me know if you are
interested in giving a presentation (probably about 20-30 minutes long) on any
of these topics or any other topological topic of your choice.
Tests
Test #1 will be given on Friday October 19 in class.
The test will include topics covered by the first five homework assignments.
Namely,
1.Topological
spaces, bases.
2.Interior,
closure, and boundary. Limit points.
3.Subspaces,
product spaces, quotient spaces.
4.Continuity
and homeomorphisms.
5.Metric
spaces.
6.Connected
spaces, not including path connectedness.
Test questions will be similar to the shorter homework
questions from the homework assignments 1-5. You will
be allowed the use of one sheet of hand-written notes.
The advanced grade is determined
by the performance on the homework assignments (65% of the grade) and the test
(35%). The final exam is optional; it will include the material covered by the homework
exercises. |
Good differential equations text for undergraduates who want to become pure mathematicians
Alright, so I have been taking a while to soak in as much advanced mathematics as an undergraduate as possible, taking courses in algebra, topology, complex analysis (a less rigorous undergraduate version of the usual graduate course at my university), analysis, model theory, and number theory. That is, I have taken enough 'abstract' (proof-based) mathematics courses to fall in love with the subject and decide to pursue it as a career.
However, I have been putting off taking a required ordinary differential equations course (colloquially referred to as 'calc 4', though this seems inappropriate) which will likely be very computational and designed to cater to the overpopulation of engineering students at my university.
So my question is, for someone who might have to actually concern themselves with the theory behind the 'rules' and theorems which will likely go unproven in this low-level course (likely of questionable mathematical content), what might be a decent supplementary text in ODE? That is, something substantive to counter-balance the 'ODE for students of science and engineering'-type text I will have to wade through. I want to study algebraic geometry further (I have gone through Karen Smith's text and the first part of Hartshorne), so something which goes from basic material through differential forms and related material would be nice.
Thanks! (and yes, it's embarrassing that I still haven't taken the 200-level ODE course, but I have been putting it off in favor of more interesting/rigorous courses... but now there's that whole graduation requirements issue).
--Lambdafunctor |
Analysis and Applications with MATLAB, 1st Edition
ISBN10: 1-4018-6481-3
ISBN13: 978-1-4018-6481-1
AUTHORS: Stanley
This text combines technical and engineering mathematical concepts at a basic level using MATLAB® for support and analysis. Once math concepts are introduced and understood using conventional techniques, MATLAB® is then used as the primary tool for performing mathematical analysis. Featuring practical technical examples and problems, the text is designed for math courses within an engineering technology or engineering program or any courses where MATLAB is used as a supporting tool. The text provides a review of differential and integral calculus with an emphasis on applications to technical problems |
The following texts were very successful in helping me make the transition from high school mathematics to university level mathematics. When I left high school in the UK system (A-levels) I had a reasonably thorough grasp of calculus, trigonometry, geometry, school level algebra, statistics and mechanics (these were covered in the A-level maths and further maths syllabi, if you're familiar with these at all).
General reasoning:
Copi and Cohen, 'Introduction to Logic'. A basic introduction to logical reasoning. Despite having studied as much mathematics as I could at high school, I was never taught to understand the logical structure of proofs. Reading this book helped me to begin reading proofs in undergraduate/graduate mathematics books.
Analysis:
Bartle and Sherbert, 'Introduction to Real Analysis'. This is useful for picking up the basics of real analysis at an elementary level and is also useful in learning to read proofs of elementary results. I found that this phase of my education was a bit tedious and that I was wanting to get ahead to a more advanced text. It is a useful complement to item 3 below.
Kolmogorov and Fomin, 'Introductory Real Analysis'. This is an excellent book for learning analysis and was used in some honors level analysis courses for students who were familiar with reading and writing proofs. I would emphasize that reading Copi and Cohen first is an imperative.
Walter Rudin, 'Principles of Mathematical Analysis'. Harder to read than Kolmogorov and Fomin, but it contains beautifully written proofs and is a great text to model your own answers on.
T. Gamelin, 'Complex Analysis'. A good book on complex analysis with lots of motivating examples.
Algebra:
Allan Clark, 'Elements of Abstract Algebra'. This is a Dover publication and is rather cheap (probably around $15 or so now). It consists of a hundred or more articles; you are given definitions and the proofs of a few important theorems. Everything else is an exercise. I believe this book did the most for me in helping to build intuition for abstract algebra.
Hoffman and Kunze, 'Linear Algebra'. A classic book on linear algebra which I do not think has been surpassed. It provides thorough and well written proofs. I believe this is a preferable text to Axler's book, unless you are somewhat heavily inclined towards analysis and/or do not enjoy doing computations.
Serge Lang, 'Algebra'. This was my second book in abstract algebra, after Clark's. It is beatifully written, which is why I prefer it to Hungerford's book. As another answerer mentioned, the typesetting in Hungerford's book is also somewhat off-putting, and Lang's book does not suffer from this defect.
Topology:
Munkres, 'Topology'. A clearly written text with a good supply of examples.
Lastly, I would second the idea of purchasing access to a university library with a good collection of mathematics textbooks. |
This one-day training course gives students direct experience with the basic Mathematica features needed for them to become proficient Mathematica users. The course is designed primarily for people who are interested in becoming proficient Mathematica users but who currently have little or no experience with the system. This course can also be helpful for experienced users who would like to broaden their basic understanding of Mathematica and for those interested in learning exactly what the system can do.
Syllabus
Introduction: step-by-step instruction on performing basic operations, description of sources for additional information, and a tour of the features of the system
Notebooks and Typesetting: discussion and practice with interactive input, output, typesetting, and formatting features |
I dont get linear algebra
I dont get linear algebra
I had a linear algebra course for my 1st year civil engineering curriculum, and I passed with a 3.2 GPA but I only conceptually understood about 10% of what was taught to me.
I don't know what an eigenvalue/eigenvector is, what the hell is a subspace, nullspace, imagespace. What the hell is a linear transformation, what the hell is a determinant of an nxn matrix, what the hell is a matrix.
How the hell was I able to get a decent mark in a subject I know nothing about?
Facepalm.
I found calculus 1 (single variable) way easier to understand than this stuff.
I can't explain the whole linear algebra curriculum in a short post, but it is a fundamental part of mathematics. It sounds like you basically know nothing about the subject but you managed to pass with a decent grade. Good job?
1. Solving systems of linear equations is part of linear algebra, and this is probably the part that is used the most by the most people.
2. Finish calculus and differential equations and then revisit linear algebra. Conceptually it might make more sense then.I dont get linear algebra
Quote by tahayassenIf you want to understand linear algebra intuitively, you'll get better advice by asking for an explanation of one concept at a time rather than by asking for an explanation of the entire subject. When it comes to intuition, people have a wide variety of ways of looking at mathematical concepts. You can get 5 different ways of looking at one simple idea.
The key with linear algebra is mathematical maturity. You need to understand that definitions are just definitions. There's nothing deeper.
An eigenvalue, λ, and eigenvector, x of a matrix A are such that Ax=λx. That's IT. There's absolutely nothing more to it than that. That's all that it means. Why you care, how it's used is a completely different question. But that's all it is.
A matrix is just an array of numbers. That's ALL. Nothing more. That's all there is to it. Nothing deeper, nothing more. An array of numbers. Don't try to pull things out of it that simply aren't there. Yes, you can do cool things with it. Yes, you apply it in weird places. But that's ALL IT IS. An array of numbers.
The one thing I think that's taught poorly is vector spaces. Why they give you an example of an algebraic structure before you understand what an algebraic structure IS, is completely past me.
An algebraic structure is a SET with ONE OR MORE operations defined on it. In a VECTOR SPACE, the set is the set of vectors. The operations are scalar multiplication and vector addition.
An algebraic structure IS math. It's such a confusing, deep subject if you don't really understand what's going on. But when you get it, it's pretty cool. Anything you do in math is in an algebraic structure (most the time, you're dealing with Euclidean space. Euclidean space is the "normal" space with "normal" rules).
A much better example of a structure is what's called a FIELD. (NOT a vector field, when you get to multivariate calculus. This is extremely important) A FIELD is a structure with elements that has two operations, + and * defined over it. It has a list of axioms; closure, 4 additive ones, 4 multiplicative ones, one associative one. An axiom is a DEFINITION.
See, in the real world we don't have wild 2s running around. "2" does NOT exist in nature. You always have 2 something. 2 rocks, 2 buildings, 2 blades of grass, 2 whatever. But "2" does NOT exist. We CREATE "2" to describe the real world. To describe the world, we create these ALGEBRAIC STRUCTURES.
A field IS numbers. When you ask your friend what 2+2 equals, you're working in a FIELD, namely R (the real numbers). Make sense? An algebraic structure IS math. Whatever you do in math is a structure. A vector space is ANOTHER example of a structure. Just one that's studied extensively in linear algebra. Anything you want to know about the operations (EXCEPT WHAT THE OPERATIONS ARE ACTUALLY DOING!), you can derive from the axioms. In a vector space, you can derive ALL you want to know about scalar multiplication or vector addition from the axioms. BUT the one thing you CAN'T derive is WHAT YOU'RE ACTUALLY DOING when you add vectors. YOU must define that.
So long story short, you probably DO understand it. You're just looking for something that's not there. Definitions are just definitionsLinear algebra isn't meaningless at all, when did I ever say anything like that? You're just learning things rigorously, without much if any physical intuition.
Like with eigenvalues/eigenvectors. There really isn't a physical intuition behind it (maybe there is? I just never heard of any). It just is. That doesn't mean that it's "meaningless". It's used to solve differential equations later, which renders them super useful.
I amend my comment to say that without context, an abstract system of rules and definitions such as linear algebra can be hard to hold onto.
Quote by johnqwertyful
Not everything in math has some physical significance.
I know at least one other poster here who would agree with this. I tend to disagree though.
In the case of an eigenvector, its physical significance is that it represents a subspace that is invariant under a linear transformation. The eigenvalue is the scaling factor applied to that invariant subspace. (geometry is physical enough for me )Since you, according to one of your recent posts, are currently studying Algebra 1, you are not yet ready to understand much of Linear Algebra. Give yourself about 2 more years.
Attitude? I was simply expressing my confusion over this newly (I can't stress the word newly enough) learned subject. It is my sole intention to strengthen my intuition with the subject in the same way I am intuitive with calculus and geometry.
I don't hate linear algebra, it not as though I want to attack it with a light saber, I just find it more abstract than any other branch of math I have been exposed to.
Perhaps soil mechanics is your bag
As I am a 1st year undergrad student with no exposure whatsoever to the specialties of civil engineering, drawing such conclusions based on the limited info and limited time of exposure I have had with linear algebra (3 months) is a little too extreme.
Funny,
I thought Linear Algebra was easier to grasp than Calculus. I guess it's because it's hard for me to visualize a mathematical concept (it took me a while to understand what a derivative is from a geometric point of view). With linear algebra you just take a system of linear equations, strip the constants and coefficients from it and viola, you have a matrice! And from there you can apply elementary row operations on it to get a solution, find it's inverse, it's determinant, etc...
To be fair though I learned Linear Algebra independently (which probably made it easier), and I've only gotten the basics (I haven't learned about eigenvalues or linear transformations yet). |
Technical Calculus I Certificate Course
Technical calculus I certificate course with online exams and instructor assistance. Learn calculus concepts at home quickly with this powerful calculus course.
Calculus course
Technical Calculus I is a distance learning math course that will show you how to master some of the basic concepts of Calculus quickly.
Learn calculus from the comfort of your own home and study when it's convenient for you - there are no time limits! Take your exams online and finish with an academic Certificate of Completion in calculus from CIE Bookstore.
Students learn calculus principles of analytic geometry, limits, derivatives, simple integration, and indefinite integrals with emphasis on applications of derivatives and integrals.
This easy-to-complete program includes 8 unique distance learning lessons and instructor tutorial help. Everything you need to graduate is sent to your home and you can take your exams online.
Our highly trained instructors are only a phone call away (or e-mail) from providing you with reassuring assisance whenever you need it.
Best of all, you'll earn an impressive Calculus Certificate of Completion from CIE Bookstore suitable for framing when you're finished!
Learn the basics at home with this distance learning calculus course and then move on to more advanced topics.
Eight Lesson Topics:
1. Basic Concepts of Calculus
Upon completion of this lesson the student will understand more about algebraic functions, limits, rates of change, and they are introduced to derivatives and integrals.
2. Calculus Part I: Analytical Geometry & Second Degree Equations
Upon completion of this lesson the student will have a basic understanding of calculus through the rotation of axes, circles, ellipses, hyperbolas, parabolas, completing the square, and identifying a conic shape from a second-degree equation.
3. Calculus Part II: Basic Concepts in Differential Calculus
Upon completion of this lesson the student will have a better understanding of the derivative and the use of standard derivative formulas.
4. Calculus Part III: Further Differentiation Techniques and Applications of the Derivative
Upon completion of this lesson the student will have strengthened their understanding of derivatives by developing derivatives of products and quotients.
5. Calculus Part IV: Fundamentals of Integration
Upon completion of this lesson the student will have an understanding of integral calculus through recognizing integrals, finding indefinite integrals and integrals of a sum.
6. Calculus Part V: Applying Integral Calculus
Upon completion of this lesson the student will have a better understanding of integrals.
7. Calculus Part VI: Derivatives of Transcendental Functions
Upon completion of this lesson the student will have an understanding of how to find the derivative of functions.
8. Calculus Part VII: Integrating Transcendental Functions
Upon completion of this lesson the student will have an understanding of how to determine the integral of exponential and logarithmic functions, trigonometric functions, using integral tables, integration by parts, and how to apply integrals to electronic circuits.
Calculus Course - Student Evaluation and Grading Method:
Students are required to complete all performance requirements above. Each of the eight assignments concludes with an examination comprising of a multiple-choice test.
The assignment examinations are open book. The final grade for this course will be determined as follows: eight examinations equals 100% of the final grade.
These are the same 8 lessons found in World College's Bachelor's Degree program. You could transfer any completed lessons from this course over to World College's nationally accredited Bachelor's Degree program and get full tuition and academic credit.
Student Privileges:
1. Instructor Assistance:
Use our toll-free Instructor Hot-line to access our faculty and staff if you ever need assistance with your calculus course work. CIE's dedicated staff of instructors do more than just grade your exams; they help guide you, step-by-step, through your studies and hands-on training.
They'll encourage you when you're doing well and give you support when you need it. Most importantly they'll see that every question you have receives careful consideration by one or more members of the staff.
You can be sure the response, whether it's a simple explanation or an in-depth theoretical discussion, will be prompt, courteous and thorough. We'll make sure that you'll never study alone.
2. Priority Grading - No waiting
Your submitted exams will be graded and sent back to you within 24 hours. You can be sure that you will get back almost instantaneous feedback from your exams. Take your exams online on our e-grade web site or mail them in to us.
3. Professional Certificate of Completion from CIE Bookstore
After finishing this course you'll receive a calculus certificate of completion suitable for framing!
How do I enroll in the Calculus Course?
1. You can order online with a credit card or PayPal (click the 'Add to Cart' button).
2. Call us at (800) 321-2155 and ask for course 01-MTH231.
3. You can mail a check or money order for $109.95
(includes $14.95 for shipping/handling) to:
CIE Bookstore
1776 E. 17th Street
Cleveland, Ohio 44114
4. Western Union or Bank transfer.
5. You can fax your order to us at 216-781-0331.
Foreign shipping expense will be higher.
Learn calculus at home with this distance learning calculus course and earn a calculus certificate!
Current rating is 5.00. Total votes 1.
Calculus course
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Very challenging and presented at a nice easy pace. instructors were very helpful; always available. I am very excited about the certificate! |
This document describes MathML and its
use within DAISY books. It is meant to be a short starter with further
references. The target audience is primarily teachers and students, as well as
publishers and developers of DAISY reading products and services.
Some of the content here is derived
from References 1 and 5 below. I hope that this document provides information
helpful to the audience!
1.Introduction to the issues
Readers with print disabilities have used
audio books for a long time. First introduced on cassette tapes for leisure
reading, audio books have also been used for educational purposes. With the adoption
of the DAISY Standard, digital talking books have become the de facto standard and content production
on CDs has been gradually replacing the cassette tape medium. DAISY books may
contain audio and/or text, as well as images.
One main problem of conventional audio
books and paper braille books affecting educational content is that mathematics
and other formulae were treated as either text or images. Hence, there wasn't
enough structure information to enable accessible technology to present the
formulae appropriately via audio or braille. Since the formal approval of the
MathML-in-DAISY Specification in February 2007 as the first extension to the
DAISY Standard, it is now possible to produce and use books that present
mathematical content in a synchronized and structured and therefore accessible
way.
2.What is the DAISY/NISO Standard?
DAISY is an acronym which stands for Digital Accessible Information SYstem. The term is used to refer to a
standard for producing accessible and navigable multimedia documents. In
current practice, these documents are digital talking books, digital text
books, or a combination of synchronized audio and text books.
DAISY is a globally recognized
technical standard to facilitate the creation of accessible content. It was
originally developed to benefit people who are unable to read print due to a visual
impairment, but it also has broad applications for improved access to printed material
and other media in the mainstream. The DAISY Standard has been evolving over
the last several years and has been officially recognized by an American standards-making
body in 2005. Whereas books produced in the DAISY 2.02 standard are the most common
ones by far, the use of math is only possible in the new DAISY/NISO Standard
that was introduced in 2005. This new standard is officially called
"ANSI/NISO Z39.86-2005" but commonly known as "DAISY 3".
The DAISY Consortium has been selected
by the National Information Standards Organization (NISO) as the official
maintenance agency for the DAISY/NISO Standard, officially, the ANSI/NISO
Z39.86, Specifications for the Digital Talking Book. A more thorough
description of the DAISY/NISO Standard is given in Reference 6, below.
3.What is the MathML Standard?
MathML is a W3C recommendation. The
W3C is the world-wide organization that creates the standards for the Web. The
MathML specification is, as a consequence, a normative document, which allows
MathML to be highly compatible. Also, it was created by the Math Working Group
composed of people from several countries and diverse scientific fields, so
MathML takes into account the needs from many different professions, countries,
and uses.
MathML is a so called "XML" (eXtensible Markup Language)
language. This means that new features can be added as needs arise – see, for instance, the Arabic mathematical notation
– or, can become deprecated if experience shows
they are useless. Finally, MathML can be used in combination with other Web
languages. As a bonus, MathML can easily be created with existing formula
editors and be exported to or imported from computer algebra systems like Maple
and Mathematica. It can be processed by search engines such as Google,
therefore providing multiple benefits to the user. Please note that the use of
so called "presentation MathML" is provided for DAISY/NISO, in contrast to
"content MathML".
An example of the formula "-
a/b" expressed in presentation MathML is:
<math
xmlns='
<mrow>
<mo>-</mo>
<mfrac>
<mi>a</mi>
<mi>b</mi>
</mfrac>
</mrow>
</math>
As you can see, no one would want to read
or write MathML directly. The use of additional tools is therefore necessary.
One of the biggest advantages of XML
is that it has to be well-formed, so that if you open a tag you have to close
it later on. This way, malformed MathML may be spotted immediately during the
validation process; inconsistencies are therefore avoided.
4.How do DAISY and MathML act together?
The MathML extension is the first
extension of the DAISY specification. The approach taken makes use of the
existing extension mechanism specified by Z39.86-2005.
There are many problems associated
with the use of images by authors and readers with and without visual
disabilities when working with digital documents containing math. These include:
§the
inability to magnify the image or change its colors
§fixed
speech (based on alt text) that cannot be tailored to an individual's needs
§no
local navigation and exploration of the mathematical structure
§no
synchronized highlighting of the text with the image and audio
§inability
to be translated to a braille math code
MathML offers a solution to these
problems. Because it is an XML application and has been designed to work with
XHTML, using MathML in Z39.86-2005 was the direction that the MathML Modular Extension
Working Group pursued.
MathML is not directly read.
Especially for a blind person using a braille display, the DAISY reader has to
convert MathML into a notation suitable for that person. Currently, there are
literally dozens of different math notations used worldwide. The use of LAMBDA,
LaTeX and Nemeth is planned by different organizations working on DAISY readers.
Using MathML within DAISY documents allows for a unified and well-defined
storage, while the presentation of the math content to the user is dependent on
the player used. For some possibilities on examples how math content may be
presented to the user see chapter 98NVaaaa@36C3@.
5.What if my reader doesn't support MathML (fallback issues)
The MathML-in-DAISY Specification
groups players into 3 categories:
§Players
that do not comply with this specification. These players know nothing about
MathML. They do not extract the altimg and/or alttext from a <math> tag
nor do they apply a stylesheet to transform the math to an image group. These
players are referred to as MathML-unaware players.
§Players
that conform to this specification but can not natively render the MathML. They
fall back to using either the XSL transform or grab the alttext or altimg
attributes from the <math> tag. These players are referred to as Basic
MathML players.
§Players
that natively support MathML. These players are referred to as Advanced MathML
players.
This modular extension is meant to
encourage advanced MathML players to provide a rich experience when reading
mathematics. However, the modular extension also recognizes that mathematics
may not be a focus for all vendors and provides a fallback mechanism. For the
common case of an audio only player, a predefined audio rendering is provided.
There are no local navigation points within that rendering, which is something
an advanced MathML player might provide. An advanced MathML player could allow
a user to explore the structure of the expression tactilely using a refreshable
braille display and/or with audio without having to listen to the expression in
its entirety. A future version of the DAISY MathML specification may add finer
SMIL granularity within the math audio stream. For players that do not support
MathML, an alternate image is provided as part of the MathML. Basic MathML
players must either recognize MathML enough to locate the image reference
provided on the MathML element, or they must support XSLT and apply a supplied
transform indicated in the metadata of the DTB Package file.
6.Where do we stand now?
The MathML-in-DAISY extension was
formally approved and is therefore ready for use. Production tools are currently
in development for the production of DAISY math books. One particular DAISY
software reader has been demonstrated as capable of displaying math content at
an international conference in March 2008. As new products and services are developed
by DAISY Member organizations, they are announced on the DAISY Consortium Web
site, and MathML capabilities are specifically tracked.
The best way to overcome the chicken and
egg problem is to produce DAISY books using the math extension. With the
fallback capabilities, their use would be possible today with existing players,
while new developments would add more possibilities and features.
7.Summary for students (users)
If you want to use digital books to
learn math, physics or chemistry, DAISY books with MathML are just for you. In
a little while, the first books should be available. Until then, keep yourself
informed, ask your library about digital math books and get yourself a new advanced
MathML DAISY reader.
8.Summary for teachers (producers)
Ask your software vendor about DAISY
production tools with math capabilities. If you don't know exactly what DAISY
books are, then have a look at the DAISY Consortium home page ( and watch out
especially for these new production tools.
9.Summary for libraries and publishers
Make yourself comfortable with DAISY
books and MathML. Explore the references and start producing and testing DAISY
books without math just to get a feeling for the issues at hand. Get yourself some
new production tools with math capabilities as soon as they are available.
Perhaps you can attend some conferences or meetings?
9qqajugGbabaaaaaaaaapeGaa8NVaaaa@36C4@. Math for the
blind - Presentation details for the curious
By separating the storage from the
presentation, the user as well as the publisher experience major benefits. In
regular digital texts, everybody generating or converting literature for the
blind has to choose the way to store math content by using a certain notation
(LaTeX, Nemeth, AMS, Marburg,
LAMBDA, or other). As the blind user would read the text exactly as it was
written, he would have to know this same notation as all of the books from this
producer usually contained math in this notation (and this notation alone). To
read these documents, everybody would have to learn this notation. Students from
other universities trying to access the different digital libraries had to
learn the different appropriate math notations as well, if only to read a
single book per notation. Student exchange and combined digital repositories
for the blind were substantially limited by this factor.
With DAISY books and MathML, the publisher
now only has to be concerned about proper MathML within the document. The
reader may then choose a DAISY player, either a hardware player, a software
player on a computer, or a mobile phone/PDA, which supports the math notation
of choice. Reading DAISY books from organizations unable to support specific
math notations is now possible because of the uniform storage of math content
as MathML. |
big supported of the Moore Method and other variations. Particularly for students who want to go on to become mathematicians, it gives them a more realistic taste of what math is than a traditional course.
supported of the Moore Method and other variations. Particularly for students who want to go on to become mathematicians, it gives them a more realistic taste of what math is than a traditional course. |
Barron's Geometry the Easy Way and Essential Math
Barron's Geometry the Easy Way
This is the sequel to my Saxon tale of woes. We've been using Barron's geometry course for almost a year now. It is a very different approach to teaching from Saxon's incremental method. Instead of learning small amounts of material and immediately applying what is learned, Barron's Geometry the Easy Way teaches large amounts of new concepts in each chapter, with an average of 28 practice exercises at the end of each chapter. There are 16 chapters in the book, which the average student will need a full school year to finish. This is a very complete plane geometry course, with training in both formal and informal proofs. There is an answer key in the back, with some brief explanations, but it is not a solution manual by any means.
Barron's books are intended to be used as self-learning tools for adults. The material is challenging, but not too tough for the average high school student. The concepts are stated very clearly in most cases, with many examples and diagrams. And although this is a secular text, Christian home school families will not find objectionable ideas assaulting their children's minds.
A major flaw is the presentation of volumes of material in one lesson. With so many new concepts being thrown at the student at one time, it becomes quite overwhelming. It is hard to build a solid foundation with too much information too soon. (Mr. Saxon's incremental method shines by comparison.) Another major difficulty is mistakes in the answer key. It is NOT helpful to show the congruence symbol when the not congruent , greater than, or less than symbol was meant! Hopefully, Barron will correct these mistakes in the future. Until then, parents will have to make their students aware of the problem. Most mistakes are quite obvious, but they may confuse the new geometry student.
I like being able to study geometry all at one time, rather than the Saxon method of interspersing geometry with algebra and advanced mathmetics. But I also like the Saxon incremental method much better than what we have experienced in the Barron's geometry. We should be able to finish this book by the end of our school year; although it is still quite time consuming, it doesn't take quite as much time as Saxon did. All in all, Barron's Geometry the Easy Way gets about a B+.
Barron's Essential Math
I have always thought that sometime before graduation it is a good idea for every high school student to brush up on the basic, everyday math skills needed to survive in life. We chose Barron's Essential Math for our consumer math course.
The presentation of material is easy to understand, interesting, thorough, and practical. There are many illustrations of various forms and tables throughout the text. The student is introduced to various banking skills, reviews fractions and decimals, measures and computes quantities needed for home improvement projects, figures sales and employment taxes, fills out order blanks, does cost estimates for a contractor, etc.
Once again, however, the problem with Barron's is the answer key. This one is far worse than Geometry the Easy Way. I discovered that every time one of my student's answers did not agree with the answer key, I needed to do the problem myself to see who was actually right! At least half of the time, the answer key was in error. This is a math book, folks. And busy home school moms don't need the added difficulty of math answer keys with wrong answers. |
Student Resources
What will you do with your math?
weusemath.org is a site dedicated to highlighting all the different ways people are using mathematics in the workplace. Take a look, you might find a career path you would never have imagined. Or pick something really outrageous to tell your parents the next time they ask.
Do you get math-news?
Math-news is an email list for Calvin students and faculty interested in receiving posts about Mathematics Department events and activities; job, research and educational opportunities; and other items of mathematical interest. To join math-news, send email to [email protected] from the email account where you wish to read math-news. The message should contain one line:
subscribe math-news
That's all there is to it.
What Can I do with a Math Major?
The variety of applications of mathematics is staggering. The AMS (American Mathematical Society) has put together a number of Mathematical Moments describing some of these applications. Examples include Describing the Oceans, Designing Aircraft, Creating Crystals, Deciphering DNA, Forecasting Weather, Seeing the World Through Fractals, Storing Fingerprints, Experimenting with the Heart, Securing Internet Communication, Making Movies Come Alive, Investing in Markets, Listening to Music, Routing Traffic Through the Internet, Tracking Products, Manufacturing Better Lenses, and Mapping the Brain. Visit the Mathematical Moments home page to find out more about any of these.
The wide applicability of mathematics also means that there is a wide range of career possibilies for students of mathematics and that the study of mathematics combines well with many other fields of study. |
Complex analysis is REALLY interesting imo. Real analysis can get kinda clunky in that differentiability, integrability, and analyticity, etc. are all separate things, but when you extend functions to the complex plane they all become synonymous. There are a lot of cool things like that. I don't know what parts of it would be useful for ChemE (besides the process control aspect), but it's been pretty invaluable for me in understanding Laplace and Fourier transforms and linear systems theory.
Real analysis is also good, but you don't get to the good stuff until much later, like with measure theory, Lp spaces, etc. (even then, only useful if you're into theory, like me!) Complex analysis will probably seem more useful right off the bat. |
Lecture 29: Level 1 multiplying expressions
Embed
Lecture Details :
(Ax+By)(Ax+By)
Course Description :
This is the original Algebra course on the Khan Academy and is where Sal continues to add videos that are not done for some other organization. It starts from very basic algebra and works its way through algebra II. |
Extent:
Availability:
Sample chapters for download
About the book
Mathematics for Year 11 Geometry and Trigonometry 5th edition has been written
to embrace the concepts outlined in the Stage 1 Mathematics Curriculum Statement.
It is not our intention to define a course.
This package is the first step in a new approach to mathematics education. You
are provided with a text book and a CD-Rom which displays the contents of the
book plus many exciting new interactive features which will assist teachers and
students.
The book is language rich and technology rich. Whilst some of the exercises are
simply designed to build skills, every effort has been made to contextualise problems,
so that students can see everyday uses and practical applications of the mathematics
they are studying.
The book contains many problems, from the basic to the advanced, to cater for
a wide range of student abilities and interests. Much emphasis has been placed
on the gradual development of concepts with appropriate worked examples. However,
we have also provided extension material for those who wish to go beyond Stage
1 and look towards further studies or applications of mathematics for their career
choices. It is not our intention that each chapter be worked through in full.
Time constraints will not allow for this. Consequently, teachers must select exercises
carefully, according to the abilities and prior knowledge of their students, in
order to make the most efficient use of time and give as thorough coverage of
work as possible.
The extensive use of graphics calculators and computer packages throughout the
book enables students to realise the importance, application and appropriate use
of technology. No single aspect of technology has been favoured. It is as important
that students work with a pen and paper as it is that they use their calculator
or graphics calculator, or use a spreadsheet or graphing package on computer.
The interactive features of the CD-Rom allow immediate access to our own specially
designed geometry packages, graphing packages and more. Teachers are provided
with a quick and easy method of demonstrating concepts, or students can discover
for themselves, and revisit when necessary.
Teachers should note that instructions appropriate to each graphics calculator
problem are available on the CD-Rom and can be printed for students. These instructions
are written for Sharp, Texas Instruments, Casio and Hewlett-Packard calculators.
In this changing world of mathematics education, we believe that the contextual
approach shown in this book, with the associated use of technology, will enhance
the students' understanding, knowledge and appreciation of mathematics. |
Next: Definition of a Limit
Previous: Binomial Theorem and Expansions
Chapter 8: Introduction to Calculus
Chapter Outline
Loading Content
Chapter Summary
Description
Students explore and learn about limits from an intuitive approach, computing limits, tangent lines and rates of change, derivatives, techniques of differentiation, conceptual basis for integration and The Fundamental Theorem of Calculus. |
At Lawrence North High School, the entire hand-picked team of Algebra 1 instructors believes passionately that mastering these skills and concepts will have a stronger influence on your future success throughout high school and beyond than any other single course in which you may choose to enroll. Algebra 1 skills and conceptual relationships are the foundation of the CORE 40 graduation exam but will also prepare you for future math and science courses. We are committed as a team to providing quality instruction and appropriate materials and supporting you with plenty of attention, patience, and other resources. We understand the importance of the content of this class and we truly want you to succeed.
Some of the "big ideas" we emphasize in Algebra 1 include properties of real numbers, solving equations and inequalities and proportions, functions and graphs, understanding lines and slope, polynomials and factoring, radicals and quadratic functions.
Our measuring sticks are that darn CORE 40 test and your future success in Algebra 2, but our focus is on mastering those "big ideas" along the way. Some of these skills will be difficult for you to understand at first. I encourage you to keep these three P's in mind:
1)Practice! Math is a skill and can only be mastered through routine,
rigorous and disciplined practice.
2)Pace! Don't try to rush or skip ahead until you fully understand what we have already done.
Take breaks and ask lots of questions.
3)Perspective! This class is imperative regardless of your goals. I encourage you to
take a step back from the mechanical steps of the arithmetic and try to understand
the concepts and relationships. When you understand why certain steps are required
Congratulations! You made it to the second semester of Algebra 1. Only the students who have demonstrated a solid understanding of the concepts in the first semester are here right now. Yes, it's that important. The second semester is notable more difficult than the first, but we're confident you'll make it through or it would not have been recommended that you be here. We have two goals this semester: 1) to make sure everyone is prepared for the Algebra 1 End-of-Course Assessment (ECA) graduation exam in May, and 2) to help ensure your future success in Algebra 2.
Our seventh unit explains the rules for exponents and multiplying and dividing factors with the same base. We'll follow that up with a unit on polynomials to get comfortable adding and subtracting like terms with exponents, then multiply polynomial groups together using the Distributive Property. In the next unit we will change directions and go backwards through the distributive process to factor polynomial expressions, especially quadratic trinomials. As the quarter draws to a close, we'll be breaking down and solving quadratic equations. |
Differential Equations Workbook For Dummies
…
(More) skills you need to master differential equations!Need to know how to solve differential equations? This easy-to-follow, hands-on workbook helps you master the basic concepts and work through the types of problems you'll encounter in your coursework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every equation. You'll also memorize the most-common types of differential equations, see how to avoid common mistakes, get tips and tricks for advanced problems, improve your exam scores, and much more!The Dummies Workbook WayQuick refresher explanationsStep-by-step proceduresHands-on practice exercisesAmple workspace to work out problemsTear-out Cheat SheetA dash of humor and funGo to Dummies.com®for videos, step-by-step photos, how-to articles, or to shop the store!More than 100 problems!Detailed, fully worked-out solutions to problemsThe inside scoop on first, second, and higher order differential equationsA wealth of advanced techniques, including power series
(Less) |
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Pre-Algebra Mathematics (DVMT 095) and Intermediate Algebra (DVMT 100) help students develop mathematics abilities that enable them to complete mathematics courses necessary for their plan of study. Personalized instruction, self-pacing, and mastery learning characterize the instruction in these classes.
In addition to the regular teacher-based course instruction sections, FSU offers computer-mediated sections of DVMT. These sections are conducted using interactive computer software and are supervised by an instructor. Each of the DVMT courses described below are offered in both a computer-mediated and instructor-based format.
DVMT 095: Pre-Algebra Mathematics
The primary focus of this course is to improve students' basic math skills: arithmetic concepts of whole numbers, integers, fractions, and decimals; problem solving skills dealing with ratios, rates, proportions, and percentages; concepts of linear, area, volume measurement in both the English and metric systems; and introductory algebra topics of solving linear equations and graphing. Completion of this course will meet the prerequisites for MATH 104, MATH 209, or DVMT 100. This course is graded on a Pass/Fail basis. It is worth three (3) credits; however, it may not be used to satisfy the requirements for a major or minor in mathematics, fulfill the Basic University Requirement in mathematics, nor count toward the 120 credit hour minimum required for graduation.
NOTE: Students are placed in this course based upon results of the Mathematics Placement Test administered by the University.
An introduction to the fundamental aspects of algebra, including properties of the real number system; integer arithmetic; operations with positive and negative exponents; variables and linear equations; graphing; second degree equations; factoring; operations with positive, negative, and fractional exponents; and quadratic equations. Completion of this course will meet the prerequisites for MATH 102, 103, and 106. This course is graded on a Pass/Fail basis. It is worth three (3) credits and is offered every semester. However, it does not fulfill the Basic University Requirement in mathematics, nor may the credits be used to fulfill the 120 credit hour minimum required for graduation.
Prerequisite: A passing score on the Mathematics Placement Test administered by the University or successful completion of DVMT 095. |
This course provides a non-rigorous introduction to the basic ideas and techniques of
differential and integral calculus, especially as they relate to applications in business,
economics, life sciences, and social sciences.
Expected Educational Results
As a result of completing this course, the student will be able to:
1. Locate and describe discontinuities in functions.
2. Evaluate limits for polynomial and rational functions.
3. Compute and interpret the derivative of a polynomial, rational, exponential,
or logarithmic function.
4. Write the equations of lines tangent to the graphs of polynomial, rational,
exponential, and logarithmic functions at given points.
5. Compute derivatives using the product, quotient, and chain rules on polynomial,
rational, exponential, and logarithmic functions.
6. Solve problems in marginal analysis in business and economics using the derivative.
7. Interpret and communicate the results of a marginal analysis.
8. Graph functions and solve optimization problems using the first and second
derivatives and interpret the results.
9. Compute antiderivatives and indefinite integrals using term-by-term integration
or substitution techniques.
10. Evaluate certain definite integrals.
11. Compute areas between curves using definite integrals.
12. Solve applications problems for which definite and indefinite integrals are
mathematical models.
13. Solve applications problems involving the continuous compound interest formul
General Education Outcomes
I. This course addresses the general education outcome relating to communication by providing
additional support as follows:
A. Students develop their listening skills through lecture and through group problem
solving.
B. Students develop their reading comprehension skills by reading the text and by
reading the instructions for text exercises, problems on tests, or on projects.
Reading the mathematics text requires recognizing symbolic notation as well as
analyzing problems written in prose.
C. Students develop their writing skills through the use of problems which require
written explanations of concepts.
II. This course addresses the general education outcome of demonstrating effective individual
and group problem solving and critical thinking skills as follows:
A. Students must apply mathematical concepts previously mastered to new problems
and situations.
B. In applications, students must analyze problems and describe problems with either
pictures, diagrams, or graphs, then determine the appropriate strategy for
solving the problem.
III. This course addresses the general education outcome of using mathematical concepts to
interpret, understand, and communicate quantitative data as follows:
A. Students must demonstrate proficiency in problems-solving skills. These include
business applications of the derivative and the integral.
B. Students must apply calculus concepts to marginal analysis and optimization
problems, using their results to make business decisions and predictions.
Course Content
1. The derivative, derivative formulas, and marginal analysis
2. Graphing and optimization
3. Special derivatives: exponential and logarithmic functions
4. Integration and applications in business and economics
ENTRY-LEVEL COMPETENCIES
Upon entering this course, the student should be able to do the following:
1. Analyze problems using critical thinking skills.
2. Construct meaningful mathematical statements using algebraic symbols and notation.
3. Solve the following kinds of equations
a. Rational (leading to linear and quadratic)
b. Logarithmic
c. Exponential
4. Solve the following kinds of inequalities
a. Rational
b. Factorable polynomial of degree 2, 3, or 4
5. State the definition of a function and use function notation.
6. Identify and graph the following types of functions in two variables
a. Linear
b. Quadratic
c. Exponential
d. Logarithmic
7. Define exponential and logarithmic functions; use the properties of logarithms.
8. Evaluate expressions involving exponential and logarithmic functions of x
using a calculator.
Assessment of Outcome Objectives
I. COURSE GRADE
The course grade will be determined by the individual instructor using a variety
of evaluation methods such as tests, quizzes, projects, homework, and writing
assignments. A comprehensive final examination is required that must count at
least one-fourth and no more than one-third of the course grade.
II. DEPARTMENTAL ASSESSMENT
The course will be assessed every 5 years. The assessment instrument will consist
of a set of free-response questions included as a portion of the final exam for
all students taking the course. The assessment instrument will be graded by a
committee appointed by the Academic Group.
USE OF ASSESSMENT FINDINGS
The Math 1433 committee, or a special assessment committee appointed by the Chair of the
Executive Committee, will analyze the results of the assessment and determine implications
for curriculum changes. The committee will prepare a report for the Academic Group
summarizing its findings. |
Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied.
Functions of Several Variables and Their Derivatives: Points and Points Sets in the Plane and in Space; Functions of Several Independent Variables; Continuity; The Partial Derivatives of a Function; The Differential of a Function and Its Geometrical Meaning; Functions of Functions (Compound Functions) and the Introduction of New Independent Variables; The mean Value Theorem and Taylor's Theorem for Functions of Several Variables; Integrals of a Function Depending on a Parameter; Differentials and Line Integrals; The Fundamental Theorem on Integrability of Linear Differential Forms; Appendix.- Vectors, Matrices, Linear Transformations: Operatios with Vectors; Matrices and Linear Transformations; Determinants; Geometrical Interpretation of Determinants; Vector Notions in Analysis.- Developments and Applications of the Differential Calculus: Implicit Functions; Curves and Surfaces in Implicit Form; Systems of Functions, Transformations, and Mappings; Applications; Families of Curves, Families of Surfaces, and Their Envelopes; Alternating Differential Forms; Maxima and Minima; Appendix.- Multiple Integrals: Areas in the Plane; Double Integrals; Integrals over Regions in three and more Dimensions; Space Differentiation. Mass and Density; Reduction of the Multiple Integral to Repeated Single Integrals; Transformation of Multiple Integrals; Improper Multiple Integrals; Geometrical Applications; Physical Applications; Multiple Integrals in Curvilinear Coordinates; Volumes and Surface Areas in Any Number of Dimensions; Improper Single Integrals as Functions of a Parameter; The Fourier Integral; The Eulerian Integrals (Gamma Function); Appendix
Reviews
Editorial reviews
Publisher Synopsis
From the reviews: "These books (Introduction to Calculus and Analysis Vol. I/II) are very well written. The mathematics are rigorous but the many examples that are given and the applications that are treated make the books extremely readable and the arguments easy to understand. These books are ideally suited for an undergraduate calculus course. Each chapter is followed by a number of interesting exercises. More difficult parts are marked with an asterisk. There are many illuminating figures...Of interest to students, mathematicians, scientists and engineers. Even more than that." Newsletter on Computational and Applied Mathematics, 1991 "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." Acta Scientiarum Mathematicarum, 1991Read more... |
This book can be strongly recommended not only to students interested in the field, but also to mathematicians collaborating with non-mathematicians in research or hard practice, moreover to engineers, physicists and other natural scientists needing effective methods in scientific computing and wanting to know their underlying theory. The authors present the treated topics in a convincing synthesis of theory and practice, with well-chosen motivating examples, and when appropriate for understanding the principles not shying away from giving occasional proofs, use of basic functional-analytic concepts (like norms) and other analytical tools. They lay emphasis on complexity considerations (as important for efficient applicability) of methods, furthermore on questions of accuracy (via condition numbers) and stability. Many exercises offer the student the opportunity to gain more insight and to aquire a solid working knowledge. For useful algorithms written in MATLAB a web page is offered. To give a rough overview on the scope of the book let us look into the list of contents. Ch. 1: Mathematical review and computer arithmetic. Ch. 2: Numerical solution of nonlinear equations of one variable. Ch. 3: Numerical linear algebra. Ch. 4: Approximation theory. Ch. 5: Eigenvalue-eigenvector computation. Ch. 6: Numerical differentiation and integration. Ch. 7: Initial value problems for ordinary differential equations. Ch. 8: Numerical solution of systems of nonlinear equations. Ch. 9: Optimization. Ch. 10: Boundary-value problems and integral equations.
Reviewer:
Rudolf Gorenflo (Berlin) |
Mathematical techniques involving differential
equations used in the analysis of physical, biological and economic phenomena.
Emphasis is placed on the use of established methods, rather than rigorous
foundations.
First and second order
differential equations. Series solutions of second
order linear equations. The Laplace transform.
Numerical methods.
This course in elementary differential equations is
designed to introduce the student for displaying the interrelations between
mathematics and physical sciences or engineering. The principal attention
is given to those methods that are capable of broad applications and that
can be extended to various problems.
The methods discussed here include not only elementary
analytical techniques that lead to exact solutions of certain classes
of problems, but also include approximations based on numerical algorithms
or series expansions, as well as qualitative or geometrical methods. The
problem sets will be assigned and discussed in subsequent class sessions.
A student is expected to learn how to use a software package (such as
Maple, Matlab, Mathematica, etc.) in solving ordinary differential equations. |
Product Description
Review
"This book will fill an interesting niche in a library collection...it should be used by browsing students interested in making sure that they are prepared for success in their graduate programs." Choice
"All the Mathematics You Missed...is a help for students going on to graduate school..Since many students beginning graduate school do not have the mathematical knowledge needed, All the Mathematics You Missed aims to fill in the gaps." Berkshire Eagle, Pittsfield, MA
"From the preface: 'The goal of this book is to give people at least a rough idea of many topics that beginning graduate students at the best graduate schools are assumed to know." Mathematical Reviews
"The writing is lucid mathematical exposition, at a level quite appropriate to beginning graduate students." The American Statistician
"Before classes began, I jump started my graduate career with the help of this book. Even though I didn't believe that I could have missed much math, it became clear that my belief was wrong during the first week of class. While proving a theorem, my professor asked if anyone remembered a previous result from calculus. While I did not remember it from my days as an undergraduate, I had read about the theorem and had even seen a sketch of the proof in Garrity's book...This will be one of the books that I keep with me as I continue as a graduate student. It has certainly helped me understand concepts that I have missed." Elizabeth D. Russell, Math Horizons
"Point set topology, complex analysis, differential forms, the curvature of surfaces, the axiom of choice, Lebesgue integration, Fourier analysis, algorithms, and differential equations.... I found these sections to be the high points of the book. They were a sound introduction to material that some but not all graduate students will need." Charles Ashbacher, School Science and Mathematics
Book Description
Beginning graduate students in mathematics and other quantitative subjects are expected to have a daunting breadth of mathematical knowledge. This book will help readers to fill in the gaps in their preparation by presenting the basic points and a few key results of the most important undergraduate topics in mathematics: linear algebra, vector calculus, geometry, real analysis, algorithms, probability, set theory, and more. By emphasizing the intuitions behind the subject, the book makes it easy for students to quickly get a feel for the topics that they have missed and to prepare for more advanced courses.
This book has a very particular purpose: to recap some basic concepts from undergraduate mathematics so that you get the "big picture". In other words, for every math course you took as an undergrad, this book provides a good outline of the major ideas and how they fit together. But, it is only an outline; nothing more. If you actually missed out on some topic, or your knowledge of a subject is shaky, then this book won't help much. It will only help by providing a bibliography of some other references for that subject.
This book is meant to organize your undergraduate math knowledge, not to supplement it.
With that said, I'll mention a few words about the content of the book. It is quite well written and definitely extracts the essential ideas for your quick consumption. There are a few topics that I personally feel are missing, such as Gram-Schmidt and Jordan Canonical Forms for Linear Algebra, and UFDs and PIDs from Algebra. In general, it seemed like the book leaned a little more towards analysis than algebra, but the vast majority of important topics were indeed encapsulated in their synopsis.
Good for a very specific audience, but otherwise not wonderfully useful.
There's no doubt about it -- this book designed for people who want to learn some real math. It doesn't take, as the title and description might lead you to believe, a "Math for Engineers" approach.
Each chapter covers, in the span of 10 or 15 pages, what would normally be an entire semester's worth of material, and as a result, is quite dense -- there are alot of ideas crammed onto each page. But unlike traditional advanced math books (which are notoriously dense) the focus is more on developing intuitions than on long strings of equations.
An important strength is that every chapter ends with suggestions on textbooks in that chapter's subject. This turns out to be quite helpful, since one can't reasonably expect to learn everything important about any of these subjects from a brief chapter in any book.
I can envision three main ways in which this book might be useful: First, in combination with one or more of the books in listed in the bibliography for learning a new subject. Second, on its own for review of topics you've seen before. Third, as a reference for "basic" definitions and theorems, as in: "What's a Hilbert space again?"
Overall, this will be a good book to have around, but not a substitute for real study.
I used this book for an opposite purpose to the one the author intended. For me it served to review all the math I *had* learned long ago in school (both undergraduate and graduate), but was starting to forget. The author's informal style and rapid-fire delivery were just right for these topics. The subjects I had truly missed, mainly the more abstract parts of algebra and geometry, I found difficult to follow, though I did come away with some feeling for them. This is not a perfect book. The informal style extends to numerous typos in equations, and modern computer-oriented approaches get short shrift. Nevertheless, I found it a unique resource and a pleasure to read. |
Algebra 2 - 03 edition
Summary: Applications with "Real" Data Since the graphics calculator is recommended, students experience excitement as they use "real" data in Algebra 2. Students investigate and extend relevant applications through engaging activities, examples, and exercises. Graphics Calculator Technology In Algebra 2, the graphics calculator is an integral tool for presenting, understanding, and reinforcing concepts. To assist student...show mores in using this tool, a detailed keystroke guide is provided for each example and activity at the end of each chapter. Functional Approach Algebra 2 examines functions through multiple representations, such as graphs, tables, and symbolic notation. Working with transformations (investigating how functions are related to each other and their parent functions) prepares students for advanced courses in mathematics by developing an extensive, workable knowledge of functions0030660542-5-0
$3.59 +$3.99 s/h
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Desert Pueblo Books AZ Tucson, AZ
2003-01-01 Hardcover Fair Book has some edgewear, scuffs, names written on inside of front cover, text inside appears unmarked. We use delivery confirmation for all domestic orders where availableAcceptable
Booksavers MD Hagerstown, MD
2003 Hardcover Fair 2003 |
Product Synopsis
This is a lucid account of the highlights in the historical development of the calculus from ancient to modern times - from the beginnings of geometry in antiquity to the nonstandard analysis of the twentieth century. It emphasizes the genesis and evolution of both fundamental concepts and computational techniques. The intended audience includes not only students of the history of mathematics, but also the wider mathematical community, specifically those who study, teach and use calculus. Among the distinctive features of this exposition are historically motivated exercises and carefully chosen illustrative examples. Numerous sections of the book are suitable for use in courses in introductory and advanced calculus as well as the general history of mathematics |
Middle-School (grades 5 through 9) math program written to provide skills in context. Students write and solve simple algebra problems, then manipulate the vertices of an on-screen triangle so that it matches given information about its anglestrxCal 1.80 - Don't spent hours writing a program for some programmable calculator while MtrxCal can perform the same calculations with just a few simple lines. Don't waste time trying to find the right maximum and minimum values for plotting your functions. |
Gauss Jordan Method
In this lesson our instructor talks about solving system of equations using matrices. He talks about two equations and using substitution or elimination to solve them. He talks about three equations or higher and their history. He then discusses row echelon form and back substitution. He then talks about Gaussian elimination and augmented matrix. He finishes with Gauss-Jordan elimination. Four extra example videos round up this lesson.
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Gauss Jordan Method
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture. |
I like using the example of magic squares when starting to go over linear algebra, usually starting with $3\times 3$ squares. They're a nice recreational maths thing that everyone has seen before, but usually not thought about.
When asked for an example, most students come up with something like $\pmatrix{6&1&8\cr 7&5&3\cr 2&9&4}$, remembering a construction from before. When prodded for a second example, someone might suggest rotating or reflecting this example. Once it's suggest that we just want the rows, columns and diagonals to sum to the same thing, and that the numbers don't have to be distinct, someone usually thinks of $\pmatrix{1&1&1\cr 1&1&1\cr 1&1&1}$.
It then usually becomes clear that linear combinations of what we have so far will also work, and this leads naturally into asking how many squares we need in a basis, and so on. (I then ask them to work out the dimension of the space of $n\times n$ magic squares as homework.)
Another "unexpected" use of linear algebra is when they're asked to prove that things like $\sqrt2+\sqrt3$ or $\sqrt2 + \sqrt[3]2$ are algebraic. Many fiddle around until they chance upon an arrangement that works, but they all like it when we show that it's sufficient to take a few powers and say "oh, some combination of those will do". This usually goes down well, as people often like playing with numbers. |
Supplementary Course Modules (Calculus)
The Supplementary Course Modules for introductory calculus courses have been created to provide students with the opportunity to review, and to demonstrate mastery of, prerequisite material. Each module covers a key skill area from secondary school mathematics, up to and including topics covered in the Ontario Grade 12 Advanced Functions course (i.e., there are no questions requiring calculus itself).
Reviewing this material through the Module Program will not only earn you bonus marks towards your final calculus course grade, but will also help you when completing course work such as problem/lab assignments and tests! See resulting grade comparisons from the 2010-11 academic year. |
Please indicate in detail the advanced subjects that you
have studied. Where possible, please indicate the books (titles, authors) that were used during your
advanced studies. You can paste a TeX document if you want. |
This eBook introduces the significant scientific notation of the very large, the intermediate and the very small in terms of numbers and algebra through an exploration of indices, the rules of indices… |
Syllabus
Summary:This three quarter topics course on Combinatorics includes
Enumeration, Graph Theory, and Algebraic Combinatorics.
Combinatorics has connections to all areas of mathematics and many
other sciences including biology, physics, computer science, and
chemistry. We have chosen core areas of study which should be
relevant to a wide audience. The main distinction between this course
and its undergraduate counterpart will be the pace and depth of
coverage. In addition we will assume students have a basic knowledge
of linear and abstract algebra. We will include many unsolved
problems and directions for future research. The outline for each
quarter is the following:
Enumeration: Every discrete process leads to questions of
existence, enumeration and optimization. This is the foundation of
Combinatorics. In this quarter we will present the basic
combinatorial objects and methods for counting various arrangements of
these objects.
Basic counting methods.
Sets, multisets, permutations, and graphs.
Inclusion-exclusion.
Recurrence relations and integer sequences.
Generating functions.
Partially ordered sets.
Complexity Theory
Graph Theory: Graphs are among the most important structures in
Combinatorics. They are universally applicable for modeling discrete
processes. We will introduce the fundamental concepts and some of the
major theorems. The existence questions of Combinatorics are very
common in graph theory.
Basic graph structures
Matchings
Planar graphs
Colorings
Ramsey Theory
Graph minor theorem
Algebraic Combinatorics: The symmetric group $S_{n}$
acts on polynomials in $n$ variables simply by permuting the
variables. Polynomials which are fixed under this action are called
symmetric polynomials. If we consider the limit as $n$ approaches
infinity we get symmetric functions. The symmetric functions appear
in many aspects of mathematics including algebra, topology,
combinatorics, and geometry. The Schur functions are an important
basis for symmetric functions. One key application of symmetric
function theory using Schur functions is to the representation theory
of $S_{n}$. Another key application of Schur functions is to the
study of the cohomology ring of the Grassmannian Manifold. A third
key application of Schur functions is to the representation theory of
$GL_{n}$. We will survey the algebraic side of combinatorics while
exploring these connections. Topics include:
Student presentations: A graduate level Combinatorics course is
surprisingly close to the frontier of research in this area.
Each student will present a recent journal article to be chosen with
the instructor. Presentations will occur during the last 2 weeks
of the quarter. The presentation will count toward 50% of the grade.
Exercises: The single most important thing a student can do to learn
combinatorics is to work out problems. This is more true in this
subject than almost any other area of mathematics. Exercises will be
assigned each week but many more good problems are to be found,
within, in your textbooks. Do as many of them as you can.
Problem sets: The other 50% of the grade will be based on weekly
problem sets due on Wednesdays. The problems be assigned during the
course of each lecture. Collaboration is encouraged among students.
Of course, don't cheat yourself by copying. We will have a problem
session on Monday or Tuesday afternoons to discuss the harder
problems. The time will be determined in the first week of class.
Computing: Use of computers to verify solutions, produce examples, and
prove theorems is highly valuable in this subject. Please turn in
documented code if your proof relies on it. If you don't already know
a computer language, then try SAGE, Maple or GAP. All three are
installed on abel and theano.
Schedule:
(T) indicates tentative.
* Lecture 1: Historical approach to Schur functions. The first
of 4 definitions to be given. |
Mathematics, General Colleges
A general program that focuses on the analysis of quantities, magnitudes, forms, and their relationships, using symbolic logic and language. Includes instruction in algebra, calculus, functional analysis, geometry, number theory, logic, topology and other mathematical specializations |
Philosophy
The
staff of the Valdés Institute believes that all students can succeed in
higher math. The goal of the José Valdés Math Institute is to
increase the number of underrepresented minorities in programs leading
to college entrance and professional careers. The intense summer
program prepares students to succeed in Algebra I upon entering high
school, with the final goal being success in Calculus before leaving
high school.
This prepares students
to succeed in other advanced high school courses, motivates them to
stay in school, and encourages them to enter a college/university
preparatory program. The project reduces the risk of students dropping
out by providing a viable intervention program at an early age, raising
self-esteem, and smoothing the transition from middle school to high
school. The high school students continue their progress toward college
entrance by either advancing or repeating a course. In addition, they
also serve as role models for the middle school students.
All students can learn math.
Teachers have to believe all students can learn math.
Sound teaching will work with all students.
Minority students do not need "watered down math" in order to be successful in high level math.
Parents must be totally involved with their children's education.
All students should enter high school with skills to be successful in Algebra I.
This project is "teacher initiated" and teachers make all the important educational decisions.
This is a common effort by elementary, middle, and high schools, and university teachers to solve an educational problem.
We believe that math is a vehicle to teach students how to think; if successful in math, anything is possible.
Truly
heterogeneous learning will be achieved when all high school students
are able to succeed in calculus before high school graduation.
Math
is a subject that can be learned by everyone. Basic skills are the
foundation for most abstract thinking. Students who come to the Valdés
Institute should be ready for a rigorous curriculum with mastery
required. We believe that students will attain high standards when we
expect that of them.
There are many
reports on math education (College Board, Calfornia standards and
framework, NCTM, CMC, TIMSS) which emphasize the importance of
understanding the concepts as well as the mathematical manipulations.
We help students acquire both.
The California Mathematics Council believes "...that
all students have the capacity to become mathematically competent and
confident when provided a rigorous and challenging mathematical program
supported by high expectations." That expresses well our belief and practice.
This
math program expects students to master each math level before
advancing on to a higher class level. A detailed description of each
math class is provided in the Classes Offered section.
Our Commitment to You
The
José Valdés Math Institute never loses sight of the fact that it is an
East Side Institution-both literally and figuratively. Its ongoing
mission is to increase the number of underrepresented students prepared
to succeed in Algebra I in East Side schools; and as a consequence,
increase the number of students taking upper level mathematics courses
in subsequent years.
Our belief is
that our population should reflect the community we serve. Acceptance
into the Valdés Institute is a three-fold process: application,
placement, and registration. And although some may think otherwise, the
Institute does not compromise these essential elements to students'
success in an effort to increase the number of one group of students
over another. |
What Is Mathematics?: An Elementary Approach to Ideas and Methods...more--a matter of the correct application of local rules. Meaningful mathematics is like journalism--it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view.(less)
Paperback, 592 pages
Published
July 18th 1996
by Oxford University Press, USA
(first published January 1st 1967)
Community Reviews
abo...more about mathematics think that it is about arithmetic or calculation - it is easy to get that impression when school mathematics centers mostly around solving uninteresting problems, which often involve a lot of calculation.
This book shows that mathematics is about understanding the properties and behaviour of mathematical objects. What are numbers? Why do they behave the way they do when we carry out operations on them? Why can some shapes be constructed with ruler and compass, but some not?
The book requires patience and time to read. Don't read it if you are in a hurry.(less)
l...more lectures in that course. This book ties it all up with a nice bow. The long chapter on maxima and minima -- went on long, I was ready to put the book down and then it made this brilliant transition to the calculus.
I'm sure the more math you've had, the more you will get out of this book -- some sections may be rough if you haven't had some trig and the calculus and I was a little lost more than once anyway.(less)
font...more fonts are difficult to read, and some of the shorthand is less than modern.
This may have been a good introduction/refresher at some point in time, but there have to be better books out there now. For one, your time would be better spent reading Heath's translation of Euclid. Some day I hope to make time for The Princeton Companion to Mathematics. I'll see how it compares. (less)
would have been nice for upper-level physics! oh well!). I think this will be my default high school graduation present to anyone with an inkling...more would have been nice for upper-level physics! oh well!). I think this will be my default high school graduation present to anyone with an inkling of mathematical talent from now on (rather than the more intimidating Road to Reality, which likely just frightens people).
As they said in Mathematical Review, "A work of extraordinary perfection."(less)
Skimmed through and it is quite useful, very similar to one of Felix Klein's books in terms of style. A little too mathematics for my purposes which is more towards physics, some insights are good nonetheless. |
Part 1: Calculus In the Calculus section of the course, we will continue the studies begun in MHF4U (Advanced Functions) regarding rates of change of functions until we get to the idea of the "instantaneous slope" of a function.
Secants Approaching Tangents Several secants are drawn above. By choosing points on the original function closer and closer together, the secant approaches becoming a tangent.
Part 2: Vectors In the Vectors section of the course, we will look at, among other things, graphing in three dimensions. We will consider equations of planes and look at intersections of planes.
Intersecting Planes Two non-parallel planes will always intersecting in a line. |
If a book or article cannot be found in PVAMU's resources, it can usually be borrowed from another library.
Fill out the Interlibrary Loan form, and please note that it may take several weeks to receive the item.
How to prepare for the TAKS : Texas assessment of knowledge and skills high school math exit exam - QA43 .E64 2004
100 math tips for the SAT and how to master them now - LB2353.57 .G85 2002
Encyclopedia of mathematics education - QA 11 E665 2001
Selected Print Mathematics Journals
Advances in mathematics
American journal of mathematics
Annals of mathematics
Journal for research in mathematics education
Journal of applied mathematics and mechanics
Mathematics teacher
Arithmetic teacher
American Mathematical Society ( - The American Mathematical Society promotes mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.
Centre For Innovation in Mathematics Teaching ( - The centre is a focus for research and curriculum development in Mathematics teaching and learning, with the aim of unifying and enhancing mathematical progress in schools and colleges.
K-6 Math Playground ( - Math Playground is an action packed site for students in grades K to 6. Practice your math skills, play a logic game
Math Forum ( - Online resource for improving math learning, teaching, and communication. This is a great Mathematics Website but the access is not free.
Mathematics Virtual Library ( This collection of Mathematics-related resources is maintained by the Florida State University Department of Mathematics.
Mathematical Association of America ( - The Mathematical Association of America is the largest professional society that focuses on mathematics accessible at the undergraduate level.
Metamath proof explorer ( This Website contains more than 5,000 computer-verified formal proofs, definitions, and axioms in logic and set theory. |
Maple V Release 5.1 - Maple
V is a comprehensive computer system for advanced mathematics. It includes facilities
for interactive algebra, calculus, discrete mathematics, graphics, numerical
computation and many other areas of mathematics. |
Students study systems of linear equations, vector spaces,
linear dependence, linear transformations and matrix
representation, determinants, eigenvectors and eigenvalues,
and a variety of applications. It is an introductory level
course in a branch of math called Modern Algebra. An
additional 0.25 quality point will be added to the quality-
point value assigned to the final grade earned in this
course. |
How to Brush Up on Your Maths Skill
August 29, 2008
I know you don't want to admit it, but you love mathematics, isn't it? Of course you want to be in the best shape possible to prepare for the long battle. You try to solve a few equations an realize in horror that all those hours watching anime have drained your brain! Fear not, let the butterfly help you!
As I mentioned before, Mnemosyne is an excellent learning tool. Someone was nice enough to enter some of the most frequently used equations in a card form. While it says Calculus, some of the equations are very basic and will be useful for other math courses.
- You need Mnemosyne software if you don't have it yet.
- You need LaTeX to display the equations correctly. That will involve some heave duty installation, but you can do it! Just download that setup file (over 600MB) and install individual packages by going to the respective folders and activating setup file.
Opening the file:
- Download zip file and unpack it
- Create new file: Open Mnemosyne, File > New > Name you file (e.g. Math)
- Import the data: File > Import > Select XML Option (that file is in XML format) > Browse to the file
- If you don't have LaTex, you 'll get an error message.
Using the file
The file contains 239 equations, but some of them might not display properly. This can be easily fixed by hitting Edit Current Card (Ctrl+E) and removing the "=" sign. For example "cos(x-y)=" will not display properly, but "cos(x-y)" will show up correctly. |
Linear Algebra
Linear Algebra provides
important mathematical tools which are not only essential to solve many
technical and computational problems, but also help in obtaining a deeper
understanding of many areas of engineering.
The aims of this course are to:
Introduce the ideas and techniques of Linear
Algebra, and illustrate some of their applications in engineering.
OBJECTIVES
For all objectives, the
student should be able to complete calculations by hand for small problems, or
by using Matlab for larger problems (the IB Computing Course deals with this in
detail). By the end of the course students should:
Be able to solve a set of linear equations
using Gaussian elimination, and complete the LU factorisation of
a matrix;
Understand, and be able to calculate bases for the
four fundamental subspaces of a matrix;
Be able to calculate the least squares
solution of a set of linear equations;
Be able to orthogonalize a set of vectors,
complete the QR factorisation of a matrix, and be able to use
this to find the least squares solution of a set of linear equations;
Be able to find the eigenvalues and
eigenvectors of a matrix, and complete the A = SL S-1
or A = QL QT factorisations as appropriate;
Be able to find the SVD of a matrix,
and to understand how this can be used to calculate the rank of the
matrix, and to provide a basis for the each of its fundamental subspaces
LECTURE SYLLABUS
Solution of the matrix equation Ax = b: Gaussian elimination, LU
factorization, the four fundamental subspaces of a matrix. |
1. Computer Arithmetic
The purpose of computing is insight, not numbers. -- R.W. Hamming, [23]
The main goal of numerical analysis is to develop efficient algorithms for computing precise numerical values of mathematical quantities, including functions, integrals, solutions of algebraic equations, solutions of differential equations (both ordinary and partial), solutions of minimization problems, and so on. The objects of interest typically (but not exclusively) arise in applications, which seek not only their qualitative properties, but also quantitative numerical data. The goal of this course of lectures is to introduce some of the most important and basic numerical algorithms that are used in practical computations. Beyond merely learning the basic techniques, it is crucial that an informed practitioner develop a thorough understanding of how the algorithms are constructed, why they work, and what their limitations are. In any applied numerical computation, there are four key sources of error: (i ) Inexactness of the mathematical model for the underlying physical phenomenon. (ii ) Errors in measurements of parameters entering the model. (iii ) Round-off errors in computer arithmetic. (iv ) Approximations used to solve the full mathematical system. Of these, (i ) is the domain of mathematical modeling, and will not concern us here. Neither will (ii ), which is the domain of the experimentalists. (iii ) arises due to the finite numerical precision imposed by the computer. (iv ) is the true domain of numerical analysis, and refers to the fact that most systems of equations are too complicated to solve explicitly, or, even in cases when an analytic solution formula is known, directly obtaining the precise numerical values may be difficult. There are two principal ways of quantifying computational errors. Definition 1.1. Let x be a real number and let x be an approximation. The absolute error in the approximation x x is defined as | x - x |. The relative error is |x - x| , which assumes defined as the ratio of the absolute error to the size of x, i.e., |x| x = 0; otherwise relative error is not defined. 3/15/06 1
c 2006 Peter J. Olver
For example, 1000001 is an approximation to 1000000 with an absolute error of 1 and a relative error of 10-6 , while 2 is an approximation to 1 with an absolute error of 1 and a relative error of 1. Typically, relative error is more intuitive and the preferred determiner of the size of the error. The present convention is that errors are always 0, and are = 0 if and only if the approximation is exact. We will say that an approximation x has k significant decimal digits if its relative error is < 5 10-k-1 . This means that the first k digits of x following its first nonzero digit are the same as those of x. Ultimately, numerical algorithms must be performed on a computer. In the old days, "computer" referred to a person or an analog machine, but nowadays inevitably means a digital, electronic machine. A most unfortunate fact of life is that all digital computers, no matter how "super", can only store finitely many quantities. Thus, there is no way that a computer can represent the (discrete) infinity of all integers or all rational numbers, let alone the (continuous) infinity of all real or all complex numbers. So the decision of how to approximate more general numbers using only the finitely many that the computer can handle becomes of critical importance. Each number in a computer is assigned a location or word , consisting of a specified number of binary digits or bits. A k bit word can store a total of N = 2 k different numbers. For example, the standard single precision computer uses 32 bit arithmetic, for a total of N = 232 4.3 109 different numbers, while double precision uses 64 bits, with N = 264 1.84 1019 different numbers. The question is how to distribute the N exactly representable numbers over the real line for maximum efficiency and accuracy in practical computations. One evident choice is to distribute them evenly, leading to fixed point arithmetic. For example, one can use the first bit in a word to represent a sign, and treat the remaining bits as integers, thereby representing the integers from 1 - 1 N = 1 - 2k-1 to 1 N = 2k-1 2 2 exactly. Of course, this does a poor job approximating most non-integral numbers. Another option is to space the numbers closely together, say with uniform gap of 2 -n , and so distribute our N numbers uniformly over the interval - 2- n-1 N < x 2- n-1 N . Real numbers lying between the gaps are represented by either rounding, meaning the closest exact representative, or chopping, meaning the exact representative immediately below (or above if negative) the number. Numbers lying beyond the range must be represented by the largest (or largest negative) representable number, which thus becomes a symbol for overflow. When processing speed is a significant bottleneck, the use of such fixed point representations is an attractive and faster alternative to the more cumbersome floating point arithmetic most commonly used in practice. The most common non-uniform distribution of our N numbers is the floating point system, which is based on scientific notation. If x is any real number it can be written in the form x = .d1 d2 d3 d4 . . . 2n , where d = 0 or 1, and n Z is an integer. We call d1 d2 d3 d4 . . . the mantissa and n the exponent. If x = 0, then we can uniquely choose n so that d1 = 1. In our computer, we approximate x by a finite number of mantissa digits x = .d1 d2 d3 d4 . . . dk-1 dk 2n , 3/15/06 2
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by either chopping or rounding the final digit. The exponent is also restricted to a finite range of integers n N N . Very small numbers, lying in the gap between 0 < | x | < 2n , are said to cause underflow . In single precision floating point arithmetic, the sign is 1 bit, the exponent is 7 bits, and the mantissa is 24 bits. The resulting nonzero numbers lie in the range 2-127 10-38 | x | 2127 1038 , and allow one to accurately represent numbers with approximately 7 significant decimal digits of real numbers lying in this range. In double precision floating point arithmetic, the sign is 1 bit, the exponent is 10 bits, and the mantissa is 53 bits, leading to floating point representations for a total of 1.84 1019 different numbers which, apart from 0. The resulting nonzero numbers lie in the range 2-1023 10-308 | x | 21023 10308 . In double precision, one can accurately represent approximately 15 decimal digits. Keep in mind floating point numbers are not uniformly spaced ! Moreover, when passing from .111111 . . . 2n to .100000 . . . 2n+1 , the inter-number spacing suddenly jumps by a factor of 2. The non-smoothly varying spacing inherent in the floating point system can cause subtle, undesirable numerical in artifacts high precision computations. Remark : Although they are overwhelmingly the most prevalent, fixed and floating point are not the only number systems that have been proposed. See [9] for another intriguing possibility. In the course of a calculation, intermediate errors interact in a complex fashion, and result in a final total error that is not just the sum of the individual errors. If x is an approximation to x, and y is an approximation to y, then, instead of arithmetic operations +, -, , / and so on, the computer uses a "pseudo-operations" to combine them. For instance, to approximate the difference x - y of two real numbers, the computer begins by replacing each by its floating point approximation x and y . It the subtracts these, and replaces the exact result x - y by its nearest floating point representative, namely (x - y ) . As the following example makes clear, this is not necessarily the same as the floating point approximation to x - y, i.e., in general (x - y ) = (x - y) . Example 1.2. . Lets see what happens if we subtract the rational numbers 301 301 .15050000 . . . , y= .150424787 . . . . 2000 2001 The exact answer is 301 x-y = .00007521239 . . . . 4002000 However, if we use rounding to approximate with 4 significant digits , then x= x= 301 .1505, 2000 y= 301 .1504 2001 and so x - y .0001,
To aid comprehension, we are using base 10 instead of base 2 arithmetic in this example.
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Peter J. Olver
3 2 1
2 -1 -2 -3
4
6
8
10
Figure 1.1.
Roots of Polynomials.
which has no significant digits in common with the actual answer. On the other hand, if we evaluate the difference using the alternative formula x-y = 301 2001 - 301 2000 602301 - 602000 = 4002000 4002000 5 5 6.023 10 - 6.020 10 .003 105 = .00007496, 4.002 106 4.002 106
we at least reproduce the first two significant digits. Thus, the result of a floating point computation depends on the order of the arithmetic operations! In particular, the associative and distributive laws are not valid in floating point arithmetic! In the development of numerical analysis, one tends to not pay attention to this "minor detail', although its effects must always be kept in the back of one's mind when evaluating the results of any serious numerical computation. Just in case you are getting a little complacent, thinking "gee, a few tiny round off errors can't really make that big a difference", let us close with two cautionary examples. Example 1.3. Consider the pair of degree 10 polynomials p(x) = (x - 1)(x - 2)(x - 3)(x - 4)(x - 5)(x - 6)(x - 7)(x - 8)(x - 9)(x - 10) and q(x) = p(x) + x5 . They only differ in the value of the coefficient of their middle term, which, by a direct expansion, is -902055 x5 in p(x), and - 902054 x5 in q(x); all other terms are the same. The relative error between the two coefficients is roughly one-thousandth of one percent. Our task is to compute the roots of these two polynomials, i.e., the solutions to p(x) = 0 and q(x) = 0. Those of p(x) are obvious. One might expect the roots of q(x) to 3/15/06 4
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1 0.8 0.6 0.4 0.2 0.5 1 1.5 2 2.5
Figure 1.2.
Sensitive Dependence on Initial Data.
be rather close to the integers 1, 2, . . . , 10. However, their approximate values are 1.0000027558, 5.24676 0.751485 i , 1.99921, 7.57271 1.11728 i , 3.02591, 9.75659 0.368389 i . 3.82275,
Surprisingly, only the smallest two roots are relatively unchanged; the third and fourth roots differ by roughly 1% and 27%, while the final six roots have mysteriously metamorphosed into three complex conjugate pairs of roots of q(x). The two sets of roots are plotted in Figure 1.1; those of p(x) are indicated by solid disks, while those of q(x) are indicated by open circles. We have thus learned that an almost negligible change in a single coefficient of a real polynomial can have dramatic and unanticipated effects on its roots. Needless to say, this indicates that finding accurate numerical values for the roots of high degree polynomials is a very challenging problem. Example 1.4. Consider the initial value problem du - 2 u = - e- t , u(0) = 1 . 3 dt The solution is easily found: u(t) = 1 e- t , 3 and is exponentially decaying as t . However, in a floating point computer, we are not able to represent the initial con1 dition 3 exactly, and make some small round-off error (depending on the precision of the computer). Let = 0 represent the error in the initial condition. The solution to the perturbed initial value problem dv - 2 v = - e- t , dt is v(t) =
1 -t 3e
v(0) = + e2 t ,
1 3
+ ,
which is exponentially growing as t increases. As sketched in Figure 1.2, the two solutions remain close only for a very short time interval, the duration of which depends on the 3/15/06 5
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size in the initial error, but then they eventually diverge far away from each other. As a consequence, a tiny error in the initial data can have a dramatic effect on the solution. This phenomenon is referred to as sensitive dependence on initial conditions. The numerical computation of the exponentially decaying exact solution in the face of round-off errors is an extreme challenge. Even the tiniest of error will immediately introduce an exponentially growing mode which will eventually swamp the true solution. Furthermore, in many important applications, the physically relevant solution is the one that decays to zero at large distances, and is usually distinguished from the vast majority of solutions that grow at large distances. So the computational problem is both important and very difficult. Examples 1.3 and 1.4 are known as ill-conditioned problems meaning that tiny changes in the data have dramatic effects on the solutions. Simple numerical methods work as advertised on well-conditioned problems, but all have their limitations and a sufficiently ill-conditioned problem will test the limits of the algorithm and/or computer, and, in many instances, require revamping a standard numerical solution scheme to adapt to the ill-conditioning. Some problems are so ill-conditioned as to defy even the most powerful computers and sophisticated algorithms. For this reason, numerical analysis will forever remain a vital and vibrant area of mathematical research. So, numerical analysis cannot be viewed in isolation as a black box, and left in the hands of the mathematical experts. Every practitioner will, sooner or later, confront a problem that tests the limitations of standard algorithms and software. Without a proper understanding of the mathematical principles involved in constructing basic numerical algorithms, one is ill-equipped, if not hopelessly handicapped, when dealing with such problems. The purpose of this series of lectures is to give you the proper mathematical grounding in modern numerical analysis.
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COMPLETE HOMESCHOOL KIT ALGEBRA 23RD EDITION
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COMPLETE HOMESCHOOL KIT ALGEBRA 23RD EDITION Algebra 2 covers all topics that are traditionally covered in second-year algebra as well as a considerable amount of geometry. In fact, students completing Algebra 2 will have studied the equivalent of one semester of informal geometry. Time is spent developing geometric concepts and writing proof outlines. Real-world problems are included along with applications to other subjects such as physics and chemistry.
includes:
Student Textbook (Hardcover)
129 Lessons
Glossary and Index
Answer Key to all Student Textbook Problem Sets
577 pages
Homeschool Packet With Test Forms
32 Test Forms for homeschooling
Answer Key to all Student Textbook Problem Sets
Answer Key to all homeschool Tests
Solutions Manual
Solutions to all textbook practices and problem sets
Early solutions contain every step. Later solutions omit obvious steps. |
Understanding Mathematics Peter Alfeld wrote this study guide for undergraduate mathematics students at the University of Utah. Alfeld discusses what it means to understand mathematics rather than just understanding how to solve problems, and how to approach mathematics in a more effective way. Links to comments, examples, and frequently asked questions are included. Author(s): No creator set |
QuickMath Automatic problem-solving site that
let students enter an expression and get an answer to math problems dealing with
polynomial factoring, multiplication, long division, integration and differentiation.
S.O.S. Mathematics Site acts as a hyperlinked
math textbook. Students who have trouble following either the textbook explanation
or their teacher's lecture can visit this site for an additional explanation of
a difficult concept.
Hotmath This site offers free tutorial solutions
to the odd-numbered homework problems from most popular math textbooks. The tutorial
solutions seek to mimic what a tutor or teacher would say if a student asked for
help on the problem. |
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Dynamic Mathematics with GeoGebra
In this article we introduce the free educational mathematics software GeoGebra. This open source tool extends concepts of dynamic geometry to the fields of algebra and calculus.
Additional Figures
Figure 6a: A light ray from point \(P\) reaches the upper parabola and is reflected to the lower one.
Figure 6b: A light ray from point \(P\) is reflected out of the mirascope.
Figure 6d: Defining a new tool to reflect light from point \(P\) out of the mirascope. In GeoGebra, click "Tools" in the menu, select "Create New Tool," and follow the onscreen directions to click the objects involved. In our case, inputs include point \(P\), point \(G\), number \(a\), and number \(c\). Outputs may include all the objects related to the light reflection or, if so desired, the light ray q only.
Figure 6e: Using the newly defined tool to reflect a second light ray from point \(P\) out of the mirascope. In GeoGebra, place point \(H\) anywhere on the downward parabola. Point \(H\) is the location where a second ray from point \(P\) touches on that parabola. Next, click the button for the new tool at the upper-right corner. For inputs, click point \(P\) and point \(H\). When prompted for numbers, type "a" and "c". The color of the second ray is changed to distinguish it from the first one.
Figure 7c: Modeling more light rays from point \(P\) is not necessary to locate the image of \(P\).
Figure 7d: The image is well above the mirascope if the two parabolas are relatively close to each other |
This is an introductory course to number theory. Topics include divisibility, prime numbers and modular arithmetic, arithmetic functions, the sum of divisors and the number of divisors, rational approximation, linear Diophantine equations, congruences, the Chinese Remainder Theorem, quadratic residues, and continued fractions.
Prerequisites: MA 232
Course Web Site:
Course Objectives
The purpose of the course is to give a simple account of classical number theory, prepare students to graduate-level courses in number theory and algebra, and to demonstrate applications of number theory (such as public-key cryptography). Upon completion of the course, students will have a working knowledge of the fundamental definitions and theorems of elementary number theory, be able to work with congruences, solve congruence equations and systems of equations with one and more variables, and be literate in the language and notation of number theory.
Learning Outcomes
Divisibility. Understand the concept and properties of divisibility. Know the definitions and properties of gcd and lcm.
Euclid algorithm and Bezout's identity. Be able to compute the greatest common divisor and least common multpiples.
Linear Diophantine equations. Describe the set of all solutions to linear Diophantine equations.
Primes, distribution of primes, and prime power factorization. Determine if a number is prime. Compute the prime power factorization of a number.
Modular arithmetic, congruences. Understand the concept of a congruence. Be able to perform basic operations with congruences (addition, multiplication, subtraction).
Linear congruences, systems of linear congruences, and Chinese remainder theorem (CRT). Compute the set of all solutions to linear congruence. Be able to apply CRT and reduce general systems of linear congruences to systems studied by CRT.
Simultaneous non-linear congruences. Describe the set of solutions of non-linear congruence equations (with relatively small moduli) and be able to solve systems of such equations.
The arithmetic of Zp. Studentís must understand and be able to use the founding theorems: Lagrange theorem, Fermat's little theorem, Wilson's theorem.
Primality-testing, pseudoprimes, and Carmichael numbers. Understand the concept of a pseudoprime and be able to determine if a number is pseudoprime or Carmichael.
Units. Euler's function phi. Understand the definition of a unit, know characterization of units, be able to compute a group of units directly. Compute Eulerís function phi, be able to use a formula for phi to study relations between numbers n and phi(n). Understand Euler's generalization of Fermat's little theorem.
The group of units Un. Understand the concepts of the order of an element, primitive root, generating set for a group, Cayley graph for a group. Be able to determine if a group Un has a primitive root and find it. Be able to find a generating set for Un and draw the Cayley graph relative to the chosen set.
The group of quadratic residues Qn. Construct the group Qn directly. Determine the size of Qn. Compute Legendre symbol, know the properties of Legendre symbol. Know and be able to use the law of quadratic reciprocity.
Arithmetic functions. Mobius inversion formula and its properties.
RSA cryptography. Understand the basics of RSA security and be able to break the simplest instances. |
A solid understanding of mathematics, also known as numeracy, is an important component of a well-rounded education. The ability to perform basic mathematical computations is a requirement of many entry-level jobs. In addition, careers in fields such as engineering, medicine, finance and all of the sciences require a solid background in higher-level university mathematics, including calculus, statistics and linear algebra.
PHOTO BY REV DAN CATT ON FLICKR WITH CC LICENSE
The first thing to point out here is that the basic mathematical computations for entry level jobs are much different than the higher-level university level mathematics needed for engineering, medicine, finance and the sciences.
I have to agree with Zwaagstra that a solid understanding of mathematics is an important component of a well-rounded education. However, his assertion that mathematics equals numeracy is definitely false, as I have had pointed out to me on a regular basis. Many mathematicians, engineers, doctors, economists, and scientists struggle with basic computational math, but are still fully capable of doing higher level mathematics. This has been true for a long time, far longer than the new math has been used in schools.
Because math is such an important skill, schools have an obligation to ensure that students learn key math concepts. Unfortunately, schools are largely failing in this regard. First-year post-secondary students are increasingly unprepared for university-level mathematics, and this has led to a proliferation of remedial math courses at universities across Canada. Many parents choose to enrol their children in special tutoring sessions with organizations such as Kumon and the Sylvan Learning Centre to fill in the gaps left by the public school system. Unfortunately, many cannot afford extra tutoring, and this creates a two-tiered system that unfairly penalizes children whose parents cannot pay for extra math lessons.
Now Zwaagstra points out that remedial math courses are on the rise in universities, but he doesn't mention a couple of key facts. First, under the old system of mathematics instruction, around 50 per cent of students failed first-year math courses, which were often included in programs as a tool with which to weed people out of university. Could it be that this issue has always been around, and universities are simply now doing something about the problem? What about the increase in students seeking a university education? Could these two issues be connected? Zwaagstra has assumed a correlation between the number of remedial math courses, and the effectiveness of K-12 math education, without actually finding research that supports his conclusion.
It is also important to point out that the "new" math education techniques are themselves not very old, and are not used by all teachers equally. The most recent iteration of the elementary school math curriculum in British Columbia is only four years old, and the secondary school curriculum is only five years old, neither of which is a long enough period of time to make the kind of determinations of effectiveness that Zwaagstra is making.
Further, he talks about parents enrolling their kids in after-school tutoring programs without discussing the reasons why parents are doing this. Are parents increasingly enrolling their kids for extra tutoring because they are dissatisfied with their children's current educational attainment? Or do they have other reasons for paying for these tutoring services? We don't know, and Zwaagstra doesn't provide us with any evidence for the reasons for parents to choose tutoring. He just cherry-picks this fact because it seems to support his argument.
Although there is solid evidence supporting the traditional approaches to teaching math that involve mastering standard algorithms, practising skills to mastery and introducing concepts in incremental steps, most provincial math curricula and textbooks employ a different approach. Constructivism, which encourages students to come up with their own understanding of the subject at hand, is the basis for this new approach to teaching math. As a result, there is very little direct instruction of important mathematics algorithms or rigorous practising and memorization of basic math facts.
The problems in our math education system are entirely due to the introduction of the new math curriculum, according to educator and author Michael Zwaagstra.
There is also solid evidence showing that the longer that people are out of school, the less likely they are to use the algorithms they use in school, but the more successful they are at solving mathematical problems they encounter, as Keith Devlin points out in his book, The Math Instinct. In other words, traditional school math seems to be a hindrance to people being able to actually solve real-world mathematical problems. It's worth pointing out that Devlin's research is reasonably old, and most of the participants in the research learned mathematics in the traditional method. Is it even worth pointing out that Zwaagstra doesn't actually include any of his "solid evidence" in his paper, and the footnote here (see the original article) leads to a definition of the word algorithm?
Our students deserve better. Pupils who are not taught math properly are being unfairly denied the opportunity to enter careers in many desirable fields. The public school system has an obligation to ensure that every child has the opportunity to learn the mathematics required for university-level mathematics courses.
It's pretty important to note that when teachers are given proper training in effective pedagogy, their students' understanding improves. To say that the problems in our math education system are entirely due to the introduction of the new math curriculum is pretty irresponsible, given that any number of other factors could be contributing to the problem. Further, many schools use the International Baccalaureate program, which itself relies on the "new math" with a focus on students understanding mathematics and being able to communicate their understanding. These students are highly sought after by universities. If the new math was so destructive, wouldn't we see these students being turned away by universities?
Zwaagstra then goes on to bash the results of the PISA examinations, citing an article (claiming it is research) written that suggests that Finnish students are not as good at math as the PISA results would claim, and that by extension, neither are Canadian students.
There is a strong consensus [emphasis mine] among math professors that the math skills of these students are much weaker than they were two or three decades ago.
Zwaagstra links to two articles (neither of which is a research study) that state that some professors have found a drop in numeracy skills (again, these are associated with mathematical ability, but are not equivalent), and the other of which makes no mention of math skills at all. In this case, Zwaagstra is completely misrepresenting the articles themselves. He then points to two professors who have done research on the computational abilities of graduates and noticed a decline, but he does not clarify whether or not this is correlated with a decline in their ability to do
university-level mathematics.
Zwaagstra continues by bemoaning the lack of standards and emphasis on accurate calculations by the National Council of Mathematics Teachers (NCTM), and the Western and Northern Canadian Protocol (WNCP). Clearly, the research these two organizations have done for decades is not sufficient for Zwaagstra.
However, there is a big difference between demonstrating a conceptual understanding of mathematics and actually being able to solve equations accurately and efficiently. Just as most people would be very uncomfortable giving a driver's licence to someone who merely demonstrates a conceptual understanding of how to drive a car, we should be concerned about a math curriculum that fails to emphasize the importance of mastering basic math skills.
To extend Zwaagstra's analogy, we should similarly be afraid of giving the keys to someone who has no real-world experience driving. If someone has spent all of their time in a flight simulator, but never actually driven a car, should they be allowed to do so? Does an emphasis on the mechanics of driving a car (or the mechanics of mathematics) turn someone into one who is capable of driving a car (or able to use mathematics)?
Zwaagstra's solution to improving math education is to move "back to basics," which is as unoriginal an idea as I've heard. It is arrogant of Zwaagstra to assume that this approach hasn't been tried before. Perhaps he could instead address the issue of elementary school teachers often lacking support and training in how to teach math? Zwaagstra points out (correctly) that having mastered one computation, students are then better able to learn another computation, but this leaves students learning a series of computations, and not spending any time actually using them.
JUMP math is mentioned in Zwaagstra's article as an antidote to the problem, but he doesn't talk about the issue of the associated training, or the lack of diverse assessment used in the JUMP math system. I think that the training manuals that go along with the JUMP math curriculum, for example, actually address the misconceptions of the people teaching the math (mostly elementary school teachers) rather than itself being a significantly better system. As one educator has told me, JUMP math is pretty useless without the training materials for teachers.
Just as someone who does not practise the piano will never learn to play well, someone who does not practise basic math skills will never become fluent in math.
Similarly, someone who has not had time to play with a piano, to improvise, and to perform music for others will never develop an appreciation for the instrument. Zwaagstra is suggesting that we should discard the extra parts of math education, like problem solving, and focus on computations, which is the musical equivalent of only learning scales, and never getting to perform music.
No one would stand for that in music education, so why should we accept it in math education?
People should have the freedom to express an opinion on what they feel is a problem. To do so otherwise is to be undemocratic. Opinions can draw attention to issues in our society that need to be addressed. However, such opinions should be clearly labelled as such, and not called studies. Peer reviewed research (which shows that the techniques advocated by the NCTM and WNCP are effective) carries with it a heavier weight of authority, and is a more reliable instrument with which to craft public policy. Instead of relying on uninformed opinions of people outside of the field of mathematics education to determine education policy, we should look at what the research says works for improving instruction. Our goal should be to replicate practices which work, and to extinguish practices which do not.
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How can educators help students improve in math? How effective is the "new" math? Share your tips in the Comments section below.
Today's students are more tech savvy than ever as they are immersed in the world of social media, "infotainment" and spectacle. As a result, many students feel they have to "power down" to succeed in a classroom environment that offers fewer options for learning than are available in the lives they live outside the classroom. In the information age, educators are faced with the pressure to stay current and come up with innovative ways to excite their students about learning. By integrating technology into the classroom, educators can make learning more engaging and present curriculum in a way that resembles the type of media that students are accustomed to consuming.
As an assistant professor of education at Brock University, I believe that relevant types of technology like 3LCD projectors can be integrated into the classroom experience to enhance learning outcomes. Incorporating technology in the classroom can be as simple as creating an agenda in PowerPoint, and showing or emailing it to the entire class. It makes the agenda a little more interactive, ensures every student is on the same page and also saves paper. Many students respond better when they are shown something visual, and they can actually see how it applies to what they're learning in class. Whether it's Skyping with others around the world or viewing a video on YouTube, the entire classroom gets to participate and see the practical component of what they're learning.
Today's students are leaders in the use of technology and as educators, we need to understand and adapt to their evolving learning styles. By using technology tools in lessons and projects that engage students, educators can increase classroom participation while students develop better critical-thinking and comprehension skills. I believe that projectors are a key component for 21st-century teachers – they help students retain information, cater to a variety of learning styles and create an authentic learning experience. In challenging economic conditions where schools face tight budgets, it is critical to allocate resources in ways that would make the greatest impact. Technology is the best investment for the future of our youths in a highly connected world.
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How are you using technology to integrate it in class? Do you have advice on how students can balance and integrate technology in their studies? Share your tips, resources and views in the Comments section below.
Dr. Maria Montessori is one of the most famous women in the world and yet a key part of her life is all but unknown. Dr. Robert Gardner, working with colleagues at Clanmore Montessori in Oakville, Ont., took a new look at a time in Maria Montessori's life that is glossed over, even by her most noted biographers. "Not to know this story is to have an incomplete understanding of one of history's most remarkable women," says Cathy Sustronk, one of the founders of Clanmore.
When Maria Montessori was 30 (in 1900) her father presented her with a book filled with 200 articles he had clipped from the national and international press, all of which wrote glowingly about his unusually talented daughter. She was known as the "beautiful scholar," and in an age when women were blocked from most professions and careers she had – against all odds – become the first woman physician in Italy. She had been interviewed by Queen Victoria and had represented her country at major international conferences. She was elegant, poised and – perhaps – just a bit vain. She was at the height of her fame, and it seemed that she could achieve anything. At this heady moment she was appointed the co-director for a school in Rome. It was an unprecedented appointment for a woman in that very conservative time. Her partner was another young physician, Giuseppe Ferruccio Montesano. Italian sources suggest that he was not in robust good health, but he was elegantly handsome. He came from the south of Italy and in his family, while the sons all entered the professions, the daughters were consigned to "womanly tasks" such as lace-making and the study of music.
He and Montessori fell in love and she became pregnant. At that time, especially in Italy, to have a child out of wedlock would have been disastrous to anyone. Montessori was facing the ignominy of being a scarlet woman. Montesano's mother, by all accounts a very severe dowager, refused to consider marriage. Montesano was desperate. Montessori, perhaps for the first time in a charmed life, was bewildered. Montesano had a solution. He would give the child his name, but the baby would have to be sent away to a wet nurse as soon as it was born. There was, however, no possibility of marriage. His mother, a woman who traced her ancestry to the House of Aragon, the rulers of southern Italy, was adamant.
Montessori was devastated. Montesano, in trying to calm her, promised that he would never marry anyone else. She was the only one for him. Montessori made the same vow. In a sense, they would have a spiritual union which made the disastrous consequences of their affair less dismal.
A Crisis, Then Remarkable Recovery
A year later Montesano betrayed her and married another woman. Montessori was in complete crisis. She had sent her baby son away to live with strangers and she could not openly acknowledge the child's relationship to her. In the next decade she would see the child occasionally, but she never indicated to the boy that she was his mother. She was a tortured soul.
In this moment of absolute defeat she did something remarkable. Instead of crumbling under the strain, she went into the seclusion of a convent to meditate. Before the crisis she was likely somewhat egotistical and her life had been filled with triumph after triumph. As a woman of her time, and as an Italian, she was – of course – a Roman Catholic. But her faith was the faith of a scientist and a scholar, skeptical and refined.
Now this proud and brilliant woman was reduced to a state of desperation. However, during the days and weeks in seclusion something incredible happened. In fact, she underwent a complete psychological transformation and she emerged from this period of self-examination with a set of goals which seem unbelievable to the modern observer. She appeared determined to totally reinvent herself. She moved forward with a resolution that is at once baffling and inspiring.
Although she was the first female medical doctor in the history of Italy, she decided to leave the practice of medicine forever. Abruptly, and without explanation, she resigned her prestigious post as co-director of an institute for developmentally challenged children. Then she enrolled at the University of Rome to master totally new areas of study. She took courses in anthropology, educational philosophy, and experimental psychology. At the same time, she made another momentous decision that changed the course of education and teaching forever. Up to this time she had been preoccupied with children who were in some ways in the language of the times, "feeble minded." Now she decided to focus all of her energies on improving pedagogy for the normal child. With that decision, Dr. Maria Montessori proceeded to revolutionize our thoughts about infancy and the incredible capacities of children from the very moment of birth.
In a strange way, if there had been no Dr. Montesano there would have been no Maria Montessori. He, inadvertently, became the catalyst for a monumental emotional crisis that led Montessori, just into her thirties, to challenge every misconception about the capacities and needs of the very young.
A Son's Influence on the Nobel Peace Prize Winner
Dr. Montesano never recognized his child, Mario Montessori, as his own. Indeed, even Maria Montessori, on her many tours where Mario was her faithful interpreter, always introduced him as either her nephew or her adopted son. It was when she was close to death that she accepted him publicly and in her will she identified him as "Il figlio mio" – my son.
Montesano, though, was never more than a footnote to history while Maria Montessori was nominated for the Nobel Peace prize three times. Among scores of honours, she was the recipient of the French Legion of Honour decoration, and she received honourary doctorates from some of the greatest universities in the world.
It was a terrible crisis that forged her untiring will to help children everywhere to reach their true potential. Without that searing ordeal her name, like that of the man who betrayed her, may have been forgotten.
It might be thought that the crisis that shaped her thinking might somehow have diminished her. Even generous modern readers may wonder why she abandoned her child for almost 15 years. The fact is, this terrible tragedy steeled her to recreate herself and caused her to focus her incredible talents in an effort to somehow make amends for the tragic loss of her son's presence during his formative years.
One day, when he was 15, the young Mario Montessori noticed an elegant woman watching him with great interest. Something told him that this was his mother. He approached her and they were reunited. For the rest of his life, although he subsequently married, he was her constant companion and confidant. They were inseparable and together they created an approach to education that exists to this day.
The remarkable ending to this story is that modern research continues to validate her findings. In a recent study by Dr. Angeline Lillard, titled The Science Behind the Genius, Dr. Lillard collects scores of modern research findings which support Dr. Montessori's earliest views on educating the child. Increasingly Dr. Montessori's observations are being employed in secondary schools with stunning results. In fact, her ideas could well be employed in the university system where students are often isolated in an arid world of abstract lectures.
Maria Montessori, in some academic settings, is ignored precisely because she had such a trenchant insight into the failings of so much of what we call education. More than half a century after her death her influence is still making itself felt, still creating a sense of discomfort amongst some professional educators, and still pointing towards a more humane form of transmitting information to young children and adolescents.
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These successful strategies can support anyone who work with or have being diagnosed as learning differently. Learn more and register today to attend.
In IT for Every Classroom, a weekly column on Dialogue Online, Paul Keery shares his practical tech advice for non-IT teachers.
Photo from The York School
Last week, we considered the factors involved in deciding what type of IT project to incorporate into your curriculum. This time around, let's look at examples of projects that would be appropriate for students in junior, intermediate and senior grades.
I Remembrance Day Podcasts
Believe it or not, Remembrance Day (Nov. 11) is fast approaching. Schools have revived and restored Remembrance Day commemorations in the last decade to recognize Canadians' service in conflicts around the world since the First World War. Students at all grades can create their own commemorative enhanced podcasts to recognize the contributions of family members (parents or grandparents) or of individual combatants. These can be played at school assemblies or in class on Nov. 11.
For the Memory Project link, select WWI under Conflict, and it will take you to a list of veterans who have provided memories of the war. Find at least one other resource online; there are several good ones.
Assignment: Imagine that you have survived the battle of Vimy Ridge, Canada's defining battle of the First World War. Write a short, one-minute Podcast about your experiences in the battle:
in the trenches; what was life like every day as a soldier living in the trenches?
describe the actions of one of four Canadians decorated at Vimy Ridge: Provate William Milne, Lance-Sergeant Ellis Sifton, Captain Thain MacDowell, or Private John Pattison.
Your podcast will be an enhanced one; it must include photographs and images of the battle (actual images of the soldiers would be wonderful, but may be impossible to find) as well as appropriate sound effects and music.
Procedure: Submit your script for evaluation before you record your podcast.
Evaluation: The script will be worth 35 per cent of the mark; the completed podcast will be worth 65 per cent of the mark.
This assignment could easily be modified to include the Second World War, Korean War, Canadian Peacekeeping Missions from the 1950s through the 1990s, the Gulf War, and the Afghanistan conflict.
Students would be expected to write a proper script (as described in an earlier blog, Scriptwriting for Podcasts), and submit it as part of their completed assignment.
II Dramatic Radio Show
Students would be expected to write and record a radio play.
Assignment: Produce a Drama or Comedy Program.
Time: You have four classes to write and produce a five-minute drama or comedy program. This can be done in groups of three.
Procedure You may use a script you write, a script of a student-written one-act play, or a script from an Old-Time Radio show. You must have actors, sounds and sound effects you record yourself. You must have music. Choose or write a drama that requires this amount of audio and complexity (not a one person introspective show). If what you choose lasts longer than five minutes, you must edit or clearly indicate that this is the first in a serial; you do not have to complete the entire script. Each student in the group must play a role in the play.
Submit your script before recording the play.
You will have four class periods to prepare the program; one of these will be used for editing your final show.
Recording will take place in the third class period. You may have to convert sound files to mp3s at home to be sure that you are ready to upload them in class.
The final edited version will be completed and due during the fourth class period.
Evaluation: The script will be worth 35 per cent of the mark; the completed Podcast will be worth 65 per cent of the mark. Your feature will be presented in class.
This project would be suitable for language arts of English classes, as well as high school drama and media classes.
The new school year will be an exciting time for Civics classes throughout Canada as provincial and territorial elections ramp up. Already, is gathering and distributing materials to make this election one of the most memorable and active in the K-12 classrooms around the province. Last year, there was a municipal and federal election to keep Greenwood College School's students reading, listening and advocating for their politics, and now this year's classes will carry on that legacy of involvement and political action. (Click here for the article on their participation in the federal election.)
Teachers and students can take advantage of a great learning opportunity during elections. CHRIS BOLIN/OUR KIDS MEDIA
At our school, students' involvement in the election is an authentic and important way for them to learn about why getting active early in politics is so important. Moving the discussions away from the nitty-gritty of political procedure and precedents and into concrete connections to their own lives will help to raise politically active citizens. We plan on calling in to radio shows, writing letters to the editor, interviewing local candidates, and holding a mock election through Student Vote. In these ways, we will be getting students politically interested, active and engaged in the hopes that when the next election comes along, they will be an informed voter, and cast their ballot.
Jack Layton's address to the youth of the country in his letter to Canadians spoke directly to the power and importance of political engagement in this demographic. Here is a link to Matt Galloway's interview with me on Metro Morning discussing his letter.
Layton's letter is being met with a myriad of resources for teachers:
is the government of Canada's website to explain and explore all about elections
gives teachers lesson plans and hooks to get students asking questions about why politics is important to them
is a place for students to read, explore and contribute to political discussions going on around the world about political issues
is a vital resource for any teacher looking to hold an election in their class or school. What makes student vote unique is that they tally the votes from all schools involved and publish the data the day after the election. This shows the city, country, and now province where students, if they had the vote, would put their ballot.
As a politics and history teacher, I hope that teachers and students take advantage of this great learning experience, and get involved with the election. The issues are important, personal and directly impact the future of this province. Good luck!
* * * * *
Do you have other tips and resources for teachers to help students get engaged in politics? Share your thoughts in the Comments section below.
In IT for Every Classroom, a weekly column on Dialogue Online, Paul Keery shares his practical tech advice for non-IT teachers.
Photo from The York School
Choosing a subject for an IT project can be challenging. There are a number of important factors to consider when deciding where and how to add a podcast project to your curriculum.
What Topics Fit Into the Course?
Every course will present different opportunities for IT integration. English and Language Arts classes could easily do book reports or dramatizations of scenes from books or plays. History and Social Sciences classes would be able to do biographies of influential people or could examine controversial issues in those subjects. ESL and Second Language classes can use IT to practice speaking and pronunciation, or to do readings from second language books. Mathematics and Science classes could create reports on experiments or biographical reports about famous mathematicians or scientists.
However, be sure to choose a topic that reflects your students' skills at using IT. Early projects in which students are learning to use IT should be kept relatively simple. Once they have become skilled users of particular hardware or software, their IT projects can become more complex.
What Resources Are Available for Students to Use?
The audio and video content of students' projects will also be affected (perhaps limited) by the resources that are available for them to add to their IT project, be it a podcast or a video project.
[a] What audio files are available to be included in the project? If your History students are assigned a podcast about a modern historical figure, do you want your students to include audio clips of the person speaking? If so, are these legally available?
[b] What still images and video files are available to be included in the project? If your Science students are doing a project about human space flight, what images can they legally download? Are public domain videos available? If so, how long will it take to download them – and will students be able to download them at school?
Before creating a project, you must be sure that resources are readily available and can legally be used. See the blog post Recording the Autobiographical Podcast for a list of online sources that students can use to find such resources to use in their project.
What Can Students Reasonably Be Expected to Produce?
There is another possibility: Students can create audio and video files themselves. This is entirely possible if students are filming their own classroom work. For example, if Science students are creating a video project analyzing a classroom experiment, they could certainly film their own experiment and include it in the project. Care will have to be taken when filming the experiment, but it is certainly feasible.
Similarly, Drama students could be assigned to create a video project analyzing their class play – if they are already doing a major play as part of the course and they have had to design and create costumes and sets. However, it may not be feasible to film a scene from a play as part of an English or Language Arts class: Where will the costumes and sets come from (especially if it is a Shakespeare play)? You can either set the play in a modern setting, or decide to do a podcast instead.
The Final Choice
It may seem, after looking at all of these factors, that it's almost impossible to design and implement an effective IT project, but it can be done.
In IT for Every Classroom, a weekly column on Dialogue Online, Paul Keery shares his practical tech advice for non-IT teachers.
Photo from The York School
When you're starting out with IT, it's hard to resist getting carried away with the wonder of it all. There are so many possibilities. Podcasts. Enhanced visual podcasts. Movies. The trouble with getting caught up in the wonder of it all is that it is so easy to try to do too much in a first project or the only IT project for the school year (if you only have access to computers in an lab setting for a few weeks). Teachers want to get a bit of everything into the project. But trying to do too much will result in a lot of frustration for students and teachers as well as a poor learning experience. Think ahead and plan carefully must be your guide.
Project Ideas – When To Do IT?
IT is time intensive. IT projects will often take half as much time as you have scheduled, especially if you're just getting into IT integration. If your students have access to computers on a regular basis, avoid busy times of the year when other events are going on and schedule your IT project at a time when your students can focus on their IT work. Make sure that there is time available if the project runs long.
However, if your access to a lab is pre-determined, you have no choice; you'll have to make the best of it. Keep the project short and simple to ensure that the students will finish on time.
Project Ideas – How To Organize Them
IT projects can best be used as summative projects (though it is very possible to do formative evaluation while the project is going on). Students should learn basic knowledge about the topic of the IT project first. Then use the IT project to have students do more research to add more specific knowledge about a particular area of the topic, as well as apply that knowledge to a problem related to the topic.
For example, suppose students are learning about the War of 1812 as part of the upcoming bicentennial celebrations. In class, start off with a basic introduction to the war: Who was fighting, the major battles, the role of native peoples in the war, how civilians were affected by the war, and the outcome (who won?).
After that is finished, students could be assigned more specific topics that would allow them to study an aspect of the War of 1812 in more detail: Why did the war start? Who were Isaac Brock, Laura Secord and Tecumseh, and what role did they play in the war? What happened at Queenston Heights (or any other battle)? What happened to York (now Toronto) during the war? Students could then analyze what happened and explain why it happened, or why an important person did or did not achieve their goals.
Students could easily create a one or two-minute podcast or enhanced podcast about one of these topics. After the students present their podcasts to the class, all the students in the class could then be given a quiz about each podcast (or about all the podcasts).
Project Ideas – What To Do?
It's best that the IT project should form all or almost all of the instruction for a unit of work, given the research, writing, recording and presentation time the students will need. Try to choose a unit that lends itself to this approach.
In Language Arts and Social Studies, a project could be built around a novel, short story, or a significant historical or geographical event; see the previous section for an example of such a project. In Art or Music, students could create an enhanced podcast about an artist or musician, including a biography and analysis of examples of their work. In Math and Science, students could create an enhanced podcast about a mathematician or scientist, including a biography and analysis of examples of their work; or they could examine and interpret a mathematical or scientific principle.
Once students have finished their work, make sure to keep copies of their projects to show their parents, or to show future classes how IT projects can be done – and how students are combining traditional and modern literacy skills.
Disclaimer: Information presented on this page may be paid advertising provided by the [advertisers/schools] and is not warranted or guaranteed by ourkidsmedia.com or its associated websites.
See Terms and Conditions. |
Mathematics enrichment program
The Mathematics Enrichment Program(PDF*350KB) has been offered by the University of Southern Queensland since 2007 and is a structured program designed to improve mathematical problem solving skills in gifted high-school students. Within Toowoomba and surrounding districts, a number of students display aptitude for mathematics beyond what is offered in the standard high school curriculum. Such students could potentially benefit from exposure to more problem solving techniques not traditionally offered.
Aims of the program
Interesting questions in selected topics will be tackled in lively sessions, to build students' range of techniques for solving problems. The aims of the program include:
to help students perform at a high level in national mathematics competitions particularly the Australian Mathematics Competition;
to encourage further study in mathematics;
to enhance satisfaction for students who quickly master school level concepts.
Who can attend?
The program is aimed to suit the mathematical ability of Year 9 and 10 students.
Interested students and schools in remote locations should contact Assoc Prof Ron Addie to discuss alternative methods of offering the program.
How do I apply?
Students will need to be registered through their Mathematics Teacher at school. Teachers will email names and contact details to Debbie White via [email protected].
Cost
There is no cost to attend the program.
Time
The program runs from 4.00 - 6.00 pm on Thursday afternoon at USQ. Refreshments are provided.
Please note that the proposed topics for discussion may not necessarily be offered on the date listed.
Presenters
Presenters will include Ron Addie from the Department of Mathematics & Computing at USQ; Ashley Plank past member of the Department of Mathematics & Computing who now works as a consultant in statistics for medical research; Tim Dalby from Open Access College at USQ; Neville de Mestre leader in research into mathematics in sport; Peter Galbraith Honorary Professor at University of Queensland; Stephen Broderick, Head of Mathematics at St Ursula's College and President of the Toowoomba Maths Teachers Association and Bob Nelder, Head of Mathematics at Mt Lofty State High School and past president of TMTA.
We look forward to creating a lively and fun Mathematics Enrichment program.
*This file is in Portable Document Format (PDF) which requires the use of Adobe Acrobat Reader. A free copy of Acrobat Reader may be obtained from Adobe . Users who are unable to access information in PDF should contact [email protected] obtain this information in an alternative format. |
Elementary Algebra is designed to provide students with the algebra background needed for further college-level mathematics courses. The unifying theme of this text is the development of the skills necessary for solving equations and ineq
Discrete Math Its Applcs
Reviewed by a reader
Reviewed by a reader
Algebra and Trigonometry
Editorial review
Written for a one- or two-semester course at the freshman/sophomore level, the text covers the principles of both college algebra and trigonometry. Trigonometry is first introduced with a right triangle approach, followed by circular func
Matrix Theory With Applications (International Series in Pure and Applied Mathematics)
Editorial review
TLAB as a computational tool, with exercises for computer solution.
Reviewed by Jaewoo, Choi, (Seoul, Korea)
I'm a student in EE dep of Seoul natl univ in korea, and have taken a class using this book, named 'Engineering mathematics 3' which deals linear algebra. The author introduced a little bit practical topics, rather than purely mathematic |
Description: The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering, as well as students headed for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. Math 115 presents the concepts of calculus from four points of view: geometric, numerical, algebraic, and verbal. Students develop their reading, writing, and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and an introduction to integration.
Text: Calculus by Hughes-Hallett, Gleason, et al, 5th Edition
Calculator: TI-84 Graphing Calculator or equivalent. If you have another model, you will be responsible for knowing how to operate the calculator on your own. No devices with a qwerty keyboard are allowed on exams.
[Note: The above sections may be modified during the semester--particularly with respect to the actual sections covered on a particular exam. Also: all math exams are cumulative! ]
Exam Dates:
First Uniform Exam:
Tuesday, October 13; 6 pm - 7:30 pm
Second Uniform Exam:
Tuesday, November 24 **; 6 pm - 7:30 pm
Uniform Final Exam:
Thursday, December 17; 10:30 am - 12:30 pm
Uniform exam dates are absolutely firm. All students enrolled must plan to take exams at their scheduled times. Travel plans willnot be considered an excuse to take an examination on a different date.
**Please note now that the second exam is during Thanksgiving week.
On all exams, standard graphing calculators are allowed. Problems will be
written with
the expectation that these calculators will be used. Devices with a qwerty keyboard are not allowed. Students are allowed both sides of one 3'' by 5''
card for
each exam.
Grading Policy: All sections of Math 115 use the same grading
guidelines to
standardize the evaluation
process. The three uniform exams are worth 25%, 30%, and 40% of the
"exam component" of each student's grade. The additional 5% of the exam component will be assigned to the web homework, beginning with Chapter 2. The final course grade
will be primarily determined by the exam component grade for each student. However, for some students, the final course grade may be modified by the section component grade or the gateway exam.
See the Student Guide
for a complete explanation.
NOTE: The inclusion of web homework as a part of the exam component grade is not reflected in the Student Guide. Other than that, the grading policy in the Student Guide is correct. You are responsible for reading and understanding the grading policy.
Gateway Exams:
There will be one gateway exam. The open dates for the gateway will be between the first and second uniform exams and will be announced later in the semester. The 115 gateway exam covers differentiation rules. Students will lose a whole letter grade (on their grade for the
course) for failing to pass the gateway during the open period. Proctored gateways are administered in the gateway lab (B069 EH) and may be taken no more than twice per day. Students may practice the gateway from any computer at any time (and many times) during the open dates for the exam. |
"The major
cause of anxiety over mathematics is the promotion of learning by memorization.
People often wonder why the anxiety is attached to mathematics instead of English,
Social Science, etc. and the answer is a combination of two facts: First - mathematics
instruction frequently encourages (forces) memorization; and Second - memorization
without understanding is a guaranteed route to failure in mathematics, but may
seem effective with other subjects. Students can be more aware of their learning
problems and students can begin taking control of those situations where anxiety
is created. This software aims its information at the student. |
Systematic Mathematics
Systematic Mathematics is a video-based home school math curriculum that explains the system of mathematics. The core of the curriculum is the lesson DVDs, alongside which there are materials that you need to print yourself from the accompanying CD.
Price: about $128-$138 per year
Reviews of Systematic Mathematics
Your situation:
Our son just returned to homeschooling, after one year back in the public school system. The large class size and fast paced introduction of math concepts were overwhelming and he was falling behind. More importantly, he felt frustrated and inadequate as a math student.
Why you liked/didn't like the book:
We chose Systematic Mathematics because it taught the why of doing math, not just rushing through concepts and hoping they would stick. The DVD is good because my son is able to watch Mr. Ziegler do the math problem(s) and is able to stop, or backup if needed. The worksheets are on CD, so you can print as many as needed. I recommend this curriculum to anyone who has a child who is discouraged with math, at any level. Our son has actually begun to say things like, "Math is fun" or "I like doing math". When he says that I know he will remember what he's been taught
Michele Tubbs
Review left February 9, 2012
Time: 1 semester
Your situation: I've been home educating for over 20 years, and currently educating my 6th grader. I've tried various other math curricula, but this is the only one that he seems to be really understanding.
Why you liked/didn't like the book:
Like:
*Covers things systematically--'old school' before all the 'modern' math. I would equate it with the way phonics used to be taught and built upon.
*Taught by a former Public School teacher in the days before modern math, and he wrote this curriculum in frustration over what he saw and didn't like in modern math textbooks.
*Short lessons
*Can be used over and over by more than one student in the family, so is cost effective
*Teacher isn't drab and boring
Dislike:
*Would like to see some of the answers completely worked out in the answer key--just for speed on my part as the teacher checking the work.
*DVD's are pretty basic (not professional), but this doesn't really bother us too much
*Would like to see the worksheets offered already printed out in workbook form--right now you print off the worksheets on the computer as a pdf file.
Any other helpful hints:
This has been great for us so far, and we have used a lot of different math programs through the years. This one fits my students needs great so far!
Sandy
Review left January 11, 2012
Time: 2 years
Your situation:
I had trouble doing math and I was falling behind! I was using AOP SOS Math, Teaching Textbooks, tried using Math Mammoth but I can't say that they worked for me.
Why you liked/didn't like the book:
There is NO textbook required and you can print as many worksheets as you want. Just watch the DVD and print out the worksheet or test. Mr. Ziegler (the teacher) is better at explaining things than many teachers. The price is very good for people with not much money. I now understand math much more than before, not just remembering what to do.
Any other helpful hints:
:)
Matthew Kwan
Review left June 19, 2011
Time: 2 years
My son was dropping further and further behind in math. He was close to 3 years behind. We used Abeka math and Saxon math and although I don't see any problems with those curricula, he was not able to grasp the mathematic principles and complete the work. His math skills (math facts) were fine, he just couldn't understand the processes especially for word problems.
Why you liked/didn't like the book:
After 1 year of intense "catch up" in math we have come to within 1 year of where he should be and with all A's and B's on exams. He really appreciates being able to see someone work the problems and being able to review the processes has really helped him. Mr. Ziegler (the teacher) makes everything easy to understand and teaches the why's and not just the how's to understanding and mastering math.
Any other helpful hints:
Another great thing about this curriculum is that I can use it with all of my children. The worksheets are all on a cd rom and can be printed as many times as you need it to be.
Scot Dyess Review left September 21, 2010
Grade: Algebra Time: 2 years
Your situation:
Algebra (beyond the very basics) was a painful process for my son and I. To this point, he had been a great math student. By the end of Algebra 2 he had given up. We were using Video Text at the time, after having used Key To. I knew I couldn't take the same approach with my younger daughter, and when I read a review for Systematic Mathematics, decided to give it a try.
Why you liked/didn't like the book:
This is a DVD curriculum with cds for printing off worksheets and tests, as needed. In comparison, it's fairly inexpensive. It is truly systematic in approach, never giving the student too much information at once. We were able to go through lessons, start to finish, in about 30 minutes. No tears, no frustration.
The writer is a former public school math teacher who realized new methods weren't getting the job done. This was the answer for our family.
You can purchase individual modules, instead of buying the whole curriculum at once. On a couple of occasions I had questions. Very promptly, I received either an email reply or a personal phone call. |
Jobs
Further Mathematics AS
Introduction to course
Further Mathematics is a second AS (or A2) in Mathematics which you could consider if you enjoy Mathematics a lot and are good at it.
You must study A Level Mathematics as well to be on this course.
Course Details
In the first year you will simply study more topics than students doing Maths as a single subject; it is not significantly harder. It means that almost 50% of your timetable will be spent doing Mathematics.
If you take Further Mathematics A Level then you will need to complete twelve modules altogether (six for Mathematics A Level and six for Further Mathematics).
If you take Further Mathematics AS then you will need to complete nine modules (six for Mathematics A Level and three for Further Mathematics AS).
In Maths & Further Maths AS you will study C1, C2, M1, S1, FP1, and D1.
At present we offer AS Further Maths to both first and second year students.
Entry Requirements
In addition to the general entry requirements, you are also required to have the following:
Grade A or A* at GCSE Maths.
Additional Maths FSMQ level 3 (at any grade) would be a great advantage to those studying this course, but is not necessary.
Where the course lead
Maths and Further Maths at A2 will put you in an excellent position if you wish to study mathematics or a subject with a very high mathematical content at university.
An increasing number of university mathematics courses ask for Further Maths AS at least.
This course combines well with
Students doing A Level Further Maths study a wide variety of other subjects - the most popular being Economics and Physics. However, students studying Humanities and the Social Sciences are also well represented in Further Maths classes.
This course is not suitable with
Use of Maths or Statistics AS/A2
Course Assessment
By 1.5 hr modular exams in either January or June
Careers
With Maths and Further Maths at A Level an enormous number of career choices are available to you from Business to Engineering to Finance to Teaching. You will be in demand!
Links
mathscareers.org (an excellent site for researching careers in maths and lots of exciting examples of how maths can be used in the real world) |
Mathematics - Algebra 2
Intended Learning Outcomes
The main intent of mathematics instruction at the secondary level is for students to develop mathematical proficiency that will enable them to efficiently use mathematics to make sense of and improve the world around them.
The Intended Learning Outcomes (ILOs) describe the skills and attitudes students should acquire as a result of successful mathematics instruction. They are an essential part of the Mathematics Core Curriculum and provide teachers with a standard for student learning in mathematics.
The ILOs for mathematics at the secondary level are:
Develop positive attitudes toward mathematics, including the confidence, creativity, enjoyment, and perseverance that come from achievement.
Course Description
A primary goal of Algebra 2 is for students to conceptualize, analyze, and identify relationships among functions. Students will develop proficiency in analyzing and solving quadratic functions using complex numbers. Students will investigate and make conjectures about absolute value, radical, exponential, logarithmic and sine and cosine functions algebraically, numerically, and graphically, with and without technology. Students Students will use technology such as graphing calculators. Students will analyze situations verbally, numerically, graphically, and symbolically. Students will apply mathematical skills and make meaningful connections to life's experiences |
id: 06145589
dt: j
an: 2013b.00649
au: Friedlander, Alex; Arcavi, Abraham
ti: Practicing algebraic skills: a conceptual approach.
so: Math. Teach. (Reston) 105, No. 8, 608-614 (2012).
py: 2012
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: H30 D30
ut: thinking skills; teaching methods; algebra; classrooms; mathematics
activities; equations; mathematical formulas; algebraic skills
ci:
li:
ab: Summary: Traditionally, a considerable part of teaching and learning
algebra has focused on routine practice and the application of rules,
procedures, and techniques. Although today's computerized
environments may have decreased the need to master algebraic skills,
procedural competence is still a central component in any mathematical
activity. However, technological tools have shifted the emphasis from
performing operations on complex algebraic expressions to understanding
their role and meaning. Consequently, learning rules and procedures
should be linked to a deeper understanding of their meaning and to a
flexible choice of solution methods. The authors write for mathematics
teachers who wish to add a conceptual dimension to the practice of
algebraic procedures. Their approach is based on the potential
advantages of the traditional approach. Short exercises are readily
accessible to students and are easy to implement in regular classrooms,
and the focus is on learning one specific skill at a time. The
activities they propose here offer opportunities for more effective
learning of algebra. They describe an approach in which rules,
procedures, algorithms, sense making, meaningful reading, and the
creation of algebraic expressions are thoroughly integrated into the
learning process. These practice-oriented activities require the
adoption of some additional higher-order thinking skills, such as
developing alternative solutions, evaluating the effectiveness of
approaches, participating in class discussions, and reflecting on
learned procedures and solution methods. The goal is to provide
teachers with an alternative to the traditional practice sections of a
beginning algebra course without changing the basic format of short
exercise sets. (ERIC)
rv: |
Course in Enumeration
9783540390329
ISBN:
3540390324
Pub Date: 2007 Publisher: Springer
Summary: Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from the basic notions to a variety of topics, ranging from algebra to statistical physics. Its aim is to introduce the student to a fascinating field, and to be a source of information for the professional mathematician who wants to learn more ...about the subject. The book is organized in three parts: Basics, Methods, and Topics. There are 666 exercises, and as a special feature every chapter ends with a highlight, discussing a particularly beautiful or famous result |
Here are 42 entertaining math activities that allow students to practice addition, subtraction, multiplication, division and coordinate geometry. Each game begins with a discussion of its objective, followed by directions for playing and
I am a musician, a classical guitarist,and have always had an interest in science. I have recently become obsessed with physics, but have always been weak in math. This book, (and author), obviously had the pedagogical acumen to see this
The Sneaky Square and Other Math Activities for Kids
Editorial review
This book is jam-packed with 139 classroom-tested, entertaining math activities that allow kids in grades 3-8 to build their capacity for critical thinking, problem-solving, and accurate estimation. An equally valuable resource for teache
The Complete Book of Business Math: Every Manager's Guide to Analyzing Facts and Figures for Smart Business De
Editorial review
Reviewed by a reader
Excellent book with practical examples very well organized. You really don't need to be a math expert to use it.
Schaum's Outline of College Algebra
Editorial review
Reviewed by Osher Doctorow, Ph.D., (Culver City, CA United States)
2 lines on back for rapid shuffling and reading. I'll have more to say about this in other reviews.
Reviewed by James Cunningham, (Lexington, KY United States)
n mind when going through the Conic Sections chapter, where - for some reason - it editing seems to have been especially bad.
Reviewed by "llh18", (Jacksonville, FL USA)
I was hoping that Schaum's Outline of College Algebra would break things down into basic explanations, but instead, I remained lost.
Reviewed by Michael Henderson, (Durham, NC USA)
This book offers a dry recitation of math topics, but it is a handy resource to have.
Reviewed by "jayden_solutions", (Long Island, NY)
Hello,I wanted a book which would give a solid and easy to read review on college algebra. It's been many years since I've studied any algebra and after reading the reviews on this site, I thought I had found a nice tool. I was wrong, and
Schaum's Outline of Intermediate Algebra
Editorial review
Reviewed by Stephen, (Tucson, Arizona USA)
Best math-problem book I have come accross. The book does all different types of problems, and works them out step by step. Highly reccomended.
Reviewed by "llh18", (Jacksonville, FL USA)
This book was a great study guide to use when I took Intermediate Algebra last term. I used it a lot with homework assignments because it broke down problems into simpler terms. If you are looking for a good stusy guide, I reccommend this
Reviewed by a reader
As a college math instructor, I bought this book to see if would be useful for students who struggle with math. I was completely impressed with the layout of this study guide! The Intermediate Algebra text by Schaum's explains every conce
Electricity and Electronics Technology Math Workbook
Reviewed by paul bufkin "paulbufkin", (wheaton, il USA)
The title indicates a workbook with math problems related to electronics or electricity but the book does not contain any. The only electronics related information is how to read an analog Multimeter when measuring voltage, resistance and
Elementary Algebra
Editorial review
The focus of this series by Hutchison and Hoelzle is to make students better problem solvers. To accomplish this goal, the authors emphasize conceptual understanding. They ask students to think critically to explore and explain concepts i
Beginning Algebra Form B
Editorial review
This book introduces students to equations and graphing. It is derived from another mid-level text, "Beginning Algebra", covering the same material, in the same order, but with new exercises. The text stresses pattern recognition through
Beginning Algebra
Editorial review
a tutorial program are also available. Designed for a one-semester beginning or introductory algebra course, this successful worktext is appropriate for lecture, learning center, laboratory, or self-paced courses.
Reviewed by a reader
The complete revision of Chapter 5, Factoring Polynomials greatly enhances the students ability to understand factoring by grouping. It is a far easier process than the trial and error in previous editions. The graphics are also greatly i
Introduction To Linear Algebra
Editorial review
This text is designed for students studying subjects such as Maths, Computer Science, Physics, Quantitative Analysis and Engineering.
Reviewed by david, (iran)
this is an elementry book about linear algebra and a reviewer who receive a first coarse in linear algebra will find it an excellent book but it is an elementry book!
Macaroni Math
Editorial review
Algebra for the Utterly Confused (Utterly Confused Series)
Editorial review
Reviewed by william borg, (chicago, IL United States)
.... and I have little to compare this book to. Relatively good, tho not perfect. On page 147, they show how to derive the lowest common denominator, go thru the steps, but appear to skip one detail-which isnt at all obvious. I was able t
Mastering Math for The Building Trades
Editorial review
How to Solve Word Problems in Mathematics (How to Solve Word Problems (McGraw-Hill))
Editorial review
Reviewed by T. Perez
In the first chapter, the first set of practice word problems numbers 2 and 4 are just WRONG. I took the book back to the bookstore at that point, and don't have time to count the errors in the book, but wish I did. This is a dangerous bo
Get Ready! For Standardized Tests : Math Grade 2
Editorial review
Get Ready! For Standardized Tests : Math Grade 3
Editorial review
Get Ready! For Standardized Tests : Math Grade 4
Editorial review
How To Solve Math Word Problems On Standardized Tests
Editorial review
Teach Yourself Algebra for Electronic Circuits
Editorial review
Easy Outline of Elementary Algebra
Editorial review
Bob Miller's Basic Math and Pre-Algebra for the Clueless
Editorial review
Reviewed by a reader, (Portland, OR United States)
s in deep trouble. Fortunately, I'm not as xenophobic as the author, and would be happy to use a math book from another country if it's written better than this one.
Reviewed by a reader
do his students, so the reader should do super well. Excuse me, but if algebra came easily to me I wouldn't have bought this book!
Reviewed by a reader
I bought this book to help me brush up on the algebra I had in college. The fact that it's for the clueless, I figured I had half a chance to recall what I already thought I knew but needed to brush up on. The writer reminded me of my col
Schaum's Easy Outline of Linear Algebra
Editorial review
Reviewed by CodE-E, (Vienna, Austria)
I really, really don't like learning mathematics, but unfortunately some maths is required by my university's computer science course.If you're a person like me who can't understand any of the stuff in your mathematics professor's cryptic
Schaum's Outline of College Mathematics (Schaum's Outline Series)
Reviewed by
Reviewed by a reader
Schaum's Outline of Abstract Algebra (Schaum's Outlines)
Reviewed by
Reviewed by a reader
McGraw-Hill's GED Mathematics : The Most Comprehensive and Reliable Study Program for the GED Math Test |
Applied Calculus Textbooks
Applied Calculus textbooks focus on calculus concepts in the real world and have a practical and pragmatic application. Applied calculus textbooks cover the calculus portion of applied mathematics in general, and provide instruction on many different calculus solutions. An applied calculus textbook is typically a college textbook used in post secondary education and an applied calculus textbook is commonly found as required a material for upper level college courses. Textbooks.com offers a wide variety of applied calculus textbooks available as both new and used so you can buy |
9th Grade Math: Polynomials Help
Related Subjects
9th Grade Math: Polynomials
In mathematics, a polynomial is an expression constructed from one or more variables and constants, using the operations of addition, subtraction, multiplication, and constant positive whole number exponents.
Polynomials are one of the most important concepts in algebra and throughout mathematics and science. They are used to form polynomial equations, which encode a wide range of problems, from elementary story problems to complicated problems in the sciences.
Many 9th grade math students find polynomials difficult. They feel overwhelmed with polynomials homework, tests and projects. And it is not always easy to find polynomials tutor who is both good and affordable. Now finding polynomials help is easy. For your polynomials homework, polynomials tests, polynomials projects, and polynomials tutoring needs, TuLyn is a one-stop solution. You can master hundreds of math topics by using TuLyn.
Our polynomials videos replace text-based tutorials in 9th grade math books and give you better, step-by-step explanations of polynomials. Watch each video repeatedly until you understand how to approach polynomials problems and how to solve them.
Tons of video tutorials on polynomials make it easy for you to better understand the concept.
Tons of word problems on polynomials give you all the practice you need.
Tons of printable worksheets on polynomials let you practice what you have learned in your 9th grade math class by watching the video tutorials.
How to do better on polynomials: TuLyn makes polynomials easy for 9th grade math students.
9th Grade: Polynomials9th Grade: Polynomials Word Problems
A box with no top is to be made from a piece of metal
A box with no top is to be made from an 8 inch by 6 inch piece of metal by cutting identical squares from each corner and turning up the sides. The volume of the box is modeled by the polynomial 4x3-28x2+48x. Factor the polynomial ...
Long Polynomial Division
How is dividing a polynomial by a binomial similar to or different from the long division you learned in elementary school?
Suppose you are at the gas stationpolynomials homework help word problems for 9th grade math students.
Ninth Grade: Polynomials Practice Questions
(9x5-4x4) / (3x-1)
(3-2r)(2-3r)
A diagram shows a rectangular region, one of whose corners lie on the graph of y = -x2 + 2x + 4...
(y-12)(y+4)
x3 + x2 +1
(5x-6)(x+2)
(2x+5)(3x-1)
2x-20
4x2 + 5x - 6 = 0
y2+2y+5-3y2-5y
2x3-3x2-2x divided by 2x-3
xw+8t+8x+wt
(x+3)(x-12)
(4a3-8a2+a2)/(4a-1)
-x3+7x-6 is divided by x-1
-4x(8+3x)
Write a polynomial for the length of the rectangle: Area is 7x4 - 14x
Find a polynomial for the perimeter and for the area using d+4 and d
Find the height and length of the container using (3t+2)(2t+4)
15-8x+x2
-5(2z)3
(3x3 – x2 + 10x – 4) ÷ (x + 3)
24x3 \ 6x
24x3 / 6x
-16t2+128t+768=1
(36b3+18b2+44b+49) / (6b+5)
f(x)=3x2-x
f(x-3)=?
If you multiply (x+1)^20 how many terms will there be?
-5c+7c
(3x-5)(x-5)(3x-5)(x-5)
Find the side length of a square whose area is 529 ft2
2ab(5a + 4b)=
(2x+2)(3x-6)
(4x-3y) (4x-3y)
x2-5x-6
polynomials homework help questions for 9th grade math students.
How Others Use Our Site
Understanding polynomials, binomials and monomials. Understand the polynomials better. I Would like to re-learn all the math lessons I\`ve had since the 6th grade, Mostly because i slept throughout the 6th grade to 9th grade. I\`ll be stuck in 9th grade again next year, and i don\`t want it to happen again..
(And i was watching Clannad and i suddenly got jealous of Kotomi Ichinose) yes, nerdy, i know. And i don`t care. To prepare for the 9th grade. Need help with division of polynomials, synthetic division. I am a student at Wake Tech Community College, taking a Developmental Math Class (Algebra) and am having some trouble with polynomials. I ned to take some test ,so i ned to learn more about 9th grade math. Because i am in 9th grade n im supposed 2 be in the 11th grade and i was told this could catch me up. It will help me with my son who`s entering 9th grade but struggles to understand teacher`s explanations and this will allow for him to practice at home. I am a resource math teacher to 8th and 9th graders and I need more resources. My daughter is in 9th grade and I don`t know how to do her math homework. Algebra - 9th grader - deciding which method to use when problem types are in random order. I am hoping it will help me understand polynomials. I am teaching special ed students algebra and geometry on grade level. I have no materials for bringing them up from 5th grade - 7th grade level to 9th grade -10th grade level. Tutoring my 9th grade son by helping me understand how to set up word problems associated with polynomials and just help me survive the next 8 weeks of math. I am a mathematics teacher and your web site can help me making my assessments and worksheets for the pupils of my class of 8th and 9th grades. |
Description: This course reviews the fundamentals of elementary and intermediate algebra with applications to business and social science. Topics include: using percents, reading and constructing graphs, Venn diagrams, developing quantitative literacy skills, organizing and analyzing data, counting techniques, and elementary probability. Students are also exposed to using technology as graphical and computational aids to solving problems. This course does not satisfy any requirements for the Interdisciplinary Science major. |
What is SINGAPORE MATH WIKIPEDIA?
In the United States, ' Singapore Math is a teaching method based on the primary textbooks and syllabus from the national curriculum of Singapore. These textbooks have a consistent and strong emphasis on problem solving and model drawing, with a focus on in-depth understanding of the essential ...
I know Singapore Math is frequently championed by traditional educators so I thought I better explain this problem on the talk page before making changes. (Believe it or not, some reform educators think highly of Singapore math too.) --seberle 12:58, 18 November 2009 (UTC) I have ...
The Singapore Mathematical Olympiad (SMO) is a mathematics competition organised by the Singapore Mathematical Society. It comprises three sections, Junior, Senior and Open, each of which is open to all pre-university students studying in Singapore who meet the age requirements for the ...
There are four standard subjects taught to all students: English, the mother tongue, mathematics, and science. Secondary school lasts from four to five years and is divided between Special, Express, Normal (Academic), and Normal ...
Singapore Math is a general term used in U.S. classrooms to describe math teaching strategies and materials modeled after the math curriculum used in Singaporean schools. If you're wondering about the philosophy and history of the Singapore Math method, here's some important information.
Singapore Mathematics is a an approach to mathematics education. This curriculum has generated considerable interest among Western APEC members because of Singapore's high performance on international assessments and the availability of Singapore's mathematics textbooks in English.
Kerrums: Singapore Math is the country of Singapore's national math curriculum. It covers primary and secondary school. Singapore is first in the world for math and second in the world for science according to the Third International Mathematics and Science study in 1999.
What Is Singapore Math? Singapore Math emphasizes the development of conceptual understanding prior to the teaching of procedures. A powerful, hands-on, visual approach—a progression from concrete to pictorial to abstract—is used to introduce concepts, which at the core include strong number ...
Answer (1 of 2): Singapore math, as a program, has a consistent and strong emphasis on problem solving. Other elements that contribute to the program's success include the program's focus on and support for building skills, concepts, and processes and its attention to developing students ...
The Puget Sound region has been involved in a series of math wars as various groups of stakeholders debate how math will be taught in school districts. In The Math Kerfuffle, Another Reason Washington Needs Charter Schools I said: There will continue to be battles between those who ...
I feel for the teachers and administrators who must tolerate hyper-competitive parents in the hyper-competitive Bay Area. Having lived here for more than 10 years, I have had my fair share of debates over curriculum, private vs. public school and the finer points of having my preschooler learn ...
Geometry is a strand that appears in Singapore's Primary Mathematics Syllabus. Singapore's approach to mathematics education has become important to many Western APEC members because their students perform well on international assessments.
A number bond is a mental picture of the relationship between a number and the parts that combine to make it. The concept of number bonds is very basic, an important foundation for understanding how numbers work.
What do two eights equal in math? 8+8=16 What are the eight steps to escape from vorkuta? 1: Secure the Keys 2: Ascend from the Darkness 3: Rain Fire 4: Unleash the Horde 5: Skewer the Winged Beast 6: Weild a Fist of Iron 7: Raise Hell 8: Freedom
This blog has been created to provide a means to communicate and collaborate with parents and community members as we strive to provide a mathematics education in Warsaw Community Schools that will allow each student to rise to their own excellence.
Elementary students at Reynolds School District share, in their own words, how new strategies learned during their first year using Math in Focus™, have given them confidence and a new appreciation for mathematics.
Recently, a day-long seminar featuring Newark Mayor Cory Booker was exclusively organized for administrators of Newark Public Schools. The seminar was an opportunity for local administrators to interact with leading educators from Singapore and gain a deeper understanding of the concepts and ...
Did you know that the tiny country of Singapore scores highest in math education? It's true. Every four years a prestigious study is done that's based in Massachusetts. It's called the TIMSS. Every four years this highly regarded study takes a look at math...
With a click of a stopwatch, 24 sixth graders were off – racing down a worksheet, figuring out as many basic subtraction problems as they could in 60 seconds.When the "sprint" ended, teacher Bill Davidson called out the answers in rapid-fire bursts: "6.1, 4.3, 2.2. . . .
Closing the Achievement Gap: Teaching Content ... The following guest post is from Barry Garelick, co-founder of the U.S. Coalition for World Class Math, an education advocacy organization that addresses mathematics education in U.S. schools.
Answer: > The Bar Model method requires students to draw diagrams in the form of rectangular bars to represent known and unknown quantities, as well as the relationships between these quantities. > > The example above would be used to solve a word problem such as: Mr. Lim read 10 pages from |
218. History of Mathematics.
Development of mathematics through calculus, with emphasis on mathematicaltheories and techniques of each period and their historical evolution. (Not offered on a regular basis.)
222. Numerical and Symbolic Methods in MATH/STAT.
Credit Hours:
3
Course Level:
200
Prerequisites:
MATH 156.
Catalog Description:
Data manipulation, data visualization in two and three dimensions including animation, scientific programming using a high level language, symbolic manipulators, and other packages. Applications to problems in mathematics and statistics. (Equiv. to STAT 222.)
232. Number and Algebra for Teachers
MATH 126A or MATH 126B or MATH 126C with a C or better. (Open to pre-service elementary education majors only.)
Catalog Description:
Use of properties of real numbers and algebra to illuminate conceptual understanding and enhance problem solving techniques. The use of technology and manipulatives is infused throughout the course.
233. Measurement and Geometry for Teachers
Credit Hours:
3
Course Level:
200
Prerequisites:
MATH 126A or MATH 126B or MATH 126C and MATH 232 with a C or better. (Open to pre-service elementary education majors only.)
Catalog Description:
Use of properties of real numbers, algebra, measurement and geometry to illuminate conceptual understanding and enhance problem solving techniques. The use of technology and manipulatives is infused throughout the course. |
Mathematics A Discrete Introduction
9780534398989
ISBN:
0534398987
Edition: 2 Pub Date: 2005 Publisher: Thomson Learning
Summary: With a wealth of learning aids and a clear presentation, this book teaches students not only how to write proofs, but how to think clearly and present cases logically beyond this course. All the material is directly applicable to computer science and engineering, but it is presented from a mathematician's perspective |
Math Properties . . . Math & Algebraic Properties
Math Properties: Understanding the properties of real numbers is incredibly useful for each one of us.
Numbers impact our lives in thousands of ways on a daily basis.
But . . . althoughNumbers are used for thousands of different purposes, their underlying properties are the same for all situations.
(Numbers behave exactly the same way whether you are calculating the sales tax on your grocery receipt, measuring the length of a table, looking at a clock, or charting the stock market.)
This is quite an advantage.
We only need to learn one small set of principles.
In addition, the variables used in algebrabehave the same way numbers behave - because variables represent numbers.
If you understand arithmetic thoroughly, you automatically understand the mechanics of algebra. . . without learning anything new.
The application of Algebra to solve math problems does require additional study, but the mechanics of Algebra (addition, multiplication, combining fractions, etc.) is exactly the same as the mechanics of arithmetic. |
For 65 million years dinosaurs ruled the Earth - until a deadly asteroid forced their extinction. But what accounts for the incredible longevity of dinosaurs? A renowned scientist now provides a ... > read more
The book clearly and concisely explains the basic principles of Lagrangian dynamicsand provides training in the actual physical and mathematical techniques of applying Lagrange's equations, laying ... > read more
THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT! Glencoe Pre-Algebra is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better ... > read more |
Answer Word Problems In Algebra? This helpful video explains precisely how it's done, and will help you get good at math. Enjoy this educational resource from the world's most comprehensive library of free factual video content online.
The expert team of certified online tutors in diverse fields at Urgenthomework is available 24x7 to provide live help to students in their homework and courses. We have also excelled in providing E-education with latest web technology. The Student can communicate with our expert tutors using voice, video and an interactive white board. We help student in solving their problems, assignments, tests and in study plans....
Algebra is the branch of mathematics which is concerned with the structure, relation and quantity. It is a very important branch of mathematics and is the part of mainstream education in high school, college and university. Historically, many students do not like doing any form of mathematics as it is something very complex for many and require the element of logical and analytical thinking skills. But as a rule of education one has to come across a number of courses and has to study in......
.... |
Welcome to the OneStone® Pebbles Home Page!
OneStone Pebbles are a new series of calculus visualization tools developed by Bright
Ideas Software®. Designed from the ground up with input from education professionals1, these unique tools meld current educational theory2 with state of the art graphics technology in
consistent, easy-to-use packages. Each 'Pebble' in the series is a stand-alone program
designed to illustrate a specific topic in the calculus syllabus. The complete list
of Pebbles currently available can be found on the
Pebbles Version History page.
Designed to Stimulate a Deep Understanding of Dynamic Relationships
While the topic of each Pebble is different, the experience of using each remains
as constant as possible, and features several elements identified as contributing
to the development of a deeper understanding of dynamic covariant relationships; e.g.:
The user is given control of the experience. This is achieved at several levels;
for instance, rather than displaying illustrations/animations of pre-defined functions,
Pebbles display representations of arbitrary user-defined expressions.
High quality graphics are used to depict the user-defined expression. To be fully
effective as an illustration of a dynamic system, and to truly trigger deeper insight
into a given covariant relationship, the graphics technology employed must be capable
of smooth animation and realistic enough so as not to distract the eye, and mind,
from the mathematical relationship being illustrated. Realistic lighting and shading
effects are essential to this goal, exploiting innate human capabilities to gather
information visually.
Information is simultaneously presented in multiple formats. Adding a three dimensional
display teases minds with possibilities beyond normal expectations, even with topics
historically treated exclusively with two dimensional visualizations.
A minimalist User Interface (UI) design is employed, with as much reuse as possible
between modules. Pebbles are designed to be used primarily as educational tools.
Paramount importance is placed on ease of use and simplicity of design, while maintaining
high-fidelity graphical output. Any student familiar with graphing calculators will
be able to make immediate use of Pebbles programs.
Installing and Using Pebbles
Written in Java and exploiting
Sun Microsystems' Java OpenGL technology, OneStone Pebbles will run on Apple OS
X, Microsoft Windows 2000 or above, Solaris and many common configurations of Linux.
They do require the installation of the appropriate Java run-time on each client
machine, available (again, free of charge) from
(or by clicking on the Java icon at left). It is also
recommended that you ensure each client machine has the most recent available video
drivers installed. Full installation instructions and hardware requirements can
be found on the Installing Pebbles
page.
As mentioned above, the UIs of the various Pebbles are largely identical. The behaviors common
to most Pebbles is described on the Using Pebbles
page; any instructions particular to a given module are included on that module's
web page. Each Pebble download also includes a Help file containing
the relevant information from these web pages.
Note!
The 3DSurface Viewer ActiveX control formerly available on our site
has been replaced by the Curve Families Pebble
module. The Curve Families Pebble is capable of all the user functionality of the
3DSurface Viewer and more. In addition, Pebbles are cross-platform and independent
of the web browser; the 3DSurface Viewer only worked on Windows systems running
Internet Explorer. We think this is a better solution.
1 Bright Ideas Software
wishes to thank the following members of the University
of Wyoming faculty for their support: Dr. Jerry Carl Hamann, Computer Science Dept; Dr. Alan Dale
Moore, College of Education and Dr. Bryan Shader, Dept. of Mathematics. |
N Ways to Apply Algebra With The New York Times
1. Mathematically Modeling Mortgages
Use algebra to evaluate the housing market. Find some homes for sale in your area (for example in Atlanta), research current interest rates for mortgages and apply this formula to determine the required monthly mortgage payment.
Experiment with different home prices, different interest rates and different mortgage lengths to explore the impact of each variable on the resulting monthly mortgage payment. Use the Real Estate section's built-in mortgage calculator to check your work.
For a given house, explore questions like "How much would you end up paying over the entire term of the mortgage, and how does this compare to the value of the house?" and "How big is the difference in monthly payments between a 15-year mortgage and a 30-year mortgage?"
Do you think it is more cost effective to rent an apartment or buy a house? Read this article and play around with this Times Interactive to explore the answer.
2. Evaluating Colleges
Check out how algebra is used to rank colleges. Read this article about the history of the Academic Index and then check out this informational graphic detailing the formulas that are used to create college rankings.
Use other available data — like tuition, acceptance rates and faculty information — to create your own algebraic formula for evaluating colleges. Can you create a ranking system that puts SUNY Binghamton ahead of U.S.C.? Can you create a different ranking that puts U.S.C. ahead of SUNY Binghamton? Can you create a ranking that puts your favorite college at the top of the list?
3. Calculating Car Costs
Use data from The Times's Automobiles section to create a model for how quickly cars lose their value.
Use the Used Car Search to collect price information on specific makes and models of cars. Select your automobile, get your list of prices (for example, there are nearly 20,000 Ford Explorers for sale nationwide), and create a scatter plot with "year" on the horizontal access and "price" on the vertical access.
Use the graph and your data to explore questions like "How much value does a used car lose per year?" and "When does an automobile depreciate fastest?" Use technology like a graphing calculator or a computer spreadsheet to generate a possible function that models this data. Use the model to project the value of a new car two, three or 10 years from now. Set up equations to solve questions like "After how long will the car be worth 50 percent of its original value?"
Ratchet up the reality and complexity by compensating for the differences in new car prices and inflation. Go deeper by exploring questions like "Do SUVs lose value faster than sedans?" and "Which cars are the best long-term investments?"
4. Algebra of the Election
To win the presidency, a candidate must secure more than half of the 538 electoral votes. Take a look at the current breakdown of electoral votes by state, and find combinations of states that add up to 270 (or more) electoral votes. Each solution to this equation (or inequality) represents a potential path to the presidency.
Compare your possibilities to those demonstrated in this Electoral Map informational graphic. Take a look at some possible situations and interact with the mathematics by moving states around and exploring other solutions to this equation. If you were running for president, where would you focus your campaign resources?
5. Do the MetroCard Math
Is it better to buy a card that gives you unlimited access to public transit, or should you just pay ride by ride? Check out this article on the mathematics of New York City MetroCards. Currently, a seven-day unlimited MetroCard costs $29 and a 30-day unlimited MetroCard costs $104. If a single ride costs $2.25, under what circumstances would you be better off buying the weekly unlimited? The monthly unlimited? Set up simple linear equations and inequalities to answer these questions. Who should buy the 30-day unlimited?
Transfer over to some harder problems by factoring in the 7 percent bonus you get when you prepay for a pay-per-ride card. How does this discount affect the above calculations? And for even more real-world complexity, consider the effect that pretax commuter benefits can have on the equation. Check your numbers against the Metropolitan Transportation Authority.'s own comparisons here, and research the commuter cards in your area to find your best local options.
6. Olympic Algebra
Use mathematics to explore the wealth of Olympic data The Times has to offer. Take a look at the world records set this year in London, and check out the history of world records for events in track, field, swimming and more at the bottom of the page. Use simple formulas like Distance = Rate * Time to compare and contrast the average speeds of athletes over time, across events and even by gender. How much faster is the fastest sprinter now than 50 years ago? How much faster is the fastest sprinter than the fastest long-distance runner? How do swimmers, runners and cyclists compare in speed?
Pick an event, like the 100-meter freestyle swim, and take a look at the history of the world-record times. Create a scatter plot of the data with the horizontal axis representing the year and the vertical axis representing the world-record time. Experiment with some simple linear equations to find a line that fits the data, and use this equation to project the possible world-record times in 2016, or to hypothesize when the fastest time might drop below 43 seconds. If appropriate, use computing technologies to generate regression equations to compare to your own work.
Be sure to check out how beautifully mathematical results can be visualized and presented by watching this amazing video showing the Jamaican sprinter Usain Bolt running against every other Olympic medalist in history.
7. Redo Those Recipes
Search this Times Topics page for some tasty recipes with your favorite ingredients like chicken with lemon and rosemary or midnight pasta. Suppose you had twice as many people coming for dinner: what would the new recipe look like? Turn your recipe into an algebra problem by converting all amounts into some standard measure (like grams) and creating expressions that tell you exactly how much you need for any number of people. How many grams of chicken will you need if N guests show up for dinner?
Use a calorie counter to determine the number of calories per serving of your dishes. Using this United States Department of Agriculture guide, plan out meals for breakfast, lunch and dinner that keep you in the healthy range for caloric intake. Or list the 10 foods you most like to eat and find out how many calories are in each of them. Set up inequalities to figure out how many you should, or shouldn't, consume to keep within your healthy range.
8. Solve for Stocks
Choose some of your favorite companies and use Times resources to collect historical stock price information: for example, check out Ford Motor Company, Apple or Amazon.com. Look at the prices over some fixed period of time, say the past two years, and determine the growth of the value of the stock over that period. If you had invested $1,000 at the beginning of that time period, how much would you have at the end?
Using the formula for compound interest, A = P(1+(r/n))nt, run the numbers on some hypothetical investments of the same principle investment over the same time period, and compare the results to the performance of the stock. Did the stock do better than a 5 percent annual rate of return? How about 8 percent? Set A equal to the final value of the stock, and solve for the rate, r, to figure out the exact rate of growth of your chosen stock.
Find the rates of return for several stocks, and put together a hypothetical investment portfolio for the school year. Watch your stocks through the year and compare their performance to your calculations. Does past performance guarantee future returns?
Read Mr. Hacker's original essay and decide for yourself. Do you use internal equations to help plan out your schedule? Or inequalities when you're spending your money? Or graphs when you are plotting your performance? Or maybe you use algebra to figure out if that frequent shopper program is worth sticking to.
Find the algebra that's around you and write a response to Professor Hacker. Maybe algebra isn't necessary, but it sure can be useful.
This lesson addresses the following Common Core domains, standards and practices under Algebra:
Domains
Create equations that describe numbers or relationships.
Solve equations or inequalities in one variable.
Represent and solve equations graphically.
Interpret the structure of expressions.
Standards
Seeing Structure in Expressions
1. Interpret expressions that represent a quantity in terms of its context.
4. Derive the formula for the sum of a finite geometric series and use the formula to solve problems. For example, calculate mortgage payments.
Creating Equations
1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
Reasoning With Equations and Inequalities
3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
C.C.S.S. Practices
Mathematical PracticesFrom 26 to 50 of 67 Comments
This piece does an excellent job of demonstrating Mr. Hacker's point – that algebra is unnecessary for most of daily life and work. Each of the above exercises is merely a more tedious and academic way of finding information that is readily available via the web or a simple calculator. Algebra is great and necessary for society, but like computer programming, not everyone needs to know it.
I agree with Hari's comment above. While it may be useful to walk through these exercises when teaching algebra, to ensure that students understand how to apply it correctly, they don't make it any more relevant to daily life. Algebra students should certainly learn how algebra is used in calculating mortgage amortization schedules, but telling a kid who's failing algebra that he needs to understand this type of material to succeed as an adult is disingenuous.
people should want to work in school to be sicsessfull later in life. like me I want to be a game tester, so I work hard im in 8th gradeI hope I becom a good game tester. let this be a lesson to others, just work hard in school. the numberts may be hard but I have to get throu it all.
For the past ten years I have been a volunteer Math Tutor in the South Bronx, Yonkers and Westchester County, working with several hundred students ranging from 5th graders through adults at a local community college. During that time, there have not been twelve students who fully knew their Multiplication Tables – a most fundamental underpinning for Math success. Of course, virtually all knew their 2x, 5x & 10x tables but beyond that they virtually hit a wall. At that point, many would immediately whip out their calculators to find the answer!
I demonstrated to these students the benefits of mastering the Tables – today and for the rest of their lives. Once they saw it, they were excited and agreed. I then devised a very simple and highly effective way to teach these students the complete Tables in a half-day.
The only resistance to any of this was from the "educators" – most teachers, principals and administrators. They objected to what they called memorization and "drill and kill". They had "no time" for teaching the Tables because it wasn't part of their syllabus, schedule or upcoming test. They wanted their students to "think", not do "drill and kill."
Once they have passed their Algebra, Geometry and Trigonometry exams/regents, most students will rarely use those subjects in real life. Some will go on to do so in the sciences, engineering and business related areas. However, each and every student can use their mastery of the Tables in everyday life from supermarket shopping to most every other transaction of their day-to-day life.
We often hear the term – "return to the basics" – used over and over but this is one area where I firmly believe Failure Is Not An Option.
I wish we could get away from the all or nothing argument that seems to be what people are using in replying as for or against the concept of Algebra being necessary (although I agree that it needs to be taught…just not required for a high school diploma). As a counselor who has worked in both high schools and colleges, math was a major stumbling block that made many students feel like they would be a drop out if they could not master it (and in high school, that is a true reality; thankfully most colleges are more flexible about their requirements). I thought stats was going to make me be a college drop out but I was fortunate to get a great teacher (I venture that is the exception rather than the rule considering how our society views or pays our teachers).
It's amazing to watch the "high achieving" kids feel like they *have* to take high level math to get accepted into college (which the colleges are promoting as well) where they then drop it like a hot potato if majoring in the humanities or non-math/science areas. Unfortunately there are MANY other children who drop out because Algebra is the gatekeeper to a high school diploma since most schools do not offer alternative, more "applicable to the average job/life" math classes (yes…math areas that NAExpat so articulately described).
Until we get more people who like both math and teaching as their career combo (which is unlikely considering what the average teacher is paid), we need to figure out more math options to enable our citizens to be successful adults. One little math class should not be causing this level of debate and problems for people. It shouldn't be something that holds the "average Joe/Joan" back in life.
I aced two algebra courses in high school, along with geometry, trigonometry, calculus, statistics, and a math-intensive physics course. Yes, I use math occasionally, but most of my course work was utterly useless to my adult life.
The examples provided are preposterous. If I want to calculate mortgage payments, I type "mortgage calculator" into Google. Anyone who earns six figures making such calculations by hand is employed by imbeciles.
While the practical applications of algebra are all over the place, I don't think the argument for the necessity of algebra should be based primarily on such applications.
Consider decisions like whether to move to a different city, or to leave one job for another. These types of complex decisions requiring weighing factors, isolating variables, relating relative values. Even though they are not inherently quantitative analyses, they still require the systematic approach found in, and developed by, algebraic thinking. (The capacity for algebraic thinking alone won't lead to success in such decision-making, but the lack does dramatically increase the likelihood of failure.)
The practical arguments for algebra, which cite the myriad quantitative applications we rely on in our lives, are important and valuable. But the fundamental argument for teaching algebra is that a mind that is demonstrably capable of algebraic thought is a mind far better prepared to engage in successful living across the board, in all areas of life.
It is very sad to see this happening…
I am just wondering what will be next to be questioned in our education system. When do you use Chemistry, Physics or even history in your line of work? Some of you might say never… Neither do I, but I can say for a fact that I am really happy that I have studied these topics as it makes me a more complete person. Some of our students are really passionate with mathematics (and specifically Algebra) and it would be a shame to remove it from the curriculum. I had a real passion for math in HS and good thing it was there to make me shine, as nothing else would passionate me as much. Instead of removing it, let's find a way to make it more relevant and interactive for them. Being an Algebra teacher myself, I will fight for it and promise to always do my best to get the kids engaged, even those who are "not good" with it. There are tons of different techniques that can be used to engage them.
@Richard Fliam, thank you for your answer. very inspiring.
I work in the building maint. dept of a local school district. In a different life time I was an industrial lab tech within the timber industry. I have a bachelors in environmental science and I would envite the academic powers to be that algebra is very important. Have I ever used it in my adult life? Not really, at least not in my everyday math ie, equations in the lab or carpentry or bank accounts etc… I was one of those born artists types that struggled with math for years. I barely passed with a D in high school and had to take it three times in college. I did not dicover until theology school why algebra matters. As a member of a liturgical branch of christianity we are required to study scholarship from several areas of study. This requires modles of thought that are critical, analytical and creative in order to try to see the larger picture. For example the dawn came for me when I realized that if; Love is truth and God is love then God is Truth. Let me put it another way…if A+B=C then A+C=B and C+B=A. I am using this as an example only. I do not claim to have all the answers nor do I believe that any one religion is better than another. I do claim the understanding of how to think using reason. I hope that the powers to be, consider carefully that a democratic republic as well as a mature understanding of liberation is what is actually at steak here. We need teachers who are gifted at teaching such a language, or consepts like ones presented in the movie The Matrix will not even be possible for the masses. Thank you for asking.
To Mr. Hacker's credit he does make a good point. His point in my opinion is not that algebra is useless but that not everyone needs algebra, specially the kind of algebra that is taught in high school, with its heavy emphasis on equations instead of creative modeling. If we notice the examples given above, they are all examples of creative modeling, They all consist of taking raw data and discovering the patterns behind it. Many, if not most, high school algebra problems are not of this sort. Instead, students are given formulas to plug numbers into. Even the infamous "word problems" are canned. They do not make you say to yourself "hey, this pattern looks familiar and interesting" they make you say " ugh, now which of the equations on this chapter do i use?." Mathematics is all around us, and can be used to solve all sorts of problems, but the way we teach it is so full of rote and so disconnected from the real joy and creativity mathematics has to offer (as part of the toolkit we use to solve real problems and find patterns) that it is no wonder poets and artists and many other people see no use for it. Look at Vi Hart and her videos for how I think mathematics and mathematical creativity could be taught:
I'm getting a PhD in Math Education. I can't see why you would use Algebra to do those things. It would be easier, and more conceptual, to do most of them other ways. Others are simply a matter of using a graphing calculator. I think the article pretty much proves that Algebra is not necessary. I am still, after many years, hoping to talk to someone other than an engineer who can give me an example of using Algebra in the workplace. As for using it in real life, I have never heard of it happening and I do not see it happening here. I support math built around concepts and technology, not one stringent model of equation solving called "algebra" over-taught as if it were the only way to understand mathematics
I think if I wanted to take over the world, nothing could be finer than raising generations of people who relied on the Internet and calculators for the answer to any math problem.
Perhaps I just live an odd life, but I have used my algebra skills for everything from creating a budget, setting my Holiday spending amounts, choosing between TV providers and cell phone providers, remodeling at home, and even playing my favorite video game.
Perhaps the reason others have not done so, is that they cannot.
Algebra combines the knowledge of computation with numbers (in all their various forms) with the presence of unknown or changing quantities. Algebra is also where we learn about functions – those sometimes correlation type relationships that allow us to quantify cause and effect.
And, as many others have said, Algebra causes me to confront the unknown, and thereby to deal with the abstract.
Students may have poor teachers who are unable or unwilling to show the value of Algebra. Or the students themselves may choose to not take on the challenge due to laziness or lack of support.
Customers want to know what something will cost them. They are interested i the particular. Entrepreneurs need to develop pricing policies. They are concerned with the general.
All policies are effectively algebraic statements; analysing the consequences of one or more policies and how they interact requires algebra.
Experience of algebraic thinking equips people to extract underlying structure and to analyse the implications of choices. Most students encounter only the manipulation of the algebra of numbers, not the expression and analysis of generalisations leading to appreciation of structure.
Algebra is a means to teach the youngsters and their brains how to "think"….you know a and c what is b? Sounds dumb, but it has been a mainstay my entire life. If you know some of the facts, you can get to the truth.
As a math teacher I understand that many of my students will eventually choose "non-mathematical" fields to go into. However, I teach my students that if they do not develop the ability to transform ordinary every day situations into algebraic equations, then they will certainly never be able to make use of the skills that we teach them. Thus, we focus on constantly looking for ways to make our world simpler by invoking Algebra. We are constantly reminded of this by the following quotes:
1. "The essence of mathematics is not to make simple things complicated, but to make complicated things simple."
I tell my ninth grade students that we learn algebra to teach us to think logically. I promise that they will have stronger, sharper minds when we have studied for just a few months – that they will have "powers" they have yet to imagine.
Students respond to learning that our goal is to help them develop as people, not just to prepare for specific tasks or vocations. Going further, I teach a short lesson on the value of learning mathematics in a republic, to teach people to make decisions based on reasoning.
Algebraic applications abound, and these are nice, but I think the value of algebra as a required subject goes beyond direct applications. I must agree with many readers that most people do not actually use formulas and direct applications in their day to day life (even though they may be able to see that an application does exist). But the essence of algebra goes much deeper than that. I wrote a blog post about the essential questions in algebra that I think speaks directly to this:
Do you see football players doing push-ups on the field during a game???? "No!!!" my students shout yet they can't deny that push-ups are an integral part of the regimen for competitive players. Algebra is push-ups for developing brain power, but not everyone acclimates to this technique as government school insists will happen. Better developed alternatives to strengthen our brains allows more people to excel, individualize and be successful. The example in the essay referring to the Mississippi Community College working with the auto plant gives credence to this philosophy.
As a high school science teacher, I believe a high school education should provide as many opportunities as possible. Math is the language of science and technology. Without high school algebra, students cannot take courses that properly explore technical fields, including medicine, and, as a result, careers in STEM fields are closed to them.
At what point do we allow students to limit their choices through specialization? Few ninth graders have a firm career path chosen and many that do change their mind within a year. Ninth grade is too early to severly limit most students' educational options.
I support all of the arguments for keeping Algebra. I do disagree that Algebra is causing students to drop out as some people have mentioned. I have found, in most cases, many of the troubled students do well in Algebra. They like that there is a set answer in the end and prefer that over the 10 page term paper.
It's about exposing students to a variety of ways to process information. We can argue every subject in school, for example why take home ec, am I ever going to sew a pair of pants or cook? Why can I just buy take-out forever and a new pair of pants? That's how silly this sounds. How can students plan for their future w/o being exposed to all of the subjects and then decide where their stregnths lie? I would rather see a student barely pass a subject and can say they can comprehend at least 65% of the material then never give them a chance to even try and learn any of it.
But before I share this debate with my students, I just want it noted that 3 + 5 does not equal 11 as someone said and the biblical reference is a good one but if A + B = C that doesn't mean A + C = B. It does however show the transitive property that if A = B and B = C then A = C.
My son is a first year student at a university. He is required to attend an algebra class for one semester to meet his admission requirement. There is not even a grade. He has no interest in math as a career. If colleges could drop the requirement that students know how to swin, why can't they stop wasting a student's time with a course not related to his or her major?
Mathematics educators love to post "activities" for individual concepts or procedures found in the Common Core math standards. The problem with activities is that they usually miss the mark when teaching for long-term memory and understanding of algebra. Teaching algebra without connections to the algebra already taught and/or to real world contextual situations while using visualizations and pattern building at the beginning of a lesson do not capitalize on core neural operations used for understanding and long-term memory with recall. Teaching algebra through isolated activities typically forces the brain to store the content taught in short term memory which it purges as soon as it perceives the memories to be no longer of value – like after a midterm.
Wow! So many interesting comments and so many points of view; as diverse as there are types of people and each point of view applicable to a group. Sort of "if the shoe fits" type of thing.
So here's mine. Where in real life do you solve for X; everywhere. The difference is there are people who don't recognize the X precisely because they don't have the skills to isolate the problem and logically strategize the steps to a solution. Many founder around, fumbling through life, doing the best they can and never even realized that there were better, more efficient, more effective, time saving, money saving, psycho-emotional drain saving ways to do it. They never knew that they never knew. What a waste.
Flexibility of thought, recognizing the possibility of multiple ways to a solution, recognizing the possibility of multiple solutions, recognizing the same type of problem in a new context, recognizing the similarities in different situations, recognizing that a new variable has thrown the balance of your equation and finally recognizing that there is perhaps no viable solution; These are the abstractions that algebra trains your brain to look for; then the brain transfers and applies.
It is the way we teach that needs a new spin, not eliminating algebra from our curriculums. The world is becoming more complex not less; accordingly it requires more complex thinkers not fewer. Perhaps it is the tendency towards this inverse proportion that is leading us towards this abyss |
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Polynomial Functions in DetailAn outline relating characteristics and concepts associated with the polynomial function by way of questions, theorems, and graphing. I have used this as a lesson plan and also given it as a handout, since space is provided for examples or notes. Although intended for PreCalculus, could be use in College Algebra, also. 3 pages.
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College Mathematics II –
mth209ca
(3 credits)
This course continues the demonstration and examination of various algebra concepts that was begun in MTH 208: College Mathematics I. It assists in building skills for performing more complex mathematical operations and problem solving than in earlier courses. These concepts and skills should serve as a foundation for subsequent quantitative business coursework. Applications to real-world problems are emphasized throughout the course.
Systems of Linear Equations
Solve systems of linear equations, linear inequalities, and linear equations with three variables.
Nonlinear Equations
Apply nonlinear equations to real-world problems.
Solve quadratic equations.
Solve equations involving radical expressions.
Solve proportion and variation problems.
Solve rational equations and formulas.
Solve quadratic equations by factoring.
Nonlinear Expressions
Apply nonlinear expressions to real-world problems.
Simplify radical expressions and complex numbers.
Multiply, divide, add, and subtract rational expressions.
Simplify rational expressions.
Factor polynomial expressions |
Hum, unfortunately I am not familiar with the Open University course, so I am just making a guess based on the course description you linked to.
Insofar as Fourier Analysis is concerned, a decent text is Stein and Shakarchi's Fourier Analysis: an introduction. ( ) You will most likely only need chapters 1, 2, 4, and 5, with a bit of knowledge of 3. One thing good about the book is that it was written as a first course in an analysis sequence, so doesn't assume too much knowledge about real and complex analysis.
For the applications to wave equations as mentioned in the course description, somehow I feel that a textbook in electromagnetism (Jackson or Griffiths) may contain more practical material (look at the sections on standing waves and wave-guides). |
Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide.
Saxon Math (Kindergarten-Grade 5)
Saxon Math's unique structure uses integrated and distributed instruction — concepts are taught in smaller increments that build logically on each other. Each increment is practiced and reviewed as new skills are added. This way, students see the connections between concepts, and learn the "why" as well as the "how."
In order to match children's developmental learning cycles, the new Saxon Math for K–5 offers two configurations:
Saxon's kit-based K–3 primary program is more teacher directed and activity-based.
Saxon's textbook-based 3–5 intermediate program is more studentdirected.
Grade 3 is often considered a transition year, and school districts differ in how they classify and configure third grade mathematics. Saxon accommodates this variation by providing a choice between a consumable kit version or a hardbound textbook version at this grade level.
Saxon Math Courses 1, 2, and 3 (Grades 6, 7 & 8)
Saxon's unique structure gives every student time to master the new standards.
The traditional unit organization is not designed to provide the time needed for the kind of long-term mastery required by today's standards — a steep learning curve and an even more dramatic forgetting curve for each unit make mastery learning a challenge for many students.
Saxon optimizes time management. It breaks apart traditional units into easily retained increments and then distributes and integrates them across the year. This creates a learning curve that allows students to master each part of every standard. No skills or concepts get dropped, and students retain what they have learned well beyond the test.
Gives students a year to master concepts instead of weeks
Creates a learning safety net for below-grade-level learners
Ensures a solid mathematical foundation for students advancing into higher mathematics
Saxon Algebra 1, Geometry, and Algebra 2 (Grades 9, 10, 11 & 12)
Practice helps to cement learning.
That's why Saxon Math allows constant review over time to promote long-term retention and proficiency. Students attain a depth of understanding on a particular concept by practicing it over time and in a variety of ways. Every day, Saxon students practice not only the day's concept, but also concepts and skills from previous lessons. |
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This highly instructive, informal text that explains step by step how and why you need to tackle maths within the biological sciences. The skills taught in this informative book are introduced using a problem-solving approach that emphasises the biological background of the book rather than the mathematical theory. |
Complex Numbers
Mathcentre provide these resources which cover aspects of complex numbers, often used in the field of engineering. They include the definition of a complex number and their associated arithmetic, the Argand diagram and polar form of a complex number, as well as the exponential form.
Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant diagrams and examples. Students wishing to review, and consolidate, their knowledge and understanding of complex numbers |
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This course provides an aggressively gentle introduction to MATLAB®. It is designed to give students fluency in MATLAB, including popular toolboxes. The course consists of interactive lectures with students doing sample MATLAB problems in real time. Problem-based MATLAB assignments are given which require significant time on MATLAB.
This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month |
Matched to the specification (2381), this book features multiple-choice practice questions to prepare students for the unit 2 stage 1 exam of Edexcel GCSE Mathematics. It contains an array of exercises that give students opportunities to practice skills and techniques. It features comprehensive worked examples that show how to approach questions. |
Designed for students having no previous experience with rigorous proofs, this text on analysis can be used immediately following standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, e.g., complex variables, differential equations, Fourier analysis, numerical analysis, several variable calculus, and statistics. It is also recommended for future secondary school teachersTotal English provides new solutions for your English classroom offering unbeatable choice and flexibility, a complete range of dynamic resources and engaging material. Each Students' Book is divided into 12 topic-based units and includes DVD pages, a Pronunciation Bank, and a Writing Bank with tips and models for writing emails, letters and so on.
Modern electronics depend on nanoscaled technologies that present new challenges in terms of testing and diagnostics. Memories are particularly prone to defects since they exploit the technology limits to get the highest density. This book is an invaluable guide to the testing and diagnostics of the latest generation of SRAM, one of the most widely applied types of memory. Classical methods for testing memory are designed to handle the so-called "static faults," but these testsolutions are not sufficient for faults that are emerging in the latest
The text provides an introduction to the variational methods used to formulate and solve mathematical and physical problems and gives the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize then the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency. It lays the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, and computer science. ...
Over 300 challenging problems in algebra, arithmetic, elementary number theory and trigonometry, selected from the archives of the Mathematical Olympiads held at Moscow University. Most presuppose only high school mathematics but some are of uncommon difficulty and will challenge any mathematician. Complete solutions to all problems. 27 black-and-white illustrations. 1962 edition.The reader who has mastered the core material acquires a strong background in elementary topology and will feel at home in the environment of abstract mathematics. With almost no prerequisites (except real numbers), the book can serve as a text for a course on general and beginning algebraic topology.
Structure of Matter: An Introductory Course with Problems and Solutions
Springer 2007 | 474 | ISBN: 8847005590 | PDF | 5 Mb
This is the second edition of this textbook, the original of which was published in 2007. Initial undergraduate studies in physics are usually in an organized format devoted to elementary aspects, which is then followed by advanced programmes in specialized fields. A difficult task is to provide a formative introduction in the early period, suitable as a base for courses more complex, thus bridging the wide gap between elementary physics and topics pertaining to research activities. This textbook remains an endeavour toward that goal, and is based on a mixture of simplified institutional theory and solved problems. In this way, the hope is to provide physical insight, basic knowledge and motivation, without impeding advanced learning....
Improve any kind of test score with easy-to-grasp insider tips and strategies. Learn the Techniques that All Successful Test Takers Know. Any kind of test-from high stakes academic tests to career qualification exams-can be faced successfully with this book. Students will learn simple but valuable tips, such as the most effective ways to memorize, the five classic methods to overcome test anxiety, the right and wrong way to cram, and the 10 most common test-day problems and solutions. This guide will even reveal how test-makers try to distract the test-taker, how to become an educated guesser, and how to predict essay-question subjects in advance. |
KS5 Alevel Maths Standards units: mostly calculus
Maths worksheet activities and lesson plans. core 1 equations and quadratics. Unit C1 Linking the Properties and Forms of Quadratics. Students classify quadratic functions according to the properties of their graphs and their algebraic forms. This is part of the "Mostly Calculus" set of materials fr More…om Standards unit: Improving learning in mathematics. To enable learners to: identify different forms and properties of quadratic functions; connect quadratic functions with their graphs and properties, including intersections with axes, maxima and minima.
This is fantastic. I'm using it an in introduction to quadratic graphs, every ability is catered for with the use of TI-nSpire for the weaker students and pen&paper for the top group. They are all so engaged at making connections. Thank you so much, I was about to create something like this, but nowhere near as good! |
SAS? Curriculum Pathways? Launches Free Common Core Algebra Course
SAS
Curriculum Pathways has launched a free
Algebra 1 course that provides teachers and students with all the
required content to address the Common
Core State Standards for Algebra. Available online, the course
engages students through real-world examples, images, animations, videos
and targeted feedback. Teachers can integrate individual components or
use the entire course as the foundation for their Algebra 1 curriculum.
"Success in Algebra 1 opens the door to STEM opportunities in high
school and beyond, and can set students on the path to some of the most
lucrative careers," said Scott McQuiggan, Director of SAS Curriculum
Pathways. "This course gives teachers engaging content to support
instruction, and will help them meet Common Core requirements."
SAS developed the Algebra 1 course in collaboration with the North
Carolina Virtual Public School, the North Carolina Department of Public
Instruction and the Triangle High Five Algebra Readiness Initiative, an
organization that promotes the important role mathematics teachers play
in preparing students for college and careers.
The course maps to publisher
requirements recently established by the lead writers of the Common
Core State Standards for Mathematics. More specifically, the course
addresses the authors' concerns for greater emphasis on mathematical
reasoning, rigor and balance. In addition, the course takes a balanced
approach to three elements the writers see as central to course rigor:
conceptual understanding, procedural skill, and opportunities to apply
key concepts. It incorporates 21st-century themes like global awareness
and financial literacy while weaving assessment opportunities throughout
the content.
While Algebra 1 is the first full course developed, SAS Curriculum
Pathways provides interactive resources in every core subject for grades
six through 12 in traditional, virtual and home schools at no cost to
all US educators. SAS Curriculum Pathways has registered more than
70,000 teachers and 18,000 schools in the US.
SAS Curriculum Pathways aligns to state and Common Core standards (a
framework to prepare students for college and for work, and adopted by
45 states), and engages students with differentiated, quality content
that targets higher-order thinking skills. It focuses on topics where
doing, seeing and listening provide information and encourage insights
in ways conventional methods cannot. SAS Curriculum Pathways features
over 200 Interactive Tools, 200 Inquiries (guided investigations,
organized around a focus question), 600 Web Lessons and 70 Audio
Tutorials.
SAS in Education
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Vineland ACT explain it all simply so that students understand. Calculus can be a difficult topic at first. Like most math classes it has a few elementary parts that once grasped lend incite to the rest of the topic. |
Mathematics
The Mathematics Department occupies the ground floor of the Academy Building and contains 8 classrooms each equipped with an overhead projector. Several rooms are equipped with interactive whiteboards. There is a Departmental Office which doubles as a store-room. The department also makes use of a small teaching room for the lowest teaching sets.
There are currently 12 full-time equivalent members of staff plus 3 members of the Leadership team who teach some Maths classes.
Course Outline/Overview
All pupils study Mathematics through Key Stage 3 up to GCSE and then around 20 take the subject at A-level in each of Year 12 and Year 13. At A Level, students have the choice of studying a Core Maths and Mechanics course or a Core and Statistics course. There is also the opportunity to take an extra A Level, called Further Mathematics, for appropriate students, as well as being prepped for Oxbridge entrance if required.
Key Stage 3
In Year 7 the focus is on teaching non-calculator skills and improving basic numeracy. Topics covered include the 4 rules of Addition, Subtraction, Multiplication, Division, Decimals and Money, Shapes, Graphs, Fractions and Percentages. As students progress through Key Stage 3 the content of their lessons will differ depending on which set they are in.
Throughout Key Stage 3, all students will sit past exam papers at regular intervals. Levels are used in their assessment throughout years 7 - 9 and targets will be based on these levels.
Mathematics is taught in sets from Day One in Year 7 based on Key Stage 2 results and CAT tests.
Key Stage 4
From 2006, mathematics at GCSE level will be taught in just 2 tiers, Higher and Foundation. Students doing the Higher tier can obtain grades from C up to A*. Students doing the Foundation tier can obtain grades from G up to C. Students in the lowest set will also take an Entry Level certificate as well as their GCSE. The examining board for this exam is Edexcel. Students will sit a final exam at the end of Year 11.
In general, the exam results for the department show good progress throughout every year group, leading to students overachieving when faced with external exams. The department and the school has a very supportive network in place so staff always have other colleagues to call upon in times of need.
Sixth Form
We follow the Edexcel A-level syllabus. All students take 3 modules in the Year 12 and 3 in the Year 13. Every AS Level student takes 2 Core modules, C1 and C2, plus their applied module, either Mechanics 1 or Statistics 1 as appropriate. In their A2 year, they will all take C3 and C4 plus their second applied module. We are also in our second year of offering Further Maths to A level. From our first group to complete the course, we produced the school's first Cambridge student, who has gone there to read Mathematics. Modules offered include all Mechanics, Statistics and Further Pure Modules, plus Decision 1, D2 and STEP preparation. Students do have the chance to resit earlier modules, but this is not encouraged. The cost of entry for any resit exam must be met by the student. |
Synopsis
An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software
In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and discusses the algorithms and associated practices that enable those models to be solved most efficiently.
The book begins with coverage of successful applications, systematic modeling procedures, typical model types, transformation of non-MIP models, combinatorial optimization problem models, and automatic preprocessing to obtain a better formulation. Subsequent chapters present algebraic and geometric basic concepts of linear programming theory and network flows needed for understanding integer programming. Finally, the book concludes with classical and modern solution approaches as well as the key components for building an integrated software system capable of solving large-scale integer programming and combinatorial optimization problems.
Throughout the book, the authors demonstrate essential concepts through numerous examples and figures. Each new concept or algorithm is accompanied by a numerical example, and, where applicable, graphics are used to draw together diverse problems or approaches into a unified whole. In addition, features of solution approaches found in today's commercial software are identified throughout the book.
Thoroughly classroom-tested, Applied Integer Programming is an excellent book for integer programming courses at the upper-undergraduate and graduate levels. It also serves as a well-organized reference for professionals, software developers, and analysts who work in the fields of applied mathematics, computer science, operations research, management science, and engineering and use integer-programming techniques to model and solve real-world optimization |
Course Description
MATH 096 — Introductory Algebra (5 cr)
This course covers introductory algebra skills. Topics include signed numbers, linear equations, graphing linear equations, linear systems of equations, polynomials and rational expressions. This course is designed for students who need a review of high school algebra. Prerequisite: MATH 021 or 090 with a 3.0 or better within the last three years; or appropriate placement score. (SCC, SFCC) |
MATH
131 – Linear Algebra I
Fall 2006
Text : Linear Algebra, 3rd Edition, by Fraleigh and Beauregard
Course
Meetings: The course lectures will be held in Sproul Hall 2340 on
Tuesdays and Thursdays at 2:10 pm-3:30 pm.Discussion sessions will be held on Wednesday with Ms. Rafizadeh (7:10
pm) or Mr. Kuang (8:10 am).You are
expected to attend both the lectures and the discussion sessions as per Math
Department decree.
Tips for
Success: * Come to class!It is
amazing how much you can learn by being attentive in class. *
Collaborative learning is encouraged but remember only YOU will be taking the
quizzes and exams... * Like all mathematics, linear algebra is not a
spectator sport; you will learn only by doing! You will find that a
consistent effort will be rewarded. * Be organized. Have a notebook
or binder for Linear Algebra alone to keep your class notes, homework, quizzes
and exams in order. * No question you have should be left
unanswered. Ask your questions in class, discussion session or take
advantage of office hours.
Homework
(100 points): Homework will be assigned daily and the starred problems
will be collected during the next week's discussion session.No late
homework will be accepted.Homework will not be graded unless it is written
in order and labeled appropriately.An answer alone will get 0 points.Make sure to justify every answer.Your lowest homework score will be dropped
and the remaining homework will be averaged to get a score out of 100.
Quizzes
(100 points): There will be a short quiz given at the beginning of each
lecture testing you on the definitions and theory that you learned from last
class.You may use your notes.Quizzes will only last 5 minutes so make sure
that your notes are organized and that you arrive on time for class.There may also be a quiz at the end of
discussion with one problem similar to the homework problems assigned during
the previous week.You may not use your
notes for this quiz.The daily quizzes
will be worth 3 points each, the lowest two will be dropped giving a total of
50 points.The discussion quizzes will
be worth 10 points each, there will be at least 6, and I will keep only the top
5 scores for a total of 50 points.
Exams (300
points): I will give one midterm (100 points) and a final (200
points). Please bring your ID to each exam.There
are no make up exams. If a test is missed, notify me
as soon as
possibleon
the day of the exam. For the midterms only, if you have a legitimate and documented
excuse, your grade will be recalculated without that test.The Midterm is tentatively scheduled on
Thursday, October 26.The Final is on
Tuesday, December 15, from 11:30 am-2:30 pm.
Grades: General
guidelines for letter grades (subject to change; but they
won't get any more strict): 90-100% - A; 80-89% - B; 70-79% - C; 60-69% - D;
below 60% - F. In assigning Final Grades for the course, I will compare
your grade on all course work (including the Final)and your grade on the Final Exam.You will receive the better of the two
grades.
Calculator
Policy: It is the Math Department's policy to forbid the use of
calculators on both exams and quizzes. |
Designed to be used in a variety of modes of teaching; direct instruction, whole group, small group, cooperative group, independent or discovery learningThese tricks cover a broad range of concepts, from simple variable equations to factored polynomials, all with an engaging twist of magic
Product Information
Subject :
Algebra
Grade Level(s) :
6-12
Usage Ideas :
Designed to be used in a variety of modes of teaching; direct instruction, whole group, small group, cooperative group, independent, or discovery learning. |
A Level Maths with Statistics Home Study Course
Course Description
develop their understanding of mathematics and mathematical processes in a way that promotes confidence and fosters enjoyment
develop abilities to reason logically and to recognise incorrect reasoning, to generalise and to construct mathematical proofs
extend their range of mathematical skills and techniques and use them in more difficult unstructured problems
develop an understanding of coherence and progression in mathematics and of how different areas of mathematics can be connected
recognise how a situation may be represented mathematically and understand the relationship between real world problems and standard and other mathematical models and how these can be refined and improved
use mathematics as an effective means of communication
acquire the skills needed to use technology such as calculators and computers effectively, to recognise when such use may be inappropriate and to be aware of limitations
develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general
take increasing responsibility for their own learning and the evaluation of their own mathematical development
Qualification Information
AS +A2 = A level in Pure Maths. Both AS and A2 level courses and examinations must be successfully completed to gain a full A level.
AQA Specification 6360
Method of Study
The course comes to you as a proper paper-based pack, not as an electronic password
You will get full tutor support via email
You will receive feedback on your assignments from our experienced tutors
You will be given guidance through the Study Guide on the nuts and bolts of studying and submitting assignments
Postal assignments cannot be accepted without prior permission from the tutor
You must have access to email in order to contact your tutor.
Method of Assessment
The course contains a number of assignments which your tutor will mark and give you valuable feedback on. We call these Tutor Marked Assignments (TMAs). You need only send the TMAs to your tutor for comment, not the self-assessment exercises which are also part of the course to help you gauge your progress.
Exams are taken at an AQA centre and we can provide an extensive list of centres for you. Please read our FAQs for further information.
Length of Course
Our A Levels come with tutor support for 18 months
Tutor Support
You will have access to a tutor via our student portal who will mark your work and guide you through the course to help you be ready for your examinations. In addition you will be supplied with a comprehensive Study Guide which will help you through the study and assessment process. |
Description
The Akst/Bragg series uses a clear and concise writing style that teaches by example, while fostering conceptual understanding with applications that are integrated throughout the text and exercise sets. The user-friendly design offers a distinctive side-by-side format that pairs examples and their solutions with corresponding practice exercises. Students understand from the very beginning that doing math is an essential part of learning it. The clear, concise writing style holds students' interest by presenting the mathematics with minimal distractions. Motivational, real-world applications demonstrate how integral mathematical understanding is to a variety of disciplines, careers, and everyday situations.
Table of Contents
1. Whole Numbers
Pretest
1.1 Introduction to Whole Numbers
1.2 Adding and Subtracting Whole Numbers
1.3 Multiplying Whole Numbers
1.4 Dividing Whole Numbers
1.5 Exponents, Order of Operations, and Averages
1.6 More on Solving Word Problems
Key Concepts and Skills
Review Exercises
Posttest
2. Fractions
Pretest
2.1 Factors and Prime Numbers
2.2 Introduction to Fractions
2.3 Adding and Subtracting Fractions
2.4 Multiplying and Dividing Fractions
Key Concepts and Skills
Review Exercises
Posttest
Cumulative Review Exercises
3. Decimals
Pretest
3.1 Introduction to Decimals
3.2 Adding and Subtracting Decimals
3.3 Multiplying Decimals
3.4 Dividing Decimals
Key Concepts and Skills
Review Exercises
Posttest
Cumulative Review Exercises
4. Basic Algebra: Solving Simple Equations
Pretest
4.1 Introduction to Basic Algebra
4.2 Solving Addition and Subtraction Equations
4.3 Solving Multiplication and Division Equations
Key Concepts and Skills
Review Exercises
Posttest
Cumulative Review Exercises
5. Ratio and Proportion
Pretest
5.1 Introduction to Ratios
5.2 Solving Proportions
Key Concepts and Skills
Review Exercises
Posttest
Cumulative Review Exercises
6. Percents
Pretest
6.1 Introduction to Percents
6.2 Solving Percent Problems
6.3 More on Percents
Key Concepts and Skills
Review Exercises
Posttest
Cumulative Review Exercises
7. Signed Numbers
Pretest
7.1 Introduction to Signed Numbers
7.2 Adding Signed Numbers
7.3 Subtracting Signed Numbers
7.4 Multiplying Signed Numbers
7.5 Dividing Signed Numbers
Key Concepts and Skills
Review Exercises
Posttest
Cumulative Review Exercises
8. Basic Statistics
Pretest
8.1 Introduction to Basic Statistics
8.2 Tables and Graphs
Key Concepts
Review Exercises
Posttest
Cumulative Review Exercises
9. More on Algebra
Pretest
9.1 Solving Equations
9.2 More on Solving Equations
9.3 Using Formulas
Key Concepts and Skills
Review Exercises
Posttest
Cumulative Review Exercises
10. Measurement and Units
Pretest
10.1 U.S. Customary Units
10.2 Metric Units and Metric/U.S. Customary Unit Conversions
Key Concepts and Skills
Review Exercises
Posttest
Cumulative Review Exercises
11. Basic Geometry
Pretest
11.1 Introduction to Basic Geometry
11.2 Perimeter and Circumference
11.3 Area
11.4 Volume
11.5 Similar Triangles
11.6 Square Roots and the Pythagorean Theorem
Key Concepts and Skills
Review Exercises
Posttest
Cumulative Review Exercises
Appendix
Scientific Notation
Answers
Gloss |
Find a Hammond, IN Precalculus
...The Complex Number System
Topics may include performing arithmetic operations with complex numbers, representing complex numbers and their operations on the complex plane, and using complex numbers in polynomial identities and equations. Algebra
Seeing Structure in Expressions
Topics may inclu... |
The guiding principles of the Mathematics syllabus direct that Mathematics as taught in Caribbean schools should be:
relevant to the existing and anticipated needs of Caribbean society;
related to the ability and interest of Caribbean students;
aligned to the philosophy of the educational system.
These principles focus attention on the use of Mathematics as a problem solving tool, as well as on some of the functional concepts which help to unify Mathematics as a body of knowledge. The syllabus explains general and unifying concepts that facilitate the study of Mathematics as a coherent rather than as a set of unrelated topics. |
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