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Posts in category Number
Casio Education have videos which clearly explain how to use their graphics calculator for the most popular applications in the General Mathematics course in NSW. There is are 2 PDFs that go with each video that can be printed and distributed to students.
While students need to be proficient at performing calculations without the graphics calculator function (as these are increasingly being included in HSC examinations), they should be familiar with using their graphics calculator to quickly perform the calculation.
When using a graphics calculator, the focus changes for mere computation to understanding of the question and problem solving. Students do not have to be concerned with the automated process of calculation getting in the way of them understanding and learning.
Topics include:
Financial Mathematics
Compound Interest
Present Value
Future Value (no video, just PDF at time of post)
Algebraic Modelling
Developing a model
Using a model
Refining a model
Verifying a model
There are many more class activites and dowloads that can be found here. |
Math 150 is an introduction to the theory and practice of mathematics with a focus on the role of creativity, experimentation and imagination. The course is intended to be accessible to anyone with three and one half years of high school mathematics. |
Mathematics
The Mathematics department at St John Fisher aspires to the highest standards of excellence in teaching and learning for all our students.
We will be a source for the promotion of problem solving, analytical thinking and utilizing technology. We will produce high quality mathematical thinking students that are well prepared to enter the work force or aspire to higher education.
We live in a mathematical world where if we decide on a purchase, choose an insurance or health plan, or use a spreadsheet we rely on mathematical understanding. The World Wide Web, CD-Roms and other media disseminate vast quantities of quantitative information. The level of mathematical thinking and problem solving needed in the workplace has increased dramatically over the years.
In such a world those who understand and can do mathematics will have opportunities that others do not. Mathematical competence opens doors to productive futures. A lack of mathematical competence closes those doors.
Students have different abilities, needs and interests yet everyone needs to use mathematics in his or her personal life, workplace and in further study. At St John Fisher we believe that all students deserve an opportunity to understand the power and beauty of mathematics and embrace it into their lives. |
MATLAB & Simulink Student Version 2012a
Description
Get the essential tools for your courses in engineering, math, and science.
MATLAB® is a high-level language and interactive environment that lets you focus on your course work and applications, rather than on programming details. It enables you to solve many numerical problems in a fraction of the time it takes to write a program in a lower-level language such as Java™, C, C++, or Fortran. You can also use MATLAB to analyze and visualize data using automation capabilities, thereby avoiding the manual repetition common with other products.
The MATLAB in Student Version provides all the features and capabilities of the professional version of MATLAB software, with no limitations. There are a few small differences between the Student Version interface and the professional version of MATLAB:
The MATLAB prompt in Student Version is EDU>>
Printouts contain this footer: Student Version of MATLAB
For more information on this product please visit the MathWorks website:
IMPORTANT NOTE:Proof of student status is required for activation of license
Features
Contains R2012a versions of:
MATLAB
Simulink
Symbolic Math Toolbox
Control System Toolbox
Signal Processing Toolbox
Signal Processing Blockset
Statistics Toolbox
Optimization Toolbox
Image Processing Toolbox
Student Version also comes with complete user documentation on the CD Rom.
IMPORTANT NOTE:Proof of student status is required for activation of license
New to this Edition
The 2012a release includes 2 important new features:
Target Hardware support directly from Simulink: Of special interest to educators is the addition of Simulink Control Design and Simulink features to enable project-based learning. Student Version now includes built-in Windows support to run Simulink models on low-cost target hardware, including LEGO MINDSTORMS NXT and BeagleBoard. With a click your model moves from simulation onto hardware, further increasing your return on Model-Based Design with Simulink |
Saint Davids, PA Precalculus...Combinatorics studies the way in which discrete structures can be combined or arranged. Graph theory deals with the study of graphs and networks and involves terms such as edges and vertices. This is often considered a very specific branch of combinatorics |
1s Upon A Time by Richard Kerr
Price: Free! 3840 words.
Language: English. Published on April 4, 2011. Nonfiction » History » History of things.
(4.00 from 1 review)Calculus Fundamentals Explained by Samuel Horelick
Price: $9.00 USD. 34400 words.
Language: English. Published on October 4, 2009. Nonfiction » Education and Study Guides » Study guides - Mathematics.
This textbook is written for everyone who has experienced challenges learning Calculus. This book really teaches you, helps you understand and master Calculus through clear and meaningful explanations of all the ideas, concepts, problems and procedures of Calculus, effective problem solving skills and strategies, fully worked problems with complete, step-by-step explanations. |
Affine flag manifolds are infinite dimensional versions of familiar objects such as Gramann varieties. The book features lecture notes, survey articles, and research notes - based on workshops held in Berlin, Essen, and Madrid - explaining the significance of these and related objects (such as double affine Hecke algebras and affine Springer fibers)... more...
There is a contest at a school to design a new playground. The students use blocks to build their models. As they build, they use three-dimensional shapes. Some students build a train out of blocks for the younger students to play on. Can you guess which three-dimensional shape they use for the train's wheels? Read to find out which design wins.... more...
The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characterizes both euclidean and hyperbolic geometry with respect to natural properties of (general) translations and general distances of X. Also for these spaces X, it studies... more...
You, Too, Can Understand Geometry - Just Ask Dr. Math ! Have you started studying geometry in math class? Do you get totally lost trying to find the perimeter of a rectangle or the circumference of a circle? Don't worry. Grasping the basics of geometry doesn't have to be as scary as it sounds. Dr. Math-the popular online math resource-is here to help!... more...
You, too, can understand geometry---- just ask Dr. Math ? ! Are things starting to get tougher in geometry class? Don't panic. Dr. Math--the popular online math resource--is here to help you figure out even the trickiest of your geometry problems. Students just like you have been turning to Dr. Math for years asking questions about math problems,... more...
The family in this book is moving to a new neighborhood. They have a lot of work to do! They need to unload the moving truck, unpack boxes, and put everything away. The kids make new friends and discover all the fun they can have with the empty boxes. While building forts from the empty packing boxes, the kids discover many new shapes and their dimensions.... more...
A genuine introduction to the geometry of lines and conics in the Euclidean plane. Example based and self contained, with numerous illustrations and several hundred worked examples and exercises. Ideal for undergraduate courses in mathematics, or for postgraduates in the engineering and physical sciences. more...
Like other areas of mathematics, geometry is a continually growing and evolving field. Computers, technology, and the sciences drive many new discoveries in mathematics. For geometry, the areas of quantum computers, computer graphics, nanotechnology, crystallography, and theoretical physics have been particularly relevant in the past few years. There... more... |
Mathematics for Physicists
9780534379971
ISBN:
0534379974
Pub Date: 2003 Publisher: Thomson Learning
Summary: This essential new text by Dr. Susan Lea will help physics undergraduate and graduate student hone their mathematical skills. Ideal for the one-semester course, MATHEMATICS FOR PHYSICISTS has been extensively class-tested at San Francisco State University--and the response has been enthusiastic from students and instructors alike. Because physics students are often uncomfortable using the mathematical tools that they... learned in their undergraduate courses, MATHEMATICS FOR PHYSICISTS provides students with the necessary tools to hone those skills. Lea designed the text specifically for physics students by using physics problems to teach mathematical concepts.[read more] |
Description
Practice Makes Perfect has established itself as a reliable practical workbook series in the language-learning category. Practice Makes Perfect: Algebra, provides students with the same clear, concise approach and extensive exercises to key fields they've come to expect from the series-but now within mathematics. This book presents thorough coverage of skills, such as handling decimals and fractions, functions, and linear and quadratic equations. Practice Makes Perfect: Algebra is not focused on any particular test or exam, but complementary to most algebra curricula. Because of this approach, the book can be used by struggling students needing extra help, readers who need to firm up skills for an exam, or those who are returning to the subject years after they first studied algebra.
Recommendations:
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Early Career Profiles:
Recent bachelors-level graduates in the mathematical sciences
Name:
Tracy Stone Johnston
Undergraduate
school: Northeastern StateUniversity
Position:
Mathematics Educator
Company:
Eagle-SagonalIndependentSchool
Industry
Sector: Education
What she does:
Tracy Stone Johnston is a first year
professional teacher for Eagle-SagonalIndependentSchool.She currently teaches eighth grade
Pre-Algebra and Honors Algebra I classes.Tracy
works to instill in young people not only the ability to solve math
problems, but the importance of math in their lives as well.
Math on the job:
In
general the math skills Tracy
uses in her job are basic math, algebra, and geometry.Of course, averaging and normalizing
scores is a big part of her paper work.Tracy
found many of the projects she was involved with during her internships
interesting, but her favorite dealt with proportions and scale.The class was split up into small groups
and was told to take accurate measurements ofa Barbie doll.Through the lesson, the students not
only learned how to use scale and proportion, but they also learned just
how unrealistic Barbie is.
Tracy's background:
Tracy graduated from NortheasternStateUniversity with a
B.S. degree in Secondary Mathematics Education in December, 2004.She says that she will be calling upon
all the math skills she has acquired through both school and 20 years of
tutoring.When asked what other
skills are needed, she simply said, "There are too many to
name."
Advice for students:
Her
very important advice to leave with any high school or college student
interested in pursuing mathematics is to "hang in there and form
study groups whenever possible.Do
your best to really understand the material that is being presented
because it is more important to learn than to make an A." |
Excellent resource for the class! I like your style and I'm interested in your products and store! I'm your new follower! You can visit my store and leave a comment if you wish! hugs and Happy Easter! Hernan
This lesson is the introduction to a unit on Functions for Algebra 2 Honors students. The lesson is taught at the beginning of the school year when students may not be quite prepared for the rigor of Algebra 2 Honors. It is just a general review of the basic vocabulary that will be needed throughout the unit. While we may think the lesson is touching only at the surface, students continue to struggle throughout the school year with domain, range, and function notation.
It is interesting to discuss the ideas of continous domains and discrete domains for Example #3 and the idea that function notation indicates the coordinate. Both of these ideas are introduced to students in this textbook here and the understanding continues to grow through the next two courses. I would be glad to send you another lesson for your dissatisfaction. Contact me at [email protected]
no, you can teach the lesson by just placing the Foldable under a document camera. I use a wireless slate and the smart notebook software. This way I can use the lesson repeatedly and write on the smart lesson fresh each class. I believe there are other ways that smart software can display. possibly with an iPad and splashtop software. you might ask a tech person in your school.
May 21, 2013
Julie Larsen re: ALG 2 UNIT: Sequences and Series FOLDABLES ONLY
The quality of the notes is great. My big question is...how do I tell which is page 1, 2, 3, etc. It seems essential in order to copy the pages correctly to make the foldable. I can figure some out based on the example numbers, however, is the Arithmetic Sequences with the vocab page 1, 2, etc. What page number is the Arithmetic sequences with the formulas?
The foldable was created in order. If your printer copies on two sides, you can choose to flip them on the short side and they copy double sided in the correct order. The vocabulary is always the first or front page and the side with the blank sheet on the third page of the document will be the last sheet or page 8 on the foldable. My students glue this blank page into their composition books to save them in order of their textbook lessons. In this particular lesson, the formulas appear on the 5th page of the foldable. If you need more assistance, you can email me at [email protected]
You might think this is a crazy question, but I am trying to figure out something. On problem B, which has 2Z + B = ____, if you only have say 6 brown or Z M&M's, how are you showing the 2 times Z with the M&M's? My husband and myself are both math teachers and we are trying to use this lesson as a dynamic lesson in an 8th grade math classroom. We love the idea. Thank you! my email is [email protected] or [email protected]
Amy, If I understand your question correctly, I think you mean since Z=Brown M&M's and B=Blue M&M's if you have 6 brown the question in the B prompt has two equations 2Z + B = ___ and Z-B = ____.
Students would write 2Z + B = 6 and Z-B=6.
Now, say that the students bag had only 3 blue M&M's, and had 6 brown M&M's. Their system would now read2Z+B=9 and Z-B=3. When students use substitution method or elimination method, they will get Z=6 and B=3 for the answer if their algebra is correct. Hope this helps.
Yes, each lesson has a full answer key. Whether you purchase the single lesson or the set of handouts only or Smartboard Lessons only, each has the answer key provided.
April 7, 2013
mhilvert
I recently bought the Families of Functions Foldable book and am having a hard time figuring out how to put it together correctly. Do you have any suggestions? Everytime I put it together the 'summary of transformations' page is between #5/6 and #7/8?
Thanks
I have uploaded a more detailed assembly directions for you which shows the layout for printing. You can see this free document at Foldable Assembly Directions.
If you still have trouble, please let me know. Thanks.
My colleague and I bought this unit but we are having a hard time with the foldables. I've created this type of booklet before. I tried to create yours several times but the pages are all out of order. The question I have is about the copies. Is there a certain way these need to be copied?
Yes, the copies should be double sided. If you have a printer that prints on both sides of the paper, you can choose to flip the paper on the short side to create the proper order. If you print the four pages single-sided and us a copy machine, orient the pages so that page 1 and page 3 are up and pages 2 and 4 are down. I will send you a snapshot personally, if you will send me your email address. I'm sorry you are having difficulty. pre-calculus and calculus threeThat's a good question. I use Smart Notebook 11 software to write my lessons for display. They are shared with my students through a projector but I use an wireless slate in order to teach the lessons "Live" to my students. The smart file that I sell is a blank document. You need to have the ability to work the problems on some wireless writing tablet. There are many that are compatible with Smart Technology products. I don't believe just a projector will work for this product. You can purchase the foldables only for this unit and write on that document under your document camera to display through the projector. If this is confusing, ask an "IT" person at your school. Unless you have a wireless tablet it would waste your money.
Thanks,
Jean Adams
Hi Chris,
Thanks for the vote on my clean writing style. Yes, I do sell the whole Quadratics Unit as a set. You can purchase the Foldables only at or Smart Notes only, as well.
My students buy a small composition book at the beginning of the school year. The last page of each Foldable is blank so they apply glue and glue them into their book each day. I have some students who work their homework after each lesson in the composition book. They use two books each year in that case. Then, I have some students who store their lessons in a Gallon-Sized Zip-Lock Bag. I really see "ownership" in what they do by the way they protect each document and never want me to skip any example.
Hi Amy,
Yes they will. I've got three more to finish. Hopefully, today. There are nine in all. I got behind with Thanksgiving and Christmas. Sorry. I know you are waiting. I'm working on them now.
Thanks for your loyalty.
Jean
Yes, it should include 5 documents, a cover page, the foldable as a PDF file, the Final notes as a PDF File, the SmartBoard Lesson, and direction for making the foldable. I'll repost the files for you. Sorry for the inconvenience.
Thanks for letting me know.
Jean Adams
Is it intended that the section of student notes on Extrema on an Interval is missing some information and examples that are in the filled in teacher version? The other units I have purchased matched up exactly to one another...
I'll check into that for you. Thanks for the watchful eye.
Jean
Yes Amy, Actually my students had a difficult time with this idea last year. They forgot to check the endpoints, so we went back to the notes, revisited the procedure, thought about a few "What if" situations, and I just left that in the presentation to give a little extra while we talked and taught the lesson. So it is intentional.
November 26, 2012
mkesselman re: Blank Unit Circle Small
You have an extra degree symbol at both 90 degrees and at 270 degrees.
Two questions: The file '4 Real Zeros of Polynomial Functions Cover.pdf' is generating an error message from Adobe that the file is damaged and cannot be repaired.
What program is needed to open the file with the 'notebook' extension? Is this a SmartBoard file?
Yes, the *.PDF file was corrupt. I have uploaded a version that should work now. Please let me know if it doesn't.
The notebook extension is a SmartNotebook 11 document. You can open with a Smart Notebook 11 software, and I believe it is compatible with Prometheus products also. I personally use my presentation files only with the Smart Airliner Wireless slate.
No, I don't. I have a Smart Airliner Wireless Slate. It costs about $200 and allows me to walk around my room. I actually had an older model of SmartBoard and gave it up when the Wireless slate came out about 3 years ago. I love it. I'm no longer tied to the front of the classroom. Even my students can write on the slate from their seats. The software SMART NOTEBOOK 11 is a separate item, I write the lessons with that software and use the slate to teach the lesson.
Jean,
I cannot get the Using Linear Models flipchart to open, the PDF's will open, and I have no problem opeining any other flipcharts. Is there any way you can email me the flipchart, my email is [email protected].
Thanks.
Amy,
I have the whole year available, but I'm currently uploading one unit at a time. There are seven total units. My future plans are to offer the entire year as a bundle, but that is in the future. I'm glad that you like my lessons and appreciate your positive feedback. I will definitely offer the entire year at a reduced price, just not sure what that will be at the present time.
Jean
Hi Layla,
When we have open house, I use a quick lesson on making a foldable with my parents then I have them take notes on the foldable about our class, their students needs, and where to go for help. They leave with a product in hand on how to contact me, my website info, where to find tutoring, and what calculator needs their student will have.
Jean
November 4, 2012
vwasmuth re: CALCULUS DIFFERENTIATION UNIT: Lesson 7 Related Rates
I have downloaded "related rates" but as I tried to extract it , a black window appeared with an error message . I updated my adobe reader. It looked for adobe air, so I updated it, but it could not continue due to an apparent error.
Hunter, I have a test with most of those items that I can share with you. It covers the entire chapter from the Larson PreCalculus text if that would interest you. Email me: [email protected]
February 4, 2012
TEACHING EXPERIENCE
Jean has taught grades 8 through 12 for over 18 years in the Central Florida area. In addition she shares her strategies with colleagues through local and national math conferences.
MY TEACHING STYLE
Jean is known for her energetic, hands-on strategies that engage students to learn cooperatively. There is always something new happening in her classroom.
HONORS/AWARDS/SHINING TEACHER MOMENT
1998-Teacher of the Year at Thomas Jefferson Junior High, Merritt Island, FL.; 2001-Teacher of the Year at George Jenkins High School, Lakeland, FL.; 2001-AIChE Mathematics Teacher of the Year,Polk County, FL.; National Board Certified Teacher, Adolescent Young Adult Mathematics,2001.2009-2010 Math Teacher of the Year, Orange County Public Schools
Jean Adams teaches AP Calculus AB, Pre-Calculus, Trigonometry,and Analytic Geometry in the Metro-Orlando area. She is the owner an eduational website with instructional lessons and teacher resources for Algebra and higher ( Jean is an active teacher-trainer when opportunities arise. |
Dfs Roots
Geometrical constructions with ruler and compass. Geometrical constructions with ruler and compass. Write a source file with a provided editor and see output of your construction. There is a step-by-step option to see all steps of a construction. Constructions of polyhedrons with many examples....With Advanced Roots Informer you will be able to create a list, automatically, of the root of numbers with certain index, to this work, you just need insert the index and a limit in this application. Create a list of root of numbers with certain index fast and easy.
The program automatically solves algebraic equations of any order written in any form. Enter your equation and click just one button! Step by step the program will solve the equation, find its roots and describe all its operations. The program allows you to solve algebraic equations in the automatic mode. You just enter an equation in any form without any preparatory operations. Step by step Equation Wizard reduces it to a canonical form performing all necessary operations....
With this software you will be free to choose what kind of root of a number or data arithmetic you want to calculate. With this software you will be free to choose what kind of root of a number or data arithmetic you want to calculate. Advanced Roots Calculator is a tiny math toolwPrime is a benchmarking software designed to use a highly multi-threaded approach to calculating the square-roots of large amounts of numbers (up to 32 billion at this stage!)....
Linear equations are equations involving only one variable, like x, and nothing complicated like powers or square roots. With this special educational program you learn how to resolve them. You can choose out of four different exercises, and to challenge your knowledge you can play the falling blocks style game 'Valgebra': By manoeuvring the falling x-terms and numbers, you resolve an equation. But take care.., if you make a mistake, you are...
Easy to use, intuitive program to visualize and study functions of one variable to find roots, maxima and minima, integral, derivatives, graph. Results, including the graph, can be saved or printed. You can also copy the graph to the clipboard, which you can then paste where you please (Word, Paint, etc.). You have one-click control of the graph with zooming, panning, centering, etc. Includes a help file with instructions, example and methodology |
New GCSE Maths - Grade A/A* Booster Workbook: Edexcel Linear
Part of the
New GCSE Maths series
Paperback • 978-0-00-741003-3 • Sep
2010
£6.25
Web-only price: £5.00
Availability:
In stock
Collins New GCSE Maths Edexcel Linear Grade A/A* Booster Workbook is an ideal tool for extra practice at the right level for students to excel and achieve an A* in their exams. It is packed full of lots of grade B-A* practice, spot the errors questions and assessing understanding and problem solving.
About this resource
•Packed full of all new content this write-in workbook is written by a trusted maths teacher •Packed full of all new content this write-in workbook is written by a trusted maths teacher •Perfect for students who are aiming for or need extra practice at grades B, A and A* •Enable progression with a section of Assessing understanding and problem solving type questions to focus on key topics required in the new exams •Encourage analytical thought processes with a Spot the errors section where students improve and annotate others' responses to questions •Assess progress with Grade progression maps that clearly show how to move from a B to A* •Provide your student with the right tools with a Formulae sheet and How to interpret language of exams pages along with a tear-out Answer section |
Algebra For College Students - 9th edition
Summary: Kaufmann and Schwitters have built this text's reputation on clear and concise exposition, numerous examples, and plentiful problem sets. This traditional text consistently reinforces the following common thread: learn a skill; practice the skill to help solve equations; and then apply what you have learned to solve application problems. This simple, straightforward approach has helped many students grasp and apply fundamental problem solving skills necessary for future mathematics c...show moreourses. Algebraic ideas are developed in a logical sequence, and in an easy-to-read manner, without excessive vocabulary and formalism. The open and uncluttered design helps keep students focused on the concepts while minimizing distractions. Problems and examples reference a broad range of topics, as well as career areas such as electronics, mechanics, and health, showing students that mathematics is part of everyday life |
This module presents a real-world context in which mathematics skills are used as part of a daily routine. The context is the textile production area of machine operations, and the module aims to help students understand the significance of mathematics skills in interpreting charts and graphs. Materials in the module, most of which are designed for the teacher to duplicate and distribute to students, include the following: (1) information on careers as textile machine operators; (2) a task to be performed with a handout sheet needed for the task; and (3) questions for analysis, related problems, and a teacher's answer key. (KC)
Abstractor:
N/A
Reference Count:
N/A
Note:
For other teacher's guides in this series, see CE 064 301-307.
Identifiers:
N/A
Record Type:
Non-Journal
Level:
1 - Available on microfiche
Institutions:
Partnership for Academic and Career Education, Pendleton, SC.
Sponsors:
South Carolina State Dept. of Education, Columbia. Office of Vocational Education.; Fund for the Improvement of Postsecondary Education (ED), Washington, DC. |
Book Description: Although Edition provides an introduction to numerical methods, incorporating theory with concrete computing exercises and programmed examples of the techniques presented. Covering a wide range of numerical applications that have immediate relevancy for engineers, the book describes forty-nine programs in Fortran 95. Many of the programs discussed use a sub-program library called nm_lib that holds twenty-three subroutines and functions. In addition, there is a precision module that controls the precision of calculations.Well-respected in their field, the authors discuss a variety of numerical topics related to engineering. Some of the chapter features include…The numerical solution of sets of linear algebraic equationsRoots of single nonlinear equations and sets of nonlinear equations Numerical quadrature, or numerical evaluation of integralsAn introduction to the solution of partial differential equations using finite difference and finite element approachesDescribing concise programs that are constructed using sub-programs wherever possible, this book presents many different contexts of numerical analysis, forming an excellent introduction to more comprehensive subroutine libraries such as the numerical algorithm group (NAG).
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$6.29
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Grading Criteria for MTH 4660 Spring 2012
Here is how the final course grade will be calculated. If your actual scores do not fit exactly into this scheme, a judgment call will be made for your final grade. Performance on presentations and the final are weighted very heavily. Try to have a very good record doing presentations going into the final. A failing grade on any of: Proof presentations, Midterm, or Final exam will result in a failing grade. Generally, you can safely assess your grade by looking at the mode of the four components of the course.
Final Grade
Components
A
B
C
F
Proof presentations
Many presentations relative to the average in class. Most presentations M with at least a few E's Ready to present 90 percent or more of the classes.
On par with the average number of presentations for the class. Most presentations at least M. Ready to present 80 percent of the classes
More than a few below M or fewer presentations than average.
Few presentations and/or several below M Often not prepared to present. Advice: Avoid this outcome !
In – Class Participation
Helpful, attentive class and team participant. Asks questions and often finds flaws in proofs.
Hints for success in Topology
Stay engaged and find ways to show that you have mastered the material. All of you have amassed a toolbox of techniques for solving problems and writing proofs. To get to this level you need to have been successful in past courses. The grading in this course may seem unfamiliar to you, but if you have succeeded in mathematics in the past you can succeed in this format. You will be required to be creative and to communicate effectively, neither the hallmark of a typical mathematics course but essential to anyone who plans to use mathematics at a high level. To succeed you may have to change the way you study. Memorization of lots of proofs probably will not help but time spent brainstorming in a quiet room with a pencil/pen will pay off. Don't expect to write down a correct proof in linear fashion. If you are used to looking for answers on the web, stop. It will be a waste of time and worse a violation of course policies. Even if you manage to find the right proof you won't be able to present it/reproduce it on a test.
If you want a good grade in this class, pay attention to detail. Take care of the things you can control, language, neatness, attendance, correctness, etc. Do all of the proofs you can then look back at the harder proofs and/or try to rework some of your proofs in a better or new way. Volunteer to present as often as you can, try all of the proofs even if you can only start them, incomplete work may be useful for presentations. Remember correctness is expected and so is not enough for an A, meeting expectations on all aspects of the course nets B. To get an A you have to go beyond what is merely expected. Lastly, try to make yourself indispensable to the class, be there and participate. |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
their education.
Solution Keys to Quiz 7 1. (10 pt) Find a vector function that represents the curve of intersection of the following two surfaces. The cylinder x2 + y 2 = 4 and the surface z = xy. Solution: From the cylinder x2 + y 2 = 4, one can parametrize x and y by t
Integrative Biology 335Introduction to PollinationThere are two critical stages in the life cycle of a flowering plant: 1. Pollinationthe transfer of pollen from anther to stigma, usually most effective on a different plant. As we saw in the lecture on
Math 102 Sections 1 and 3 Final Exam ReviewAs you know, the final exam will be held on Tuesday, May 6, from 10:30-12:30 in CLAS 110. The exam will consist of six questions, possibly consisting of multiple parts, and a bonus opportunity. Each question wil follo
Scribed Notes for 10-24-07Class cancelled next week.DISCOURSE REPRESENTATION THEORY-> DRT is a kind of algebra for interpreting discourses as opposed to sentences. Sentences are no longer the scope over which an interpretation is calculated. -> Discou
Fundamentals of CS I (CS151 2001S)The DrScheme programming environmentNote: Each member of your group should do this lab working within his or her own account. Starting DrScheme DrScheme language options DrScheme's Interactions Window DrScheme's definit
Fundamentals of CS I (CS151 2001S)Laboratory: Input and OutputSummary: In this laboratory, you will experiment with the use and application of some of Scheme's basic input and output procedures. Procedures Covered: read, write, and display. Contents Exe
Fundamentals of CS I (CS151 2001S)Laboratory: More Higher-Order ProceduresExercise 1: Insertinsert is a procedure which takes two parameters, a binary procedure and a list, and gives the result of applying the procedure to neighboring values. There are
Fundamentals of CS I (CS151 2001S)Numbers in SchemeWhile Scheme excels at symbolic and list processing, it is also quite capable of doing numeric computation. Scheme provides a variety of procedures for dealing with a variety of categories of numbers. P
Fundamentals of CS I (CS151 2001S)Boolean Values and Predicate ProceduresA Boolean value is a datum that reflects the outcome of a single yes-or-no test. For instance, if one were to ask Scheme to compute whether the empty list has five elements, it wou
Fundamentals of CS I (CS151 2001S)Conditional EvaluationWhen Scheme encounters a procedure call, it looks at all of the subexpressions within the parentheses and evaluates each one. Sometimes, however, the programmer wants Scheme to exercise more discre
Fundamentals of CS I (CS151 2001S)Comments in SchemePrograms are intended to be read both by people and by computers. Because people understand much richer and more flexible notations than computers - real languages, as opposed to the extremely limited
Fundamentals of CS I (CS151 2001S)Pairs and Pair StructuresBox-and-pointer diagrams Pairs that are not lists A Pair Predicate Recursion with pairs As we have seen, Scheme uses cons to build lists. As you may recall, cons takes two arguments. Up to this
Fundamentals of CS I (CS151 2001S)Recursion with Natural NumbersWhile the recursive procedures weve written so far have used lists as arguments, we can also write recursive procedures with numbers as arguments. Like lists, natural numbers have a recursi
Fundamentals of CS I (CS151 2001S)Preconditions and PostconditionsProcedures as Contracts Generating Explicit Errors Husks and Kernels Documentation Several of the Scheme procedures that we have written or studied in preceding labs presuppose that their
Fundamentals of CS I (CS151 2001S)Naming Values with Local BindingsRedundant Work Let Sequencing Bindings with let* Local Procedures So far we've seen three ways in which a value can be associated with a name in Scheme: The names of built-in procedures,
Fundamentals of CS I (CS151 2001S)Randomness and SimulationIntroduction The random Procedure Simulating a DieIntroductionMany computing applications involve the simulation of games or events, with the hope of gaining insights and identifying underlyin
Fundamentals of CS I (CS151 2001S)Local Procedure Bindings and RecursionIntroduction Local Procedure Bindings A Problem: Recursive Procedure Bindings A Solution: letrec Husk-and-Kernel with Local Kernels An Alternative: The Named letIntroductionAs you
Fundamentals of CS I (CS151 2001S)Tail RecursionSummary: How to make your recursive procedures run more quickly by taking advantage of a program design strategy called tail recursion.Recursive StrategiesIn writing recursive procedures, you may have no
Fundamentals of CS I (CS151 2001S)Procedures that Return Multiple ValuesWhen we invoke any of the procedures that we have discussed so far in the course, we get back a single result. However, there are many computations that we can describe most natural
Fundamentals of CS I (CS151 2001S)Variable-Arity ProceduresA procedure's arity is the number of arguments it takes. For instance, the arity of the cons procedure is 2 and the arity of the predicate char-uppercase? is 1. You'll probably have noticed that
Fundamentals of CS I (CS151 2001S)Merge SortSummary: In a past reading and the corresponding laboratory, we've explored the basics of sorting using insertion sort. In this reading, we turn to another sorting algorithm, merge sort.The Costs of Insertion
Fundamentals of CS I (CS151 2001S)RecordsIn our exploration of Scheme, we've seen a number of data structures that allow us to organize data. A list is a dynamic data structure with a variable number of components. A vector is a data structure with a fi
Fundamentals of CS I (CS151 2001S)Object-Oriented ProgrammingRecords, RevisitedAs you may recall, one of the key issues in the design of records is that the record designer have some control over the use of records. In particular, the designer might wa
ProjectChE 400 Applied Chemical Engineering Calculations Fall 2007 Project Due 11/09/07 General Comments 1. As explained in the syllabus you will need to write a report in the format of a technical memorandum about your project. Examples of how to write |
Welcome Back!!! updated January 8, 2012
Welcome to my class! I am so excited about this year. We are going to learn a lot and have fun doing so. In order for this to happen, I need you to do a few things for...
CCGPS Coordinate Algebra
This is the first course in a sequence of courses designed to provide students with a rigorous
program of study in mathematics. It includes radical, polynomial and rational expressions, basic
functions and their graphs, simple equations, complex numbers; quadratic and piecewise
functions, sample statistics, and curve fitting.
I have scheduled weekly help sessions for Coordinate Algebra on Monday afternoons, Wednesday mornings, and Thursday afternoons. I will be available on these days and times unless I have a department meeting, faculty meeting, or parent conference.
This is the second in a sequence of mathematics courses designed to prepare students to take AB or BC Advanced Placement Calculus. It includes right triangle trigonometry; exponential, logarithmic, and higher degree polynomial functions; matrices; linear programming; vertex-edge graphs; conic sections; planes and spheres; population means, standard deviations, and normal distributions.
I have scheduled weekly help sessions for Accelerated Math 2 on Tuesday mornings, Tuesday afternoons, and Thursday mornings. I will be available on these days and times unless I have a department meeting, faculty meeting, or parent conference. |
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Probability
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Probability | Basic Probability, basic rules
This is a brief article on probability that includes interpretations of probability and a few probability rules: the addition rule, the inclusion-exclusion rule, and the law of total probability. There are links to related Wolfram MathWorld articles. |
Appropriate for one- or two-semester Advanced Engineering Mathematics courses in departments of Mathematics and Engineering. This clear, pedagogically rich book develops a strong understanding of the mathematical principles and practices that today's engineers and scientists need to know. Equal authors help students "see the math" through their focus on functions; visual emphasis; side-by-side algebraic and graphical solutions; real-data applications; and examples and exercises. By remaining focused on today's students and their needs, the authors lead students to ma |
This course is designed to teach students spatial and relational mathematics through the use of logic, reasoning, coordinate planes, diagrams, constructions, and real world applications. Students will be using a variety of technology and media to explore basic geometry problems and how geometry plays a role in our daily lives. Basic knowledge of Algebra concepts in finding solutions, using real numbers and basic operations, and problem solving are the basis for starting this course.
Goals/Objectives:
To teach and apply the skills to use reason and think logically when confronted with geometrical and real life situations.
To build an understanding of spatial relationships to be used in practical applications.
To foster a greater appreciation for the art of mathematics.
To fulfill the credit requirement for high school mathematics and graduation. |
tion reform. A parent armed with the advice in this book could do a lot to help improve a child's education.?Amy Brunvand, Univ. of Utah Lib., Salt Lake CityCopyright 1998 Reed Business Information, Inc.
Reviewed by aardwolf11, (Calgary, AB)
athematical journey".
Reviewed by "gloriungus", (albuquerque, nm)
kind of results we want from their students.
Reviewed by Daryl R. Anderson "dander", (Trumansburg, NY USA)
You've probably heard that youngsters who are anxious about math also do poorly in math. A lot of folks thought this was just because students with limited ability appropriately worried about the subject. Not so!Just the other day I clipp
Reviewed by "mangelone", (NUTLEY, NJ USA)
When I think of Dr. Patricia Kenschaft, the first image that enters my mind is that of a Unicorn. Dr. Kenschaft is a unique person for which you would be hard pressed to find an equal. Her ability to teach mathematics to virtually anyone
Algebra and Trigonometry
Reviewed by "the_big_smooth", (New York)
This book comprehensively and completely covers all topics of advanced Algebra, and allows the reader to fully understand both the basics of Trigonometry, as well as enlighten him/her on some advanced topics in this field. It is well-writ |
Game-theoretic reasoning pervades economic theory and is used
widely in other social and behavioral sciences. An Introduction
to Game Theory, by Martin J. Osborne, presents the main
principles of game theory and shows how they can be used to
understand economic, social, political, and biological phenomena.
The book introduces in an accessible manner the main ideas behind
the theory rather than their mathematical expression. All concepts
are defined... more...
The Sixth Edition of this acclaimed differential equations book remains the same classic volume it's always been, but has been polished and sharpened to serve readers even more effectively. Offers precise and clear-cut statements of fundamental existence and uniqueness theorems to allow understanding of their role in this subject. Features a strong numerical approach that emphasizes that the effective and reliable use of numerical methods often... more...
Clear and Concise. Varberg focuses on the most critical concepts. This popular calculus text remains the shortest mainstream calculus book available – yet covers all relevant material needed by, and appropriate to, the study of calculus at this level. It's conciseness and clarity helps you focus on, and understand, critical concepts in calculus without them getting bogged down and lost in excessive and unnecessary detail. It is accurate,... more...
While many think of algorithms as specific to computer science, at its core algorithmic thinking is defined by the use of analytical logic to solve problems. This logic extends far beyond the realm of computer science and into the wide and entertaining world of puzzles. In Algorithmic Puzzles, Anany and Maria Levitin use many classic brainteasers as well as newer examples from job interviews with major corporations to show readers how to apply... more...
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Success in your calculus course starts here! James Stewart's
CALCULUS: EARLY TRANSCENDENTALS texts are world-wide best-sellers
for a reason: they are clear, accurate, and filled with relevant,
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Help your students see the light.With its myriad of techniques, concepts and formulas, business statistics can be overwhelming for many students. They can have trouble recognizing the importance of studying statistics, and making connections between concepts.Ken Black's fifth edition of Business Statistics: For Contemporary Decision Making helps students see the big picture of the business statistics course by giving clearer paths to learn and choose |
Book Description: Unlike reviewing the basics of graph theory, elementary counting formulas, fields, and vector spaces, the book explains the algebra of matrices and uses the König digraph to carry out simple matrix operations. It then discusses matrix powers, provides a graph-theoretical definition of the determinant using the Coates digraph of a matrix, and presents a graph-theoretical interpretation of matrix inverses. The authors develop the elementary theory of solutions of systems of linear equations and show how to use the Coates digraph to solve a linear system. They also explore the eigenvalues, eigenvectors, and characteristic polynomial of a matrix; examine the important properties of nonnegative matrices that are part of the Perron–Frobenius theory; and study eigenvalue inclusion regions and sign-nonsingular matrices. The final chapter presents applications to electrical engineering, physics, and chemistry. Using combinatorial and graph-theoretical tools, this book enables a solid understanding of the fundamentals of matrix theory and its application to scientific areas.
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As a middle school teacher and coach, I have very little spare time. This year, I was asked to teach 2 subjects (one of which I have never taught). Lesson Planet has helped me become more prepared without having to spend hours on the internet searching for ideas. Almost everything I need can now be found with one click of the mouse! calculus worksheet, students evaluate functions and solve problems using the derivative. They apply the rules of limits to solve functions where the limit of x approaches zero. There are 12 problems to solve.
Design an experiment to model a leaky faucet and determine the amount of water wasted due to the leak. Middle schoolers graph and write an equation for a line of best fit. They use their derived equation to make predictions about the amount of water that whould be wasted from one leak over a long period of time or the amount wasted by serveral leaks during a specific time period.
Twelfth graders investigate derivatives. In this calculus lesson plan, 12th graders use technology to explore the basic derivatives and how to choose the proper formula to use them. The lesson plan requires the use of the TI-89 or Voyage and the appropriate application.
Students review vocabulary words for calculus. In this calculus lesson, a list of vocabulary words is provided for students to review. Students may use this list as a review of important terms to know for calculus.
Students practice the concept of graphing associated to a function with its derivative. They define the concepts of increasing and decreasing function behavior and explore graphical and symbolic designs to show why the derivative can be used as an indicator for the behavior.
In this time constant worksheet, students answer 52 questions about the rate of current changes and voltage changes in capacitors. They analyze circuits and determine the time it takes for capacitors to change voltage and they specify voltages at specified times.
In this time constant circuits activity, students answer 23 questions about the design of circuits that need time delays, about capacitors and inductors, and about resistors and the design of circuits. |
This is a test prep CD-ROM. It is self-paced and easy to use, provides feedback on correct and incorrect responses, gives hints that help students work independently, is appropriate for use at school or at home, has a fully automatice man
Multimedia Applications (Glencoe Algebra 2)
Editorial review
This CD-ROM has over 25 virtual activities, is closely correlated to chapter content, has more than 15 career-oriented video clips of mathematics in action, and is appropriate for individual, small group, or whole class instruction.
Glencoe Algebra 1 Spanish Student Edition
Editorial review
An Algebra Program designed for Student Success! From the first day your students begin to learn the vocabulary of algebra until the day they take final exams and standardized tests, these programs strengthen student understanding and pro |
This is a 297 page workbook for Mathematical Literacy, developed by Brombacher and Associates for the Department of Education and published in 2009. Is is aimed at FET Colleges but nothing prevents it from being used at schools. It deals with the basic skills pertaining to Numbers, Patterns and Relationships as well as Space, Shape and Orientation. The solutions to the questions are provided at the back of the workbook. |
Milwaukee, WI AlgebraThe, or in combination with college level algebra.
...It can offer insight into less than informative news articles, medical research, internet polls and more. Once a student understands statistics, he or she is capable of critically evaluating those things people take for granted. Even statistics knowledge is power. |
Locating the Basis of Mathematics in the Self-Interacting Dynamics of Consciousness
Arithmetic is the study of patterns, relations, and operations on numbers. Topics include the arithmetic of integers, fractions, decimal fractions, ratios, and percents, with an emphasis on applications. (0 credits)
Name and Form — Locating the Patterns of Orderliness That Connect a Function with Its Graph and Describe Numerical Relationships
A mathematical function quantifies the relationship between two related quantities and can be used to model change. Functions and their graphs are essential to all branches of mathematics and their applications. Topics: domain and range, average rate of change, graphs, functions (linear, exponential, logarithmic, and quadratic), and applications. (4 credits) Prerequisite: MATH 153
Name and Form — Learning to Relate the Shape of a Graph to Its Corresponding Function
A mathematical function quantifies the relationship between two related quantities and can be used to model change. Functions and their graphs are essential to all branches of mathematics and their applications. Topics: trigonometry, algebra of functions, compositions and inverses of functions, functions (trigonometric, power, polynomial, and rational), and applications. (4 credits) Prerequisite: MATH 161
This course is designed especially for students entering the major in Sustainable Living who do not have the basic algebraic prerequisites for that major. Topics are drawn from college algebra, geometry, functions, and graphs, and these topics are related to problems in Sustainable Living such as landscaping, heat loss, solar and wind energy, and water management. (4 credits) Prerequisite: MATH 152
Exploring the Full Range of Mathematics and Seeing Its Source in Your Self
Mathematics takes place in the imagination, in consciousness, unlimited either by finite measuring instruments, by the senses, or even by the feelings. At the same time, mathematics has strict criteria for right knowledge. The power of mathematics lies in bringing infinity out into the finite and making it useful in everyday life — from deciding which bank offers the best return on money, to medical imaging, to designing textiles, to creating a work of art, to putting a man on the moon. In this course, students explore many different ways in which mathematics expresses, emerges from, and uses infinity and its self-interacting dynamics. They look at the foundation of mathematics in the infinitary processes of set theory, the universe of sets, different sizes of infinity, the continuum and its limit process, sequences and series, infinite replication, and applications of infinity in many areas of life. (4 credits)
Applying Abstractions of Shape and Form to Create Beautiful Concrete Images
Geometry, the study of shape and form, is an essential tool for the visual artist. Topics in this course include symmetry, Euclidean and non-Euclidean geometry, perspective and projective geometry, and fractals. Materials fee: $10 (4 credits)
From Point to Infinity — Using Properties of Shape and Form to Handle Visual and Spatial Data
Geometry gives an understanding of shape, form, and structure that has many applications in mathematics, science, and technology. In-depth study of Euclidean and non-Euclidean geometries and their applications. (4 credits) Prerequisite: MATH 162
Derivatives as the Mathematics of Transcending, Used to Handle Changing Quantities limits, continuity, derivatives, applications of derivatives, integrals, and the fundamental theorem of calculus. (4 credits) Prerequisite: MATH 162 techniques of integration, further applications of derivatives, and applications of integration. (4 credits) Prerequisite: MATH 281 infinite series, functions of several variables and their derivatives, gradient, directional derivatives, vector-valued functions and their derivatives, the Jacobian matrix, and chain rule. (4 credits) Prerequisite: MATH 286
Linear algebra studies linearity, the simplest form of quantitative relationship, and provides a basis for the study of many areas of pure and applied mathematics, as well as key applications in the physical, biological, and social sciences. Topics include systems of linear equations, vectors, vector equations, matrices, determinants, vector spaces, bases, and linear transformations. (4 credits) Prerequisite: MATH 282
This course extends the calculus of a function of a single real variable to functions of several real variables. Topics include maxima and minima, curvilinear coordinates, line integrals, multiple integrals, change of variables, gradient fields, surface integrals, and the theorems of Green, Stokes, and Gauss. (4 credits) Prerequisite: MATH 283
The most concise mathematical expression that describes a continuously changing physical system is a differential equation, which uses derivatives to quantify all possible states of an evolving system in one equation. Topics include first-order differential equations, second-order linear differential equations, power-series solutions, Laplace transforms, numerical methods of solution, and systems of differential equations. (4 credits) Prerequisite: MATH 283
Mathematical logic is the mathematical description of the structure and function of the symbolic language of mathematics. This course develops a rigorous symbolic language, suitable for expressing all mathematical concepts, demonstrates the soundness and completeness of the language, and shows the inherent limitations of such formal systems indicated by Gödel's Incompleteness Theorems. (4 credits) Prerequisite: consent of the instructor
Under the direction of a senior faculty member, students prepare and give lectures, lead tutorial sessions, and write and grade quizzes and exams for a college-level mathematics course. (4 credits) Prerequisite: consent of the instructor
Locating the Finest Impulses of Dynamism within the Continuum of Real Numbers
Analysis is the mathematically rigorous development of calculus based on the theory of infinite sets. The analysis sequence begins with the application of the infinitary methods of set theory to construct the uncountable continuum of real numbers and unfold its topological structure, and then shows how the basic principles of calculus can be logically unfolded from this set-theoretic understanding of the continuum. Topics: infinite sets, completeness, numerical sequences and series, open sets, closed sets, compact sets, connected sets, and continuous functions. (4 credits) Prerequisite: MATH 283
Analysis is the mathematically rigorous development of calculus based on the theory of infinite sets. The analysis sequence begins with the application of the infinitary methods of set theory to construct the uncountable continuum of real numbers and unfold its topological structure, and then shows how the basic principles of calculus can be logically unfolded from this set-theoretic understanding of the continuum. Topics: properties of continuous functions, differentiation, mean value theorem, Riemann integral. (4 credits) Prerequisite: MATH 423
Algebraic Operations as the Self-Interacting Dynamics of a Mathematical System
Algebra is the study of the structures given to sets of elements by operations or relations as well as the structure-preserving transformations between these sets. Topics: groups and subgroups, quotient groups, group homomorphisms, direct sum, kernel, image, Noether isomorphism theorems, and the structure of finitely generated abelian groups. (4 credits) Prerequisite: MATH 286
The Integration and Interaction of Two Algebraic Operations on a Mathematical System
Algebra is the study of the structures given to sets of elements by operations or relations as well as the structure-preserving transformations between these sets. Topics: rings, integral domains, fields, principal ideal domains, unique factorization domains, modules and submodules, tensor products, and exact sequences. (4 credits) Prerequisite: MATH 431
Mathematics Unfolding the Path to the Unified Field — the Most Fundamental Field of Natural Law
Set theory provides a unified foundation for the diverse theories of modern mathematics based upon the single concept of a set. Topics include axioms of set theory, ordinals, transfinite induction, the universe of sets, cardinal arithmetic, large cardinals, and independence results. (4 credits) Prerequisite: MATH 370
Topology shows how all mathematical aspects of shape, structure, and form can be expressed in terms of set theory. Students study topologies and their properties of separation, connectedness and compactness, topological mappings, and the fundamental group of a topological space. (4 credits) Prerequisites: MATH 423 and 431
Students write a substantial paper unifying the knowledge gained from the courses taken during their major and relating this knowledge to deep principles from Maharishi Vedic Science. This paper may take the form of: 1) An integrated summary of main ideas from the courses taken during their major, addressing themes and questions to be provided by the Department of Mathematics, or 2) A paper integrating the 40 Aspects of the Vedic Literature and Raja Raam's discoveries to mathematics. They may relate mathematics to the 40 Aspects of the Vedic Literature as Raja Raam has done for physiology in his book "Human Physiology: Expression of the Veda" and "Ramayan in Human Physiology", or they may explore the significance and consequences of Raja Raam's discoveries for mathematics, or 3) A report of research conducted by the student on a mathematical topic or problem chosen in conjunction with the Department of Mathematics. In all of these cases, the paper will be made by the student into a poster for submission for presentation at the annual Knowledge Celebration in May of the year of completion of the major. (4 credits) Prerequisite: consent of the instructor |
This book provides a transition from the formula-full aspects of the beginning study of college level mathematics to the rich and creative world of more advanced topics. It is designed to assist the student in mastering the techniques of analysis and proof that are required to do mathematics.
Along with the standard material such as linear algebra, construction of the real numbers via Cauchy sequences, metric spaces and complete metric spaces, there are three projects at the end of each chapter that form an integral part of the text. These projects include a detailed discussion of topics such as group theory, convergence of infinite series, decimal expansions of real numbers, point set topology and topological groups. They are carefully designed to guide the student through the subject matter. Together with numerous exercises included in the book, these projects may be used as part of the regular classroom presentation, as self-study projects for students, or for Inquiry Based Learning activities presented by the students.
Readership
Undergraduate and graduate students interested in studying advanced mathematics. |
Student Support Edition of Basic College Mathematics, 8/e, brings comprehensive study skills support to students and the latest technology tools to instructors. In addition, the program now includes concept and vocabulary review material, assignment tracking and time management resources, and practice exercises and online homework to enhance student learning and instruction. With its interactive, objective-based approach, Basic College Mathematics provides comprehensive, mathematically sound coverage of topics essential to the basic college math course. The Eighth Edition features chapter-opening Prep Tests, real-world applications, and a fresh design--all of which engage students and help them succeed in the course. The Aufmann Interactive Method (AIM) is incorporated throughout the text, ensuring that students interact with and master concepts as they are presented.
Note: Each chapter begins with a Prep Test and concludes with a Chapter Summary, a Chapter Review, and a Chapter Test |
A calculator that shows how it got its answer! It supports variables (X, Y, Z etc.) and many pre-defined constants such as Pi etc. It also has most if not all the functions of a Scientific calculator.
It was coded in VB6 but was updated and is now VB.NE
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and moreFuniter (FUNction ITERation) is developed for educational purposes, generating graphs of several types for iteration of real and complex functions with comfortable switching between related types of graphs.
An efficient 2D Simple Graphing program for windows, perfect for plotting collected data incorporating features of cricket graph which allow you to apply a function to all your data.
Regression Lines for data.
The algorithm allows any kind of weights (costs, frequencies), including non-numerical ones. The {0, 1, ..., n-1} alphabet is used to encode message. Built tree is n-ary one.The algorithm is based on a set of template classes : Cell(SYMBOL, WEIGHT), Node(
GeoCalculator, the new latest thing in geometrical math. GeoCalculator is your one stop for solving any geometry-related equations. Features such as Triangle Solvers, Polygon Finders, and TONS of equations lets you solve ALL equations that you need.
This is an attempt to make a portable, efficient, and abstract set of C++ classes which manipulate algebraic expressions. I wrote it to explore C++ inheritance and polymorphism and it's extremely likely this project is the wrong solution for you. |
Curriculum Design: Pre-requisites/Co-requisites/Exclusions
The specific aim of this module is to introduce the notion of matrices and their basic uses, mainly in algebra.
The main goals are to learn how the algorithm of elementary row and column operations is used to solve systems of linear equations, the concept and use of determinant, and the notion of a linear transformation of the euclidean space. The course also aims at defining the main concepts underlying linear transformations, namely singularity, the characteristic equation and the eigenspaces.
Educational Aims: General: Knowledge, Understanding and Skills
The aim of this module is to give an introduction to the theory of matrices together with some basic applications. These are needed for later courses, such as linear algebra, and they are also of practical use for applications to geometry.
The student will learn the important algebraic concepts that are matrices, determinants and linear transformations, together with their applications in mathematics, with an emphasis in algebra.
The student will also know how to solve a system of linear equations, how to express a linear transformation of the real euclidean space using a matrix, from which the student will be able to determine whether it is singular or not and obtain its characteristic equation and eigenspaces.
At the end of this module, the student will have understood how to work with matrices, in particular by means of elementary row and column operations, and how they can be used to solve systems of linear equations with or without parameters.
Learning Outcomes: General: Knowledge, Understanding and Skills
The student will learn the elementary theory pertaining to matrices and their applications in mathematics, including solving systems of linear equations, determinants and linear transformations. At the end of this module, the student will have understood how these algebraic notions may relate to each other, and he/she will have learned the basic algorithms which allow their analysis. |
This class expands on the mathematical content of Algebra 1 and Geometry. Review of those concepts is integrated throughout the course. Emphasis is placed on abstract thinking skills, the function concept, and the algebraic solution of problems. Topics include the solution of systems of quadratic equations, logarithmic and exponential series, the complex number system, and trigonometric applications. Calculators are used in solving problems and in making estimates and approximations.
This course is a formal development of the geometric skills and concepts necessary for students taking Algebra 2/Trig and other advanced math courses. The course explores the principles of formal logic and their application to geometric proofs, and uses problem-solving skills in the development of geometric concepts. Specific topics emphasized are: Postulates, theorems, perpendicularity, parallelism, congruence, similarity, coordinate geometry, relationships in circles and polygons, introduction to transformational geometry, and right triangle geometry and trigonometry. |
MATH 108. Pre-Calculus Mathematics
Description:
This course provides a detailed study of topics needed for success in calculus: algebra, trigonometry, analytic geometry, and functions. Intended for students who need to take at least one semester of calculus for their major. |
Based on recent research on the adolescent brain, Active Algebra presents a living, working example of how teachers can use active learning techniques to make linear relationships more meaningful for students. In addition to the 10 reproducible, sequenced lessons, this award-winning resource offers seven chapters of guidance in teaching algebra.
Review by Kay Gilliland, from the the 2010 NCSM Spring Newsletter.
After describing a hilarious incident in his classroom, Dan Brutlag comments in Active Algebra: Strategies for Successfully Teaching Linear Relationships ". . . the truth is that the mathematical logic often makes no sense at all to these students. That is why textbook presentations consisting of clear, logical examples and explanations, although necessary, usually are not sufficient to teach mathematics to adolescents." How true, and how often we as mathematics leaders have tried to say this! Active Algebra does this for us, helping teachers build awareness of adolescents' thinking and behavior. Brutleg explains what he considers to be active learning in algebra involving the whole brain: listening, reading, writing, speaking, movement, social interaction, visualizing, and imagining. He includes lessons designed to build connections across large areas of the brain, mental mathematics exercises designed to stretch students' memory and recall, and a 10-lesson unit that focuses on understanding linear functions numerically, graphically, and symbolically. A CD of the 10 lessons comes with the book. Brutleg carefully explains the teacher's role in the lessons and peppers the text with real incidents from his own classroom.
2010 Winner Distinguished Achievement Award:
Professional Development: Learning Styles
The Association of Educational Publishers (AEP) Awards seal is recognized by teachers and parents as a mark of excellence in education. Finalist or winner status in the awards tells readers that the product has met rigorous standards for quality, professional content for education. |
Math
MA002 Pre-Algebra Fall and Spring: 2 semesters: 10 units
This course builds a strong foundation for further study in algebra, geometry and statistics. Topics covered include problem solving, order of operations, work with decimals and fractions, solving and graphing equations and inequalities, proportion and percent, probability and statistics, and introduction to geometry.
MA100 Algebra I Fall and Spring: 2 semesters: 10 units
This course covers the basics of algebraic reasoning including writing, graphing, and solving equations and inequalities with variables, real numbers, exponents, and square roots. Other topics covered include work with ratios, proportions, percents, and polynomials. Much emphasis is given to the study of slope and y-intercepts of linear functions, but also quadratic, exponential and radical functions are introduced (for further study in Algebra II). The graphing calculator is used as a tool for graphing any type of function quickly, as well as for data analysis (histograms, scatterplots, and line graphs) and probability (random numbers, combinations, and permutations). Upon completion of this course the student will be prepared to take Geometry. Pre-requisite: Successful completion of Pre-Algebra
MA200 Geometry Fall and Spring: 2 semesters: 10 units
The focus of this course is on reasoning with logic and geometric shapes, starting with the basic foundation of points, segments and angles. Also covered are properties of parallel and perpendicular lines, circles, and triangles, quadrilaterals, and other polygons. Formulas for perimeter, circumference, area and volume of both two and three dimensional figures are studied. Trigonometry is introduced with the study of right triangles. Transformations (reflections, translations, and rotations) are explored and geometric reasoning and proof is encouraged throughout the year. Upon completion of the course the student will be prepared to take Algebra II. Pre-requisite: Successful completion of Algebra I
MA300 Algebra II Fall and Spring: 2 semesters: 10 units
This course addresses the basic properties of functions (domain, range, zeros, and local extrema). The main functions studied are polynomial, exponential, logarithmic, rational, and radical. Other topics include curve fitting, linear systems, matrices, sequences, and an introduction into complex numbers, probability and statistics, trigonometry, and conic sections. Upon completion of the course the student will be prepared to take Pre-Calculus or a similar-level course. Pre-requisite: Successful completion of Algebra I and Geometry
MA302 Life Skills Math Fall: 1 semester: 5 units
This course includes math skills for everyday living, covering topics such as proportions, percents, fractions, decimals, and problem solving. It also builds a solid foundation for further study in algebra, geometry, and statistics. This course does not meet standards for regents university entry requirements.
MA303 Personal Finance Spring: 1 semester: 5 units
This course teaches students how to save and invest money, create and maintain a budget, manage credit, control debt, and set financial goals. The course also helps students develop consumer awareness of all types of insurance, renting and buying a home, and paying taxes.
MA400 Pre-Calculus Fall and Spring: 2 semesters: 10 units
This course guides students through an in-depth analysis of the basic types of functions (polynomial, power, rational, exponential, logistic, logarithmic, and trigonometric). The analysis addresses continuity, extrema, asymptotes, symmetry, transformations, and end behavior. Other topics include complex numbers, limits, writing mathematical proofs, vector manipulation, conic sections, combinatorics, discrete mathematics and statistics. Upon completion of the course the student will be prepared for AP Calculus or any college-level calculus course. Pre-requisite: Successful completion of Algebra II or a similar course
This course covers the topics of limits of functions, continuity, derivatives and their applications, integrals and methods of integration, and simple differential equations. Upon completion of the course, the student will be prepared to take the Advanced Placement Calculus AB Exam. The AP exam fee is $84. Pre-requisite: Successful completion of Pre-Calculus or a similar course and the consent of the |
Developing Skills in Algebra
Developing Skills in Algebra is designed for the
student who needs a comprehensive review of the topics from elementary and
intermediate algebra. This textbook uses the topics covered by many schools
in an intermediate algebra course. Within the reader friendly styled text,
students will find the algebraic skills necessary to prepare them for courses
in college algebra and trigonometry. New topics are presented with expanded
explanations, a progression of examples and colorful diagrams, aiding visual
learners in their understanding of formulas. To help build a strong foundation
and ensure understanding, students will have plenty of opportunity for practice
before proceeding to the next concept. |
Westley Calculus...As the student to grasp the concept |
Linear Algebra II
Linear algebra is the study of vector spaces and linear mappings between them. In this course, we will begin by reviewing topics you learned in Linear Algebra I, starting with linear equations, followed by a review of vectors and matrices in the context of linear equations. The review will refresh your knowledge of the fundamentals of vectors and of matrix theory, how to perform operations on matrices, and how to solve systems of equations. After the review, you should be able to understand complex numbers from algebraic and geometric viewpoints to the fundamental theorem of algebra. Next, we will focus on eigenvalues and eigenvectors. Today, these have applications in such diverse fields as computer science (Google's PageRank algorithm), physics (quantum mechanics, vibration analysis, etc.), economics (equilibrium states of Markov models), and more. We will end with the spectral theorem, which provides a decomposition of the vector space on which operators act, and singular-value decomposition, which is a generalization of the spectral theorem to arbitrary matrices. Then, we will study vector spaces: real, complex, and abstract (i.e., vector space of dimension N over an arbitrary field K) linear transformations. Vector spaces are structures formed by a collection of vectors and are characterized by their dimensions. We will then introduce a new structure on vector spaces: an inner product. Inner products allow us to introduce geometric aspects, such as length of a vector, and to define the notion of orthogonality between vectors. In this context, we will study the geometric aspects of linear algebra by using Euclidean spaces as a guide. If you encounter a theorem that seems difficult or does not seem intuitive, try to study that theorem in the simplest case possible and then move on to more abstract cases. For example, if you are uncomfortable with abstract vector spaces (V) over an arbitrary field (K), then you can fall back on intuition from such spaces as R and C (real and complex). Alternatively, you can reduce the dimension of the vector spaces involved as many notions can be understood in the two-dimensional case.
Note that you will only receive an official grade on your Final Exam. However, in order to adequately prepare for this exam, you will need to work through the resources in each unit and the activities listed above 117.5 hours to complete. This is only an approximation, and the course may take longer 32.5 hours to complete. Perhaps you can sit down with your calendar and decide to complete subunit 1.1 (a total of 11.5 hours) over three days, for example by completing sub-subunits 1.1.1, 1.1.2, and half of 1.1.3 (a total of 4.5 hours) on Monday; the second half of sub-subunit 1.1.3 and sub-subunit 1.1.4 (a total of 5 hours) on Tuesday; and sub-subunit 1.1.5 and 1.1.6 (about 2 hours) on Wednesday; etc.
Tips/Suggestions: As noted in the "Course Requirements," Linear Algebra I is a pre-requisite for this course. If you are struggling with the material as you progress through this course, consider taking a break to revisit MA211 Linear Algebra. It will likely be helpful to have a graphing calculator on hand for this course. If you do not own or have access to one, consider using this free graphing calculator. As you read, take careful notes on a separate sheet of paper. Mark down any important equations, formulas, and definitions that stand out to you. These notes will serve as a useful review as you study for the Final Exam.
Preliminary Information
Linear Algebra, Theory and Applications was written and submitted by Dr. Kenneth Kuttler of Brigham Young University. Dr. Kuttler wrote this textbook for use by his students at BYU. According to the preface of the text, "This is a book on linear algebra and matrix theory. While it is self-contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however." A solutions manual to the textbook is included.
This unit serves as a review of some of the material covered in Linear Algebra I, including linear equations, matrices, and determinants. Specifically, you will review properties of the real numbers and complex numbers. You will then learn the Fundamental Theorem of Algebra, which states that every polynomial equation in one variable with complex coefficients has at least one complex solution. You will also review how to solve linear systems of equations and perform operations on matrices. The key is to read through all the material below and complete all the exercises in this unit. The goal of this unit is to ensure that you are comfortable with the key matrix algebra concepts related to Euclidean spaces as these concepts will be referred to throughout this course. The skills and techniques you learn working with matrix theory will be generalized later in the course when you work in a more abstract linear algebra setting.
Instructions: Please click on the link above, select the "PDF version of book" link, and read Appendix A for a definition of sets and functions as well as to learn about associated vocabulary for these concepts. You will be using this text throughout the course, so it may help to save the PDF to your desktop for easy reference.
Studying this reading should take approximately 1 hour to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
Instructions: If you have not already downloaded the text, please click on the link above. Read Chapter 2. Pay particular attention to the polar decomposition of complex numbers and the associated geometric interpretationCompleting this activity should take approximately 3.5 hours text, please click on the link above. Read Chapter 3. Here, you will read about the important Fundamental Theorem of Algebra. In particular, note how the theorem is false when considering polynomials in the real number system document, please click on the link above. Complete calculational exercise 2 and the proof-writing exercise 3 (pages 34 and 35).
Completing this activity should take approximately 1.5 hours to complete.
Terms of Use: These materials have been reproduced for educational and non-commercial purposes, and can be viewed in their original format here. Any reproduction or redistribution for commercial use is strictly prohibited.
Studying this reading should take approximately 30 minutes to complete.
Terms of Use: These materials have been and select the "PDF version of book" link. Complete exercises 1b and 2 on page 9 and proof-writing exercise 1 on page 10. Read Sections 12.1–12.3 in their entirety. Most of this material should be a review PDF document, click on the link above and select the "PDF version of book" link. Read Sections 12.4 and 12.5 in their entirety. Note the relationship between matrices and linear transformations.
Studying this reading should take approximately 45 minutes Chapter 3 (pages 77–104) in its entirety. The determinant of a matrix is an extremely important number associated to the matrix as it provides us with a lot of information about the associated linear transformation.
Studying this reading should take approximately 1 click on the link above, and work through problems 2, 3, 6, 9, 11, 13, and 15 in Section 3.2 (pages 82 and 83) and problems 5, 6, 8, 9, and 11 in Section 3.6 (pages 102 and 103). When you are done, check your solutions with the answers on page 489.
Completing this activity should take approximately 5 hours.
Terms of Use: An Introduction to Linear Algebra was written by Kenneth Kuttler and was relicensed as CC-BY 3.0 as part of the Saylor Foundation's Open Textbook Challenge.
In this unit, you will study Spectral Theory, which refers to the study of eigenvalues and eigenvectors of a matrix. The name Spectral Theory is due to David Hilbert, who coined the phrase in his study of Hilbert space theory. Hilbert's original work was in the setting of quadratic forms, and only later was it discovered that Spectral Theory had applications to quantum mechanics, where it could be used to describe the behavior of atomic spectra. Eigenvalues and eigenvectors of a linear operator are two of the most important concepts in Linear Algebra with applications to many fields, such as computer science (Google's PageRank algorithm), physics (quantum mechanics, vibration analysis), and economics (equilibrium states of Markov models). You will then learn about trace and determinants, two important numbers associated to a matrix. There are several operations that can be applied to a square matrix, and the determinant is a very important operation of this type. The determinant is a number that is calculated from a square matrix and is used to check for many different properties of that matrix, including invertibility. We will learn to compute the determinant and study properties of determinants and the effects of row operations on them. The trace of a matrix is related to the characteristic polynomial of the matrix and can be used to detect nilpotency. You will then learn about Schur's Theorem, which describes how every matrix is related to an upper triangular matrix. Finally, you will learn about quadratic forms, the second derivative test, and some advanced theorems.
Instructions: Please read Sections 7.1–7.5. The eigenvectors and eigenvalues of a matrix help to describe the behavior of the associated linear transformation1 (pages 157–164) in its entirety. Work through the eigenvalue/eigenvector examples on your own and check your work with that in the text. Being able to accurately and efficiently perform these computations is essential Section 7.6. Note the relationship between the eigenvectors for a rotation matrix and the angle of rotation4 (pages 173–180) in its entirety. Schur's Theorem relates any matrix to an associated upper triangular matrix in which the eigenvalues for the original matrix appear on the diagonal. Read through the proof of this theorem and the accompanying lemmas and corollaries.
Studying this reading should take approximately 2 Chapter 8 in its entirety. Pay particular attention to the algebraic properties of the determinantIn this unit, we will begin by defining fields and discussing some important examples. Complex numbers (C) will give us insight into some of the key mathematical concepts of linear algebra. We will define vector spaces and study their basic properties before studying finite dimensional vectors spaces. Then, concepts of linear independence, span, bases, subspaces, and dimension are examined in the context of vector spaces. A strong understanding of vector spaces is necessary, because linear algebra is the study of linear maps on vectors spaces. Without a good grasp of vector spaces, understanding linear algebra becomes difficult. After studying vectors spaces, we will begin to study a special kind of function known as a linear map. These functions arise naturally in linear algebra. We will study linear maps from one vector space to another, as well as linear maps from a vector space to itself (these maps are known as operators and are extremely important in linear algebra). Keep in mind that most of the results in this unit are for finite-dimensional vector spaces only. We will then learn how some matrices can be transformed into Jordan canonical form, an upper triangular form for the matrix in which the eigenvalues appear on the diagonal. Note that linear maps have many applications in fields outside of mathematics, such as physics (quantum mechanics, etc.) and engineering (traffic flow, difference equations, etc.). You will finally learn about a certain kind of matrices, called Markov matrices, and see that the existence of the Jordan form is the basis for the proof of limit theorems for Markov matrices.
Instructions: Please read Section 8.1 (pages 199 and 200) in its entirety. The definition of a vector space is an important one, and you should compare the axioms with their more familiar analogs from algebra Pleaseread Sections 4.1 and 4.2. Here the notion of a vector is abstracted. Pay particular attention to the example of polynomial functions, which is the first example of a vector space which is not simply an ordered n-tuple of numbersInstructions: Please read Sections 8.2.1 and 8.2.2 (pages 200–205) in their entirety. The notions of basis and subspace are extremely important ones to master. Read through the examples and proofs on your own. If the proofs are confusing, try working them out in a low dimensional case first 4.3 and 4.4 Sections 5.1 and 5.2. The notions of span, basis, independence, and dimension are crucial to understanding linear algebra and its applications.
Studying this reading should take approximately 1.5 hour 5.3 and 5.4. Work through the examples on your own, and compare your work with that in the text 8.3 (pages 205–219) in its entirety. Note how the existence of roots of a particular polynomial depends heavily on the field being considered. You should also compare this to the situation regarding the Fundamental Theorem of Algebra 6.1–6.5 in their entirety. Linear maps are those which preserve the structure of a vector space and are a rich source of additional vector spaces. Work through the examples on your own, and compare your work with that in the text.
Studying this reading 6.6 and 6.7 in their entirety. A linear map between two vector spaces can be represented by a matrix, once a basis is chosen for each vector space click on the link above, and work through problems 1, 7, 11, 13, 15, and 19 in Section 9.5 on pages 242 through 244. When you are done, check your solutions with the answers on page 494.
Completing this activity should take approximately 2 2, 8, 10, 11, and 16 in Section 10.6 (pages 262 and 264) and problems 4–8 in Section 10.9 (pages 273 and 274). When you are done, check your solutions with the answers on pages 494 and 495.
Completing this activity should take approximately 4Linear algebra deals with not only Euclidean spaces but also abstract vector spaces. This unit will discuss lengths and angles in an abstract vector space. Inner products allow us to generalize notions such as length, because an inner product is a generalization of a dot product for Euclidean n-space. Having notions of length, angles, and distances in an abstract vector space allow us to apply more tools and methods which help us to better understand the structure of the space.
In this unit, we will discuss inner product spaces, which are vector spaces with an additional structure known as an inner product. Much of the motivation for the subject grew from the need to generalize some geometric properties of two-dimensional and three-dimensional Euclidean spaces to higher dimensional spaces. In this unit, we will finally begin to understand the geometric aspects of linear algebra, such as representing rotations in the three-dimensional Euclidean space as matrices. From this we will understand how to generalize and represent rotations in higher dimensional Euclidean spaces as matrices. The concepts in this unit, such as norm and inner product, provide structure on spaces. We will finally study the basic properties of inner product spaces, orthonormal bases, and the Gram-Schmidt orthogonalization procedure. We will further study range-nullspace decomposition, orthogonal decomposition, and singular-value decomposition of spaces.
Next, we will try to understand and answer the question of when a linear operator on an inner product space is diagonalizable. We will study the notion of an adjoint of an operator as well as normal operators and then discuss the spectral theorem, which characterizes the linear operators for which an orthonormal basis consisting of eigenvectors exists. The spectral theory studied here is closely related to that studied in Unit 2. In fact, the eigenvalues and eigenvectors for a matrix are the same as those for the linear transformation determined by the matrix. We will then learn about finding the singular-value decomposition of an operator. We will conclude by exploring some advanced topics.
Studying this reading should take approximately 1.5 hours to complete.
Terms of Use: . These materials have been reproduced for educational and non-commercial purposes and can be viewed in their original format here. Any reproduction or redistribution for commercial use is strictly prohibited.
Instructions: Please read Section 9.5. The Gram-Schmidt process can be used to turn any basis for an inner product space into an orthogonal basis 9.6 on pages 128–132 1–3, 9, 11, 14, 16, 21, and 22 in Section 12.7 (pages 299–302) and problems 1 and 3 in Section 12.9 (page 306). When you are done, check your solutions with the answers on pages 495 and 496.
This activity should take approximately 4.5 hours to complete.
Terms of UseAn Introduction to Linear Algebra was written by Kenneth Kuttler and was relicensed as CC-BY 3.0 as part of the Saylor Foundation's Open Textbook Challenge.
Instructions: Please read Sections 11.1 and 11.2 11.3 and 11.4. The Spectral Theorem describes the relationship between normal operators and eigenvectors 11.5 13.6–13.11 (pages 322–334) in their entirety. Here, you will learn about the singular-value decomposition of a matrix, which has applications in statistics and image analysis |
APPENDIX B
A Topical Listing
The list below of mathematics topics, IF LACED WITH GOOD
APPLICATIONS, addresses all of the issues raised in Part II at
least minimally. Although the topics are displayed here according
to subject matter components of traditional mathematics curricula,
one should NOT infer that this is the best organization with
which to address quantitative literacy . In fact, this kind of layer-cake organization
may inhibit the very essence of quantitative literacy : encouraging multiple
perspectives; informally developing intuition; and searching for
connections. It may actually deepen the pitfall of just preparing for
the next course. Nevertheless, the list suggests a common ground
from which to begin. How much time will need to be spent on topics
that the students have studied before will depend on circumstances,
but deadly reviews of more or less familiar material should be
avoided. (* means "less essential")
ARITHMETIC
estimation
percentage change
use of calculator:
rounding and truncation errors; order of operations.
OTHER
optimization: the notions of maxima and minima of functions with
or without constraints; graphical and computational methods for
finding them; simple analytic methods, such as completing the
square for quadratic polynomials.
linear programming*:
systems of equations in two variables with a linear objective
function. |
Synopsis
Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics, as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the AtiyahñSinger index theorem, to provide double covers (spin groups) of the classical groups and to generalize the Hilbert transform. They also have their place in physics, setting the scene for Maxwell's equations in electromagnetic theory, for the spin of elementary particles and for the Dirac equation. This straightforward introduction to Clifford algebras makes the necessary algebraic background ñ including multilinear algebra, quadratic spaces and finite-dimensional real algebras ñ easily accessible to research students and final-year undergraduates. The author also introduces many applications in mathematics and physics, equipping the reader with Clifford algebras as a working tool in a variety of contexts.
Found In
eBook Information
ISBN: 9781139066389 |
Algebraic Geometry
To become acquainted with basic techniques of algebraic geometry, through the study of the proof of the Riemann Hypothesis for curves over finite fields.
Description
Riemann's zeta function has a natural generalisation to zeta functions associated to finitely generated (commutative) rings, and more generally, to schemes of finite type. For nonsingular projective curves over finite fields the Riemann hypothesis has been proved by Hasse (elliptic curves) and Weil (arbitrary genus, 1940's). The case of higher dimensional varieties over finite fields (see was proved by Deligne (1974), building on the work of Grothendieck.
In this course we will treat the case of curves over finite fields, using intersection theory on surfaces. The course will start with some explicit examples of zeta functions, including Riemann's and those of curves over finite fields. Then slowly we will develop those techniques necessary to treat Weil's proof, from Hartshorne's book `Algebraic Geometry' together with a syllabus based on a previous version of this course. Finally, we will present Weil's proof.
Our goal is to provide a good overview of Weil's proof. Obviously, it is not desirable nor possible to treat all of Hartshorne's book.
Organization
Two 45 minute lectures and one 45 minute problem session, weekly.
Examination
Each week, students hand in solutions to exercises that are given on the website of this course. Late homework is not accepted. At the end of the course, each student is required to take an oral exam. The deadline for the oral exams is June 30th. On the exam, students will be questioned about the homework exercises. In order to be admitted to the exam, a student has to pass at least 7 of the homework sets. Questions may be asked about all the homework exercises, not just those for which the student has received a pass.
The standard undergraduate algebra courses on groups, rings and fields (for more details see the three algebra syllabi (in Dutch) available at and some basic topology. No prior knowledge of algebraic geometry is necessary. |
Problem Solving
9780759342644
0759342644
Summary: Problem Solving provides students with a general approach and strategies to solve problems in real life. The text is easy to read and geared mainly for students who dislike math. Problems throughout the book range from easy to difficult, and require minimal mathematical experience. While possessing knowledge is one important requirement to solving problems, there are many others. Problem Solving focuses on providing ...strategies to help students become proactive, successful, and confident problem solvers.[read more] |
Açıklama
Universal application of higher mathematics, which helps you not only to solve the problem, but also to see and understand the process of solving it, step by step.
MathHelper's marks of quality and excellence:
– The application is included in the Intel ® Learning Series Alliance software packs
– It is rated above 4.7 on Google Play with many positive reviews.
Here are just a few user reviews:
> "Perfect companion for the challenges on the linear and probability theories!"
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This application is a universal assistant for those who deal with advanced mathematics. You can be a higher school student, a university student or even a graduate – If you need immediate mathematical assistance – MathHelper is always at hand!
You can forget about all the heavy books and numerous tricks with the tips, which in most cases do not guarantee that you'll solve your maths problem.
MathHelper enables you to not only to solve the problem, but also to understand the process of solving it, step by step. This convenient multifunctional calculator includes an extensive theoretical guide in several languages. You'll get an algebraic mini-laboratory that is stored conveniently and compactly on your Android! Now, you can not only quickly find the answer, but also handle similar problems in the future. Your classmates and teachers will be very surprised with the results of your work.
MathHelper allows calculating propositions and solving problems in linear and vector algebra in six sections at the moment:
1. Operations with matrices: * Transpose of a Matrix * Finding the determinant of a Matrix * Finding the inverse of a Matrix * Addition and subtraction of matrices * Matrix multiplication * Scalar multiplication of Matrices * Calculating the rank of a matrix
3. Vectors: * Finding the length (magnitude) of a vector * Checking if two vectors are collinear * Orthogonal vectors * Sum, difference, scalar product * Finding the cross product * Finding the angle between two vectors * Finding the cosine of the angle between two vectors * Finding the projection of a vector onto another * Coplanar vectors
4. Figures: * Finding the area of a triangle * Show that four points lie on the same plane * Finding the volume of a tetrahedron (pyramid) * Finding the volume and height of the tetrahedron (pyramid)
NEW! 5. Mathematical analysis - Derivatives: * Derivative of the function * Derivative of the function given parametrically * The derivative of the implicit function
6. Probability theory: * Finding expectation sample * Finding the sampling variance * Finding the number of permutations of a set of n elements * Finding the number of placements and combinations (n, k)
7. Number theory and sequence: * Prime factorization * Finding GCD and LCM * The least common multiple and greatest common divisor * Complex numbers: Addition, subtraction, multiplication and division * Raising a complex number to a power * The first terms of a progression (arithmetric and geometric) * Finding Fibonacci numbers * Solution of linear Diophantine equations * Finding the values of Euler's function * The factorial n! |
Find the Relationship: An Exercise in Graphing Analysis
Recommended for grades 9–12.
Introduction
In several laboratory investigations you do this year, a primary purpose will be to find the mathematical relationship between two variables. For example, you might want to know the relationship between the pressure exerted by a gas and its temperature. In one experiment you do, you will be asked to determine the relationship between the volume of a confined gas and the pressure it exerts. A very important method for determining mathematical relationships in laboratory science makes use of graphical methods.
Objectives
In this experiment, you will determine several mathematical relationships using graphical methods |
Mathematics for Physicists
9780534379971
ISBN:
0534379974
Pub Date: 2003 Publisher: Thomson Learning
Summary: This essential new text by Dr. Susan Lea will help physics undergraduate and graduate student hone their mathematical skills. Ideal for the one-semester course, MATHEMATICS FOR PHYSICISTS has been extensively class-tested at San Francisco State University--and the response has been enthusiastic from students and instructors alike. Because physics students are often uncomfortable using the mathematical tools that they... learned in their undergraduate courses, MATHEMATICS FOR PHYSICISTS provides students with the necessary tools to hone those skills. Lea designed the text specifically for physics students by using physics problems to teach mathematical concepts.[read more] |
Dinah Zike's Big Book of Math for Middle and High School features instructions for 28 manipulatives, with approximately 100 full-color photographed examples. Math topics are divided into five catagories, Number Systems, Algebraic Patterns and Functions, Geometry, Measurement, Data Analysis and Probablility. The book contains thousands of ideas for teaching math concepts using graphic organizers, as well as five black-line art examples per page and an additional 40 black and white photographed examples throughout the book. 128 pages, 8 1/2" x 11" |
MATH32012 Commutative Algebra - 2012/13, Semester 2
Online Test
The Online Test is currently accessible via the MATH32012 course content page in Blackboard.
You may retake the test for revision purposes (e.g., to practise
the computation of Gröbner bases). It will not affect your coursework mark.
(The coursework marks have been finalised and are available via the Grade
Centre in Blackboard.)
Module description and prerequisites
You should have general facility for dealing with algebraic structures: complex numbers, sets, groups, rings, fields. For this reason, MATH20212 Algebraic Structures 2 is a prerequisite.
About the course
Many find MATH32012 Commutative Algebra the most advanced abstract algebra course they take as part of their degree.
Nevertheless, the content of the course is not just a sequence of theorems and proofs.
You are expected to learn methods of algebraic computation relating to polynomials in several variables.
Solving equations has been a driving force of algebra at least since the Babylonians learned to solve quadratic equations some 3700 years ago. The subject matter of this course is, however, informed by more recent developments.
The work of Hilbert in late 19th - 20th century was key to the modern treatment of multivariate polynomials and provided a basis for commutative algebra and algebraic geometry. His result that every (consistent) system of polynomial equations over an algebraically closed field has at least one solution is known as the Nullstellensatz.
But an efficient method of finding such solutions by elimination was not found until 1965, when Buchberger invented Gröbner bases.
In the course, key theorems about the ring of polynomials in several variables will be rigorously proved.
Algorithms relating to polynomials will be explained and supported by examples. This includes factorising polynomials into irreducible factors and computing a Gröbner basis of an ideal.
Results and methods of Commutative Algebra have applications in various branches of mathematics and computer science. Here are some puzzles which we may use in the course as an illustration for the main content. You are welcome to have a go at solving them!
Question 1 (Fermat, 17th century).
Find all integers a "sandwiched" between a square and a cube.
Question 2.
How many ways are there of placing 8 queens on a chessboard so that no two queens attack each other? What about n queens on an n×n chessboard?
Question 3.
How many distinct Sudoku boards are there? (A Sudoku board is a 9×9 square
with a number from 1 to 9 in each cell, satisfying the Sudoku constraints.)
images from Wikimedia commons
Coursework
There will be 2 pieces of assessed coursework:
Assessed homework 1 (see a link above): a take-home problem sheet
set on Wednesday 27 February (week 5),
due on Tuesday 12 March (week 7) at 4pm.
Blackboard-based online test: a timed, open-book test which the students complete online; multiple attempts are allowed
Previous years' exams
Commutative algebra exam papers from years 2008-2012 are available here. |
The
course develops fundamental geometric tools of mathematical analysis,
in particular integration theory, and is a preparation for further
geometry/topology courses. The central statement is the famous Stokes
theorem, a classical version of which appeared for the first time
as an examination problem in Cambridge in 1854. Various manifestations
of the general Stokes theorem are associated with the names of Newton,
Leibniz, Ostrogradski, Gauss, Green. This theorem, both in its
infinitesimal and global forms, relates integral over a boundary of a
surface or of a solid domain ("circulation" or "flux") with a natural
differential operator, known in particular cases as "curl" or
"divergence". The prototype and the simplest case of the Stokes theorem
is the Newton-Leibniz formula linking the difference of the values of f
on endpoints of a segment with the integral of df . The
standard modern language for these topics is differential forms
and the exterior derivative. Differential forms are used
everywhere from pure mathematics to engineering. We give an
introduction to the theory of forms, as well as a simplifying treatment
for the traditional technique of operations with vector fields in the
Euclidean three-space. |
Download Mathematics: introduction to units of time
Mathematics: introduction to units of time is an educational software. It is very basic but helpful software that will help every mathematics and physics student. This program is focused to help students get hold of time and its units in a better way. This program will help students to learn the units of time in effective manner without getting confused. It has some unique automatically generated questions that will assist students in learning the units. These questions will test the student's knowledge and if they are not able to solve them then they can learn it using this program within no time. |
This item is printed on demand. If you've ever taken a graduate statistics course and discovered that you've forgotten how to divide a fraction or turn a fraction into a perc [more]
This item is printed on demand. If you've ever taken a graduate statistics course and discovered that you've forgotten how to divide a fraction or turn a fraction into a percentage, then this handy guide to mathematics is for you. Each topic is provided.[less] |
it is basic introduction to pre-algebra. In includes the arithmetic operations on directed numbers. simplifying algebraic expression, solving equations, inequality of open and closed type, two inequalities at the same time, compound inequalities, how to construct formula, change subject of the formula, find the value of the formula |
GCSE Mathematics
Content of Course
The GCSE in Mathematics gives students the opportunity to develop the ability to acquire and use problem-solving strategies, select and apply mathematical techniques and methods in mathematical, every day and real-world situations. It also allows you to be able to reason mathematically, make deductions and inferences and draw conclusions and interpret and communicate mathematical information in a variety of forms.
Teaching of this Mathematics GCSE began in 2010 (first examination is in June 2012) and it still has its focus on number, algebra, geometry, measures, statistics and probability but also allows you to apply the functional elements and problem solving strategies required to use mathematics in everyday life. Within the department there is a Co-ordinator of Mathematics and a member of staff in charge of each key stage.
The course has 2 examinations of 1 hour 45 minutes per paper (Higher tier – Grades A* to C) and 1 hour 30 minutes per paper (Foundation tier – Grades C to G). One paper is non-calculator, the other a calculator is allowed. There is no coursework or controlled assessment.
3 good reasons why a good grade in maths is so important:
A vast array of potential future careers will be opened up to you, for example: |
Study Skills: Math & Science
Translate problems into English
Putting problems into words aids your understanding. When you study equations and formulae, put those into words as well. The words help you see a variety of applications for each formula.
For example, the Pythagorean Theorem, C2 = A2 + B2 can be translated as 'The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.'
Perform opposite operations
If a problem involves multiplication, check your work by dividing; if addition then subtract and check your work, if divide then check with multiply; if square root then check with square; if differentiate then integrate.
Use time drills
Practice working problems fast. Time yourself. Exchange problems with a friend and time each other. Do this in the Study Group.
Analyze before you compute
Set up the problem before you begin to solve it. When a problem is worth a lot of points, read it twice, slowly. Analyze it carefully. When you take time to analyze a problem you can often see ways to take computational short-cuts.
Make a picture
Draw a picture or a diagram if you are stuck. Sometimes a visual representation will clear a blocked mind.
Estimate first
Estimation is a good way to double-check your work. Doing this first can help you notice if your computations go awry, and then you can correct the error quickly.
Check your work systematically
When you check your work, ask yourself: Did I read the problem correctly? Did I use the correct formula or equation? Is my arithmetic correct? Is my answer in the proper form?
Avoid the temptation to change an answer in the last few minutes - unless you are sure the answer is wrong. In a last minute rush to finish the test, it's easier to choose the wrong answer.
Review formula
Right before the test, review any formulas you will need to use. Then write them out on scratch paper as soon as possible during the test. |
Mathematics for the Trades : A Guided Basic Math, Math for the Trades, Occupational Math, and similar basic math skills courses servicing trade or technical programs at the undergraduate/graduate level.THE leader in trades and occupational mathematics,Mathematics for the Trades: A Guided Approach focuses on fundamental concepts of arithmetic, algebra, geometry, and trigonometry. It supports these concepts with practical applications in a variety of technical and career vocations, including automotive, allied health, welding, plumbing, machine tool, carpentry, auto mechanics, HV... MOREAC, and many other fields. The workbook format of this text makes it appropriate for use in the traditional classroom as well as in self-paced or lab settings. For this revision, the authors have added over 150 new applications, new chapter summaries for quick review, and a new chapter on basic statistics. Student will find success in this clear and easy to follow format which provides immediate feedback for each step the student takes to ensure understanding and continued attention.
MATHEMATICS FOR THE TRADES: A GUIDED APPROACH, 9/e focuses on the fundamental concepts of arithmetic, algebra, geometry and trigonometry needed by learners in technical trade programs.
The authors interviewed trades workers, apprentices, teachers, and training program directors to ensure realistic problems and applications and added over 100 new exercises to this edition. Geometry, triangle trigonometry, and advanced algebra. For individuals who will need technical math skills to succeed in a wide variety of trades. |
Week 1 (USC classes begin on Monday; Friday is the last day to drop without a grade of W)
Jan 12 (Mon)
Read page xv from the preface as well as sections 1.1 and 1.2. In 1.1 do #2, 4, 7, 9, 14, 17. In 1.2 do #3, 7, 11, 12, 14, 15, 16. Get a graphing calculator by Wednesday. If you don't already own one, I suggest any of the TI-83 or TI-84 calculators. If you need to take or retake the Algebra Placement Test, go to and select the third link Take Me To The Tests. You could also look at the first two links which include practice tests.
Jan 14 (Wed)
Finish the assigned homework from 1.1-1.2 and read section 1.3. Bring your calculator to class from now on.
Jan 16 (Fri)
Read section 1.5. In 1.3 do #5, 9, 10, 11, 12, 20, 25, 26, 31. In 1.5 do #11, 12, 17, 18. There will be a quiz Wednesday on sections 1.1-1.3. Today we spent a lot of time on calculator usage. We discussed how to use the Y=, 2nd-TBLSET, and 2nd-TABLE features of your calculator in order to get a table of values for a function. We also discussed how to use the GRAPH and 2nd-CALC features of your calculator in order to find the intersection of two graphs. The quiz will include testing your ability to use your calculator effectively. We did not spend much class time on section 1.3 today but it will still be included on the quiz so be sure to read the book carefully and do all of the homework.
Read section 1.6 and do #2, 5, 10, 21, 22, 23, 24, 31, 36 from that section. For many of the problems in sections 1.5 and 1.6, I recommend that you try solving them 3 ways — (1) with a table of values on your calculator, (2) with a graph along with the intersect or trace features of your calculator, (3) by hand with rules of algebra including logarithm rules.
Week 3
Jan 26 (Mon)
Read section 1.7. For now do #1, 5, 8. If you want to get ahead then do #10, 11, 15, 16, 18, 19. There will be a quiz Friday on sections 1.5-1.6.
Jan 28 (Wed)
Finish the problems from 1.7. There will be a quiz Friday on sections 1.5-1.6.
Jan 30 (Fri)
If you missed today's quiz, download a copy and allow yourself around 20 minutes to complete it. For homework read section 2.1 and do #1, 3, 5, 6, 12, 13, 15 from that section.
Week 4
Feb 2 (Mon)
Read section 2.2 and do #13, 17, 20, 24, 26, 27 from that section. There will be a quiz Friday on sections 1.7, 2.1, 2.2.
Monday's test will cover sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 2.1, 2.2, and 2.3. You should also be able to use your calculator effectively. In particular you should be able to easily generate graphs and tables of values. You should also know how to use the 2nd-CALC features of your calculator to find intersections. For this test, in section 1.4 you may skip the part on "marginal cost", "marginal revenue", and "marginal profit" at the bottom of page 25. You may also skip the part on "supply and demand curves" from the middle of page 26 to the end of page 28. You should be able to solve any of this semester's assigned homework problems or quiz problems. I recommend that you look at past quizzes and tests with solutions from every semester I have taught this course. Remember to bring a student ID and a graphing calculator with fresh batteries.
Read section 3.3 and do the odd problems from #1–33 for practice with the chain rule. Also do #35, 36, 37, 39, 42, 43, 44, 45. There will be a quiz Wednesday on sections 3.1-3.2 and another quiz Friday on section 3.3. Now is a great time to use the free services of the Math Tutoring Center as well as Supplemental Instruction.
Feb 25 (Wed)
If you missed today's quiz, download a copy and allow yourself around 15 minutes to complete it. Read section 3.4 and do the odd problems #1–27 for practice with the product rule and quotient rule. Also do #34, 35, 36, 39, 41. There will be a quiz Friday on section 3.3 and a quiz Monday on section 3.4.
Feb 27 (Fri)
If you missed today's quiz, download a copy and allow yourself around 15 minutes to complete it. There will be a quiz Monday on section 3.4. There is no new homework - just get caught up this weekend.
Week 8
Mar 2 (Mon)
If you missed today's quiz, download a copy and allow yourself around 15 minutes to complete it. Read sections 4.1-4.2. Without using a calculator, graph the functions found in #8, 9, 10, 11, 12 in section 4.1. Don't be too concerned with the terminology just yet – we'll get to that next time.
Mar 4 (Wed)
Read section 4.3. Without using a calculator, graph the functions found in section 4.2 (#11, 12, 13, 14, 15, 16, 17, 18, 19, 20) and section 4.3 (#24, 25, 26). Now compare your results to graphs obtained with your calculator. Be able to state the intervals upon which the function is increasing, decreasing, concave up, or concave down. Be able to find any local max/min, global max/min, or inflection points. There will be a quiz Friday on this material.
There will be a quiz Wednesday based on the homework from sections 4.3 and 4.4 assigned the Friday before Spring Break.
Mar 18 (Wed)
If you missed today's quiz, download a copy and allow yourself around 15 minutes to complete it.
Mar 20 (Fri)
Monday's test will cover sections 3.1, 3.2, 3.3, 3.4, 4.1, 4.2, 4.3, 4.4. No calculators are allowed for this test. You should be able to solve any assigned homework problem from these sections as well as any problem from quiz 4, quiz 5, quiz 6, quiz 7 or quiz 8. I also recommend that you look at past quizzes and tests with solutions from every semester I have taught this course. Remember to bring a student ID.
Week 11
Mar 23 (Mon)
Test 2
Mar 25 (Wed)
Read sections 5.1-5.2. In section 5.1 do #6, 8, 9, 11, 14, 15, 17. In class we worked on the following problem.
A population changes at a rate of 5e0.05t people per year where t is the number of years since 1980. If the population is 4000 in 1980 then estimate the population in 2000. First we approximate the total change in population between 1980 and 2000.
Estimate 3 (average of the two estimates above): 172.7 people (do you know if this is an overestimate or underestimate?)
This tells us that the population in 2000 is somewhere between 4151.2 and 4194.2 people. An estimate of 4172.7 is probably closer to the actual population but it is more difficult to say whether this is an underestimate or an overestimate. For homework get more refined estimates by choosing Δ t = 1. Be sure to make all 3 estimates and state when you know that your estimate is an overestimate or an underestimate.
Mar 27 (Fri)
No new homework.
Week 12
Mar 30 (Mon)
In section 5.2 do #3, 6, 10, 11, 12, 17.
Apr 1 (Wed)
Read section 5.3. No new homework.
Apr 3 (Fri)
Do #1-11 on the handout Old test and quiz problems — Chapter 5. There will be a quiz Monday on sections 5.1-5.2 and #1-6, 11 on the handout. There will be a quiz Wednesday on section 5.3 and #7-10 on the handout.
Week 13
Apr 6 (Mon)
If you missed today's quiz, download a copy and allow yourself around 10 minutes to complete it. Do #3, 4, 5, 6, 7, 8, 11, 19 from section 5.3. There will be a quiz Wednesday on section 5.3 and problems #7-10 on the recent handout Old test and quiz problems — Chapter 5.
Monday's test will cover sections 5.1, 5.2, 5.3, 5.4, and 5.5. It will include a non-calculator part. Bring your student ID. Be sure to look carefully over quiz 9 (blank copy, solutions), quiz 10 (blank copy, solutions), the handout on old tests and quiz problems (blank copy, solutions), and the handout on the Fundamental Theorem of Calculus (blank copy, solutions). On the Fundamental Theorem of Calculus handout, problems #1 and #2 will definitely be on the test. I also strongly suggest looking at my tests and quizzes from past semesters. |
This GCSE Mathematics Studies Revision Guide provides students with essential and stimulating material to improve understanding of all the key topics on the specification and achieve exam success. Each topic includes a set of questions so that you can test your knowledge and understanding as your revision progresses, and answers to all questions are provided at the end of the book.
Top page |
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This book was featured during OMK last couple of months...but if you missed about the information, you may inquire/ order the book directly from us at ArdentEdu....
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vseehua
03-08-2009, 09:08 AM
Thread moved to the advertisement section
jagandecapri
04-08-2009, 05:02 PM
I saw the book during the mathematics olympiad 2009. It is really good but RM 25 per book is quite expensive for a locally published book. 25 multiply 4 is RM 100. It is way beyond what many students can afford. I hope in the mist of writing text for number theories, geometries and so on........you all didn't miss this point to consider.........the price of the book.:wink
youngyew
04-08-2009, 08:55 PM
How much does a typical pelangi reference book cost?
vseehua
05-08-2009, 06:23 AM
How much does a typical pelangi reference book cost?
At least 20 Ringgit during my time... For a book that deals with a very specific theme, I don't think it's expensive at all, considering the amount of effort put into compiling the methods and answers in the book...
nummerzwei
21-10-2009, 12:52 PM
At least 20 Ringgit during my time... For a book that deals with a very specific theme, I don't think it's expensive at all, considering the amount of effort put into compiling the methods and answers in the book...
Thank you vseehua for the remarks
If you buy the set of 4 books directly from us, we will give you discount. The price after discount is RM 85 only..... |
Using the Spreadsheet to Develop an Intuitive Understanding of the Limit Concept
Phyllis Brudney, Marilyn Keir and Mary Viruleg
Abstract
Students who have successfully completed algebra and have studied some geometry should have success with this module. The purpose is to lead the student to an intuitive understanding of the limit concept. It includes three activities which may be used independently or sequentially. The activities take the student from the discreet to the continuous beginning with a geometric model which is easily visualized and culminating with the more theoretical case of the limit of a function.
Technology
This module requires the use of a spreadsheet program such as Excel or Microsoft WORKS. Students should be familiar with basic spreadsheet capabilities, including the use of formulas and replication.
Teacher Notes
The three activities which accompany this module may be used independently. Each involves the use of the spreadsheet to observe and draw conclusions based on patterns in a sequence. Activity 0 is a geometry activity. Activity 1 should be introduced once students have studied and discussed different kinds of sequences and their behavior. Activity 2 gives students who understand sequences an opportunity to explore infinite geometric series and to discover the conditions under which they have a sum. Activity 3 allows students to examine the classic - definition of the limit of a function and to work toward an intuitive understanding of this fundamental idea.
Activity 0 : Using Spreadsheets to Study Circle Measurements
Use your spreadsheet to find a relationship between regular polygons and circles. If we consider regular polygons with radius, r, and n sides, beginning with n = 3 and watch what happens to the perimeter of the polygon as the number of sides increases, we will discover a relationship between the sequence of perimeters and the circumference of the circle with the same radius. A similar relationship exists between polygonal areas and the area of the circle.
To set up your worksheet:
Col A number of sides, n
Col B perimeter of polygon with n sides
Col C area of polygon with n sides.
Set aside cells for the value of r, and for the circumference and area of the circle with radius, r.
To calculate the perimeter of an n-sides polygon with radius, r:, (Column C)
= = x =
s = 2 r sin (/n)
perimeter = n s
= 2 n r sin(/n)
To calculate the area of each regular polygon: (Column D)
Area = .5 a p (perimeter is in Col C)
= .5 (r cos (/n) p
Calculate the circumference of the circle with radius, r. Compare your result with the sequence of perimeters. What do you find?
Calculate the area of the circle with radius, r. Compare it with the sequence of areas. What do you find?
Activity 0: Circumference and area of a circle using limits
You must enter the radius of your polygon.
Circle with radius r:
radius =
4
Perimeter =
Area =
25.1327412
50.2654825
Number of sides
Perimeter
Area
3
20.7846
20.7846
4
22.6274
32.0000
5
23.5114
38.0423
6
24.0000
41.5692
7
24.2975
43.7826
8
24.4917
45.2548
9
24.6255
46.2807
10
24.7214
47.0228
11
24.7925
47.5764
12
24.8466
48.0000
13
24.8888
48.3312
14
24.9223
48.5950
A
C B
D
Formulas for spreadsheet
Number of sides
Perimeter
Area
3
=A8*2*C$4*SIN(PI()/A8)
=C8/2*C$4*COS(PI()/A8)
=A8+1
=A9*2*C$4*SIN(PI()/A9)
=C9/2*C$4*COS(PI()/A9)
=A9+1
=A10*2*C$4*SIN(PI()/A10)
=C10/2*C$4*COS(PI()/A10)
Activity 1: Infinite Geometric Sequence and Iteration
INSTRUCTIONS:
1. Set up spreadsheet to find N(R) = .
2. Label columns N, N(R), and N(N(R)).
3. Off to the side, label entry R and put a constant value in for R.
4. Start N at 0 counting by increases of 1 for the first experiment.
5. Increment N by more than 1 for following trials in each experiment.
EXPERIMENT #1:
1. Set an arbitrary R in a cell off to the right.
2. Fill in down columns labeled N, R, N(R), and N(N(R)).
3. Record observations about N(R) & N(N(R)).
4. Reset increments of N. Record observations.
5. Reset values for R 20 times. Record observations each time.
6. Answer questions: For which values of R do N(R) and N(N(R)) have limits?
Does incrementing N differently make any difference?
Are there different limits for N(R) and N(N(R))?
EXPERIMENT #2:
1. Now try N(R) = K *.
2. Set up a cell off to the right for K and enter a value.
3. Repeat process in experiment #1 for different values of R and K.
4. Record observations.
5. Answer the same questions as #6 in experiment #1.
EXPERIMENT #3:
1. Now try N(R) = K*+C where C is a constant.
2. Set up a cell off to the right for C and enter a value.
3. Repeat process in experiments #1 and #2 for different values of R, K, and C.
4. Record observations.
5. Answer the same set of questions as before.
CONCLUSION:
1. Do you see any overall patterns? Explain.
2. Do any specific R's produce different results? Explain.
3. Do any specific K's produce different results? Explain.
4. Do any specific C's produce different results? Explain.
5. Do any of your observations suggest that N(R) approaches a limit?
6. Do any of your observations suggest that N(N(R)) approaches a limit?
7. Is this a discrete or a continuous model?
8. What can you say overall for N(R) = K* + C?
INFINITE SEQUENCE
N(R)=R^N
N(N(R))=PREVIOUS N(R)^N
REMEMBER TO NOTE OBSERVATIONS OF THE CHANGE IN N(R) & N(N(R))
PERFORM THE EXPERIMENT WITH ONE R; RECORD OBSERVATIONS;
CHANGE R; REPEAT TRIAL; USE R>1 & 0<R<1
N
N(R)
N(N(R))
R
0
1
1
0.01
1
0.01
0.01
2
0.0001
1E-08
3
0.000001
1E-18
4
0.00000001
1E-32
5
1E-10
1E-50
6
1E-12
1E-72
7
1E-14
1E-98
8
1E-16
1E-128
9
1E-18
1E-162
10
1E-20
1E-200
11
1E-22
1E-242
12
1E-24
1E-288
13
1E-26
0
14
1E-28
0
15
1E-30
0
16
1E-32
0
17
1E-34
0
18
1E-36
0
19
1E-38
0
20
1E-40
0
21
1E-42
0
22
1E-44
0
23
1E-46
0
24
1E-48
0
EXPERIMENT #1
Trial#
R2
Trial#
R
K3
Trial#
R
K
CInvestigating the Sum of an Infinite Geometric Series
Technology: This activity requires the use of a spreadsheet program such as Excel or Microsoft WORKS. Students should be familiar with basic spreadsheet capabilities, including the use of formulas and replication.
Teacher notes: Introduce this activity once students have studied the behavior of different kinds of sequences and have been introduced to series.
Series: If you add the terms of a sequence, the sum is called a series. For example, the sequence: 3, 7, 11, 15,... yields the series: 3 + 7 + 11 + 15 + ...
The n-th partial sum of a series is the sum of the first n terms of that series and is represented by Sn . For the example above,
S1 = 3
S2 = 3 + 7 = 10
S3 = 3 + 7 + 11 = 21
S4 = 3 + 7 + 11 + 15 = 36
Notice that the partial sums also form a sequence: 3, 10, 21, 36, ... A partial sum is often represented using "sigma" notation. If t k represents the k-th term of the sequence, the n-th partial sum can be represented:
Sn =
If the series is infinite, it may or may not be useful to study the behavior of the sequence of its partial sums. For example, the series: 1 + 6 + 11 + 16 + 21 + ... has partial sums that just keep getting bigger as n increases. Examining the partial sums of infinite geometric series leads to more interesting conclusions.
Consider the infinite geometric series:5 + + + + ...
The first few partial sums are: S1 = 5
S2 =5 + = 7
S3 = 5 + + = 8
S4 =5 + + + = 9
S5 =5 + + + + = 9
The partial sums are increasing, but they seem to be getting closer (converging) to 10. We say that series converges to a number, S, if its sequence of partial sums, Sn , converges to that number, S.
Exploring Infinite Series on the Spreadsheet
Use your spreadsheet to construct the following:
Col A The value of n (the number of the term).
Col B The terms of the sequence from 1 to n.
Col C The sequence of partial sums.
For each sequence, list an approximation for the i-th term requested and for the i-th partial sum. Also, give the limit of the sequence, if it exists, and the limit of the sequence of partial sums. Generate at least twenty terms of each sequence and associated series.
1. The geometric sequence with first term: 4 and r =
t18 = __________________ S10 = __________________________
limit tn = ______________ limit Sn = ______________________
2. The geometric sequence with first term: .4 and r = -1.2
t14 = __________________ S14 = _________________________
limit tn = ______________ limit Sn = _____________________
3. The geometric sequence with first term: 1.75 and r =
t19 = __________________ S13= _________________________
limit tn = ______________ limit Sn = _____________________
4. The geometric sequence with first term: 4 and r =
t9 = __________________ S14 = _________________________
limit tn = ______________ limit Sn = _____________________
5. The geometric sequence with first term: 100 and r = .8
t12= __________________ S20 = _________________________
limit tn = ______________ limit Sn = _____________________
Conjecture: An infinite geometric series converges to a number, S, when the value
Bouncing Ball Problem. Suppose that you drop a ball from a window 18 meters above the ground. The ball bounces up to 80% of its previous height with each bounce. How far does the ball travel between the first and second bounce? Between the second and third bounce? Between the third and fourth bounce?
If the ball continues to bounce this way until coming to rest, how far has it traveled from the time it was dropped from the window?
Nested Squares Problem. A set of nested squares is drawn inside a square of edge 1 unit. The corners of the next square are the midpoints of the sides of the preceding square.
Set up four columns on your spreadsheet:
Col A The level of your drawing. Let the original square be level 1.
Col B The length of a side of each new square in the figure.
Col C The area of each new square formed.
Col D The cumulative sum of all the squares starting with square 1.
Use your worksheet to answer the following:
1. What is the length of the side of the 11th square formed by this process? _______
2. How is the length of the sides of the squares changing? ____________________
3. What is the area of the fourth square? _____ ...of the eighth square? _________
4. How is the area of the squares changing? ________________________________
5. What is the sum of the areas of the first 6 squares? _____ ...of the first 7? _____
6. What finite number does this area sum seem to be approaching?______________
7. Does the sum of the perimeters seem to be approaching a finite number? _______
Activity 3: Informal Investigation of the Limit of a Function
Technology: This activity requires the use of a spreadsheet program such as Excel. The students should have enough familiarity with spreadsheet use to put the appropriate formulas in the spreadsheet.
Teacher notes:The teacher should set up the spreadsheet in advance. The formulas used are listed here: (Thanks to David Bannard for the spreadsheet layout.)
C D E F G H
Right
Left
x
y =
x
y =
=B11
=SIN(C11)/C11
=$B$12-($B$11-$B$12)
=SIN(E11)/E11
=$B$14+$B$15
=$B$14-$B$15
=(C11+$B$12)/2
=SIN(C12)/C12
=(E11+$B$12)/2
=SIN(E12)/E12
=$B$14+$B$15
=$B$14-$B$15
=(C12+$B$12)/2
=SIN(C13)/C13
=(E12+$B$12)/2
=SIN(E13)/E13
=$B$14+$B$15
=$B$14-$B$15
Setting up the graph chart takes a bit of doing. To get both left and right limits on the same graph, you must begin with the , , [add series] commands after you have the initial graph. To set it up for the right, chart C to D for the function, C to G and C to H for the epsilon line. On the left for the same lines, chart E to F, E to G and E to H.
The student screen should be so that the chart shows as well as the spreadsheet. The students should be encouraged to play around with it awhile and get comfortable with what each of the columns is showing, and how to tell what the limit is and when you have selected a good epsilon for a given delta.
Student Activity Sheet on the Limit of a Function
Idea of a limit: The mathematical statement of a limit is written : f(x) = L
The intuitive idea of a function approaching a limit says that as x gets close to some value, a the value of the function f(x) gets close to some limit, L. You can generally get a good idea of what limit a function is approaching by using your graphing calculator.
A more formal definition of a limit:
f(x) = L means that for any small epsilon (e) you select, you can find a delta ( ) such that whenever 0<|x-a| < then 0<|f(x)-L|< e.
Instructions: Enter each function on the spreadsheet in both column D and F using column C and column E as the x value, respectively. Be certain to copy the formula down in the column. For each, pick an x start value near the a value and try to determine the limit of the function. When you have determined the limit, find a delta which will give you an epsilon < .001. When you have succeeded, your graph on the spread sheet should `fill' the area between the two lines of the epsilon. Like this:
If the function crosses the epsilon line, then your delta is too large. If it doesn't `fill' the area, it is too small. |
Algebra 1
Class.com algebra courses provide the rigorous curriculum of a traditional classroom, with ample opportunities to practice concepts, refine skills, learn new material, and build math vocabulary. Among many cutting-edge and interactive features, our algebra courses include the following:
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Writing assignments and discussion groups
Computer-graded self-checks, quizzes, and final exam
Algebra 1A
Algebra 1A, designed as the first semester of a middle- or high school math course, introduces students to algebra and illustrates its relevance in today's world. Students evaluate expressions, graph and solve linear functions and inequalities, and learn problem-solving strategies. Scope and Sequence
Algebra 1B
Algebra 1B is the second semester of a middle- or high school math course. Students continue their progression through algebraic concepts, expanding their knowledge of functions and relations, simplifying rational and radical expressions, solving and graphing radical and quadratic equations and inequalities, and analyzing data and making predictions. Students are introduced to graphing calculators in this course. Scope and Sequence |
Connecting to prior knowledge and real-world experiences can help students become comfortable and familiar with new mathematics vocabulary.
Many times students struggle with the mathematics vocabulary necessary to pass the GED® test and to cope with daily life. One way to introduce new terms is to help students connect with what they already know or can guess about the word or term. A real-world connection can also help to increase students' comfort level with new words, concepts, and terms. Students express a sense of relief and accomplishment when new terms can be self-defined using vocabulary and concepts with which they are familiar and comfortable |
What is Calculus About?
W. W. Sawyer
What is Calculus About? gives students the big picture of calculus. It should be read by prospective and current calculus students and by their teachers. Even someone who has completely mastered the technical side of the subject can benefit from being reminded of the essentially simple ideas and the calculational needs that led mathematicians to develop the rather complex machinery of calculus. Sawyer deals with it all, from what background a student needs to begin, to the study of speed and acceleration, to graphing (slope and curvature), to areas, volumes, and the integral. |
Problem solving through an optimization problem in geometry. (English)
Teach. Math. Appl. 30, No. 2, 53-61 (2011).
Summary: This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect on the different aspects of the problem and its solution. In addition, other than the traditional calculus approach to solve this problem, an elegant geometric approach is introduced. (ERIC) |
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Program Features
Our unique approach involves splitting instructional time between student-centered instruction in the classroom and self-paced learning using our adaptive software. Students spend 60% of the time in the classroom using our textbooks in an approach that involves task-based lessons, collaborative learning, and real-world problems and contexts. The remaining 40% of students' time is spent learning via our Cognitive Tutor software, which offers the most precise method for differentiating instruction available |
LinkPlug! - Science and Technology - Mathematics is about providing a directory of quality sites for world wide web users. Our goal is to list the best sites for a wide variety of topics giving our users the most relevant results for their searches. Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change. Includes links to a glossary of terms. Material ranges from undergraduate to research level. Learn about the foundations of mathematics, logic, algebra, geometry, probability, and statistics. Find math lesson plans, problems, help, and games. Explore a wide range of recent research in mathematics.Statistical Analysis Software We specialize in different statistical analysis software to conduct statistics analysis in Microsoft Excel, for both PC and MAC users!Tue, 17 May 2011 06:37:10 GMT |
Welcome to the Orange High School
Math Department
The Mathematics Department offers a variety of courses to help students acquire prerequisite skills needed for future careers. The number of units a student needs for graduation depends upon the course of study chosen at the high school level. Please refer to the State of North Carolina Department of Public Instruction web site about graduation requirements at:
The use of calculators is required in all math classes at Orange High School. Many upper-level math classes assume that a student has access to a graphing calculator at home. Consistently paced practice of mathematics is a necessity and thus students will usually have homework daily. Mathematics is the language for many subjects and applications allow students to use mathematics. Students will be expected to solve problems allowing them to see to power of mathematics in their daily lives. Having students become better problem solvers is a goal of the mathematics department. |
Product Description
Have additional students using Teaching Textbooks Math 6? This additional student workbook and answer booklet will allow extra students to complete the course in their own book. Perfect for co-ops or siblings! Workbook is 623 pages, softcover, spiral-bound. Answer booklet is 46 pages, softcover. This set does NOT include CD-ROMs; this book is not designed to be used without the Math 6 CD-ROMs. Teaching Textbooks Grade 6.
Product Reviews
Math 6: Teaching Textbooks, Extra Workbook
5
5
3
3
Excellent curriculum for independent math learning
My daughter completed the Teaching Textbooks 5 and wanted to continue on with level 6. For 5 we used both CDs and the workbook, but she often didn't need the book. So for 6 I bought the CDs only. After a few lessons, she requested a workbook. She realized that copying the problems onto paper introduced more possibility for error and took longer. She also told me that the book had information that she liked to turn back and reference.
You certainly can use TT curriculum without the workbook, but having the book makes it much easier.
April 4, 2011
These math books are wonderful. Easy to learn!!
I am so glad that we found the Teaching Textbook. They make learning math so much easier. We will absolutely continue to use them each year. Each lesson teaches something new, but reviews the past lessons. That way you continue to keep reviewing what you have learned. We did not get the cd's this year, but we will for next year.
March 26, 2011
The content is wonderful!
This is the first time I have changed our math curriculum in seven yrs. of homeschooling. I love the teaching textbooks.
The workbook is great practice to reinforce what is on the CDs. I would highly recommend this program.
November 3, 2010 |
Subject overview
Why mathematics?
Mathematics is core to most modern-day science, technology and business. When you turn on a computer or use a mobile phone, you are using sophisticated technology that mathematics has played a fundamental role in developing. Unravelling the human genome or modelling the financial markets relies on mathematics.
As well as playing a major role in the physical and life sciences, and in such disciplines as economics and psychology, mathematics has its own attraction and beauty. Mathematics is flourishing: more research has been published in the last 20 years than in the previous 200, and celebrated mathematical problems that had defeated strenuous attempts to settle them have recently been solved.
The breadth and relevance of mathematics leads to a wide choice of potential careers. Employers value the numeracy, clarity of thought and capacity for logical argument that the study of mathematics develops, so a degree in mathematics will give you great flexibility in career choice.
Why mathematics at Sussex?
Mathematics at Sussex was ranked in the top 20 in the UK in The Sunday Times University Guide 2012.
In the 2008 Research Assessment Exercise (RAE) 90 per cent of our mathematics research and 97 per cent of our mathematics publications were rated as recognised internationally or higher, and 50 per cent of our research and 64 per cent of our publications were rated as internationally excellent or higher.
The Department awards prizes for the best student results each year, including £1,000 for the best final-year student.
In 2011, US careers website Jobs ratedranked mathematician to be the second most popular job out of the 200 considered.
You will find that our Department is a warm, supportive and enjoyable place to study, with staff who have a genuine concern for their students.
Our teaching is informed by current research and understanding and we update our courses to reflect the latest developments in the field of mathematics.
MMath or BSc?
The MMath courses are aimed at students who have a strong interest in pursuing a deeper study of mathematics and who wish to use it extensively in careers where advanced mathematical skills are important, such as mathematical modelling in finance or industry, advanced-level teaching or postgraduate research.
Applicants unsure about whether to do an MMath or a BSc are strongly advised to opt initially for the MMath course. If your eventual A level grades meet the offer level for a BSc but not an MMath we will automatically offer you a place on the BSc course. Students on the MMath course can opt to transfer to the BSc at the end of the second year.
Programme content
This course is ideal if you want to take a degree in mathematics, but your qualifications do not meet the entry requirements for a three-year course. The final honours degree is equivalent to a standard three-year BSc (Hons) degree.
In the foundation year, you develop your basic mathematical skills and understanding. You take modules on calculus, geometry and algebra, including concepts of proof and logical argument. Throughout the year you will be introduced to many mathematical applications from statistics, mechanics and computer science. On satisfactory completion of the foundation year, you may transfer to any BSc mathematics degree recognise that new students have a range of mathematical backgrounds and that the transition from A level to university-level study can be challenging, so we have designed our first-term modules to ease this. Although university modes of teaching place more emphasis on independent learning, you will have access to a wide range of support from tutors.
Teaching and learning is by a combination of lectures, workshops, lab sessions and independent study. All modules are supported by small-group teaching in which you can discuss topics raised in lectures. We emphasise the 'doing' of mathematics as it cannot be passively learnt. Our workshops are designed to support the solution of exercises and problems.
Most modules consist of regular lectures, supported by classes for smaller groups. You receive regular feedback on your work from your tutor. If you need further help, all tutors and lecturers have weekly office hours when you can drop in for advice, individually or in groups. Most of the lecture notes, problem sheets and background material are available on the Department's website.
Upon arrival at Sussex you will be assigned an academic advisor for the period of your study. They also operate office hours and in the first year they will see you weekly. This will help you settle in quickly and offers a great opportunity to work through any academic problems.
What will I achieve?
understanding of the structures and techniques of mathematics, including methods of proof and logical arguments
written and oral communication skills
organisational and time-management skills
an ability to make effective use of information and to evaluate numerical data
IT skills and computer literacy through computational and mathematical projects
you will learn to manage your personal professional career development in preparation for further study, or the world of work.
Core content
Foundation year
You develop your basic mathematical skills and understanding. You take modules on calculus, geometry and algebra, including concepts of proof and logical argument. Throughout the year, you will be introduced to many mathematical applications from statistics, mechanics and computer science.
Year 1
You take modules on topics such as calculus • introduction to pure mathematics • geometry • analysis • mathematical modelling • linear algebra • numerical analysis. You also work on a project on mathematics in everyday life.
Year 2
You take modules on topics such as calculus of several variables • an introduction to probability • further analysis • group theory • probability and statistics • differential equations • complex analysis • further numerical analysis.
Year 0
Decision Mathematics
15 credits
Autumn teaching, Year 0
This module will cover some basic ideas of decision maths, probability and statistics, with an emphasis on applications in management. We will cover algorithms such as critical path analysis and linear programming. There will be a discussion of probability, looking at simple discrete and continuous distributions, and an introduction to statistics, covering descriptive statistics, regression and time series.
Foundation Mathematics
30 credits
Autumn & spring teaching, Year 0
This module covers the mathematics required for progression to year 1 of courses in physics, engineering or mathematics. You cover algebra, geometry, trigonometry, calculus (differential and integral), vectors, complex numbers and series. Including:
Calculus 1: (differentiation) basic differentiation. The product and quotient rule. Function of a function. Differentiation of parametric forms and implicit functions. Second order differentiation and turning points.
Calculus 2: (Integration) basic integration. Standard integrals, integration by inspection, by substitution, by parts, using partial fractions. Definite integrals. Solution of first order differential equations by separation of variables.
Series and approximations: permutations and combinations. Arithmetic and geometric progressions. Binomial theorem. Maclaurin's and Taylor's theorem.
Further Mathematics
60 credits
Autumn & spring teaching, Year 0
This module develops essential elements of mathematics, concentrating on the fundamentals of algebra, calculus and geometry. The module is broadly equivalent to an A-level Further Mathematics course concentrating on these elements.
Project
15 credits
Spring teaching, Year 0
You produce two projects- 3,000 words and 6,000 words, on subjects of your own choosing, possibly from a list of suggested titles.
Entry requirements
Sussex welcomes applications CC
Specific entry requirements: A levels must include Mathematics with at least grade C prepare you for employment in fields such as software development, actuarial work, financial consultancy, accountancy, business research and development, teaching, academia and the civil service. All of our courses give you a high-level qualification for further training in mathematics.
Recent graduates have taken up a wide range of posts with employers including:
actuary at MetLife
assistant accountant at World Archipelago
audit trainee at BDO LLP UK
credit underwriter at Citigroup
graduate trainee for aerospace and defence at Cobham plc
pricing analyst at RSA Insurance Group plc
assistant analytics manager at The Royal Bank of Scotland
associate tutor at the University of Sussex
health economics consultant at the University of York
risk control analyst at Total Gas & Power
supply chain manager at Unipart Group
technology analyst at J P Morgan
digital marketing consultant at DC Storm
junior financial advisor at Barclays
audit associate at Ernst & Young
claims graduate trainee at Lloyds of London
development analyst at Axa PPP healthcare
fraud analyst at American Express
futures trader at Trading Tower Group Ltd
accountant at KPMG |
Short Course In Discrete Mathematics
9780486439464
ISBN:
0486439461
Pub Date: 2004 Publisher: Dover Pubns
Summary: What sort of mathematics do I need for computer science? In response, a pair of professors at the University of California at San Diego created this text. Explores Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, sequences, and series. Assumes some familiarity with calculus. Original 2005 edition. |
Product Details:
GDZ1361: Assist students to easily transition from arithmetic to algebra! Teachers can use the Helping Students Understand series as a full unit of study or as a supplement to their curriculum while parents can use this series to help their struggling students grasp algebraic concepts. This book includes step-by-step instructions with examples, practice problems using the concepts, real-life applications, a list of symbols and terms, tips, answer keys, reference, and NCTM Standards and Expectations for 2004. 128 pages.
Description:
GIV1001: Rising Readers Science Set (1 copy of each Science
book; total of 12 booksAbout this seriesEncourage young readers to ask questions and explore the world of Science. Each title introduces a life, earth, or physical science concept through ...
Description:
GDZ3779: Help students make the transition from Algebra to Algebra
II! Written for teachers to use as a full unit of study or as a supplement to their curriculum, this book helps simplify algebraic concepts. Parents and students can ... |
Lulu Marketplace
Math Mammoth Geometry 2
Math Mammoth Geometry 2 continues the study of geometry and is suitable for grades 6-7.
The main topics include:angle relationships, classifying triangles and quadrilaterals. angle sum of triangles and quadrilaterals, congruent transformations, including some in the coordinate grid, similar figures, including using ratios and proportions, review of the area of all common polygons, circumference of a circle (Pi),area of a circle,conversions between units of area (bothmetric and customary), volume and surface, area of common solids, conversions between units of volume (both metric and customary),some common compass-and-ruler constructions. |
Cl, you'll be ready to tackle other concepts in this book such as
Arithmetic and algebraic skills
Functions and their graphs
Polynomials, including binomial expansion
Right and oblique angle trigonometry
Equations and graphs of conic sections
Matrices and their application to systems of equations
Get all you need to know with Super Reviews! Each Super Review is packed with in-depth, student-friendly topic reviews that fully explain everything about the subject. The Pre-Calculus Super Review includes sets, numbers, operations and properties, coordinate geometry, fundamental algebraic topics, solving equations and inequalities, functions, trigonometry, exponents and logarithms, conic sections, matrices, and determinants. Take the Super Review quizzes to see how much you've learned - and where you need more study. Makes an excellent study aid and textbook companion. Great for self-study!
Calculus Equations & Answers ( Quickstudy: Academic ) For every student who has ever found the answer to a particular calculus equation elusive or a certain theorem impossible to remember, QuickStudy comes to the rescue! This 3-panel (6-page) comprehensive guide offers clear and concise examples, detailed explanations and colorful graphsall guaranteed to make calculus a breeze! Easy-to-use icons help students go right to the equations and problems they need to learn, and call out helpful tips to use and common pitfalls to avoid. Item:142320856
.
Well, the good news is that you can master calculus. It's not nearly as tough as its mystique would lead you to think. Much of calculus is really just very advanced algebra, geometry, and trig. It builds upon and is a logical extension of those subjects. If you can do algebra, geometry, and trig, you can do calculus.
Calculus For Dummies is intended for three groups of readers:
Students taking their first calculus course – If you're enrolled in a calculus course and you find your textbook less than crystal clear, this is the book for you. It covers the most important topics in the first year of calculus: differentiation, integration, and infinite series.
Students who need to brush up on their calculus to prepare for other studies – If you've had elementary calculus, but it's been a couple of years and you want to review the concepts to prepare for, say, some graduate program, Calculus For Dummies will give you a thorough, no-nonsense refresher course.
Adults of all ages who'd like a good introduction to the subject – Non-student readers will find the book's exposition clear and accessible. Calculus For Dummies takes calculus out of the ivory tower and brings it down to earth.
This useful guide helps both new students and those who need a refresher course to acquire practical skills in calculus through a series of 20 lesson plans that require a minimal time commitment. All key calculus topics are covered, from common functions and their graphs to differentiation, integration, and infinite series. The book contains hundreds of practice exercises without a lot of unnecessary theory or math jargon. Bonus sections offer additional resources and tips for taking standardized tests. |
Elementary Linear Algebra with Applications - 3rd edition
This book is intended for the first course in linear algebra, taken by mathematics, science, engineering and economics majors. The new edition presents a stronger geometric intuition for the ensuing concepts of span and linear independence. Applications are integrated throughout to illustrate the mathematics and to motivate the student.Edition/Copyright: 3RD 96 Cover: Hardback Publisher: Saunders College Division Published: 09/08/1995 International: No
View Table of Contents
Preface. List of Applications.
1. Introduction to Linear Equations and Matrices.
Introduction to Linear Systems and Matrices. Gaussian Elimination. The Algebra of Matrices: Four Descriptions of the Product. Inverses and Elementary Matrices. Gaussian Elimination as a Matrix Factorization. Transposes, Symmetry, and Band Matrices: An Application. Numerical and Programming Considerations: Partial Pivoting, Overwriting Matrices, and Ill-Conditioned Systems. Review Exercises.
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Discrete Mathematics and Combinatorics provides a concise and practical introduction to the core components of discrete mathematics, featuring a balanced mix of basic theories and applications. The book covers both fundamental concepts such as sets and logic, as well as advanced topics such as graph theory and Turing machines. The example-driven approach will help readers in understanding and applying the concepts. Other pedagogical tools-illustrations, practice questions, and suggested reading-facilitate learning and mastering the subject. |
There's something about calculus that can evoke a mixture of both wonder and dread.
I was recently reminded of my first encounter with calculus by the announcement of the
publication later this year of a new edition of the book Calculus Made Easy. More
than 30 years ago, the same title had proved irresistibly inviting to me as a high school
student facing the mysterious realm of limits, derivatives, and integrals. I ended up
purchasing a copy of the 1965 reprinting of the third edition, originally published in
1946. I still have the book.
There were several things about Calculus Made Easy that made it immensely
attractive. The author's name, Sylvanus P. Thompson (1851- 1916), carried an air of
authority and trustworthiness. At the same time, the book's bold, yet self-effacing
subtitle was heartening: BEING A VERY- SIMPLEST INTRODUCTION TO THOSE BEAUTIFUL METHODS OF
RECKONING WHICH ARE GENERALLY CALLED BY THE TERRIFYING NAMES OF THE DIFFERENTIAL CALCULUS
AND THE INTEGRAL CALCULUS. The ancient Simian proverb quoted at the beginning provided
just the right sort of encouragement: "What one fool can do, another can." I was
hooked.
The text proceeded about its business of unveiling the secrets of calculus in a
reassuringly straightforward, direct manner. The new edition has maintained that structure
and style, preserving the many examples and exercises that proved so useful to me. The
main change is the addition of three "preliminary" chapters, written by Martin
Gardner, explaining the concepts of function, limit, and derivative. An appendix, also by
Gardner, introduces some recreational math problems that involve calculus.
"It is true that [Thompson's] book is old-fashioned, intuitive, and traditionally
oriented," Gardner writes in the preface to the new edition. "Yet no author has
written about calculus with greater clarity and humor." Interestingly, Thompson
himself was a physicist and electrical engineer, and his book usually doesn't get much
respect from mathematicians.
Calculus Made Easy proved a valuable reference and source of examples when I
taught high school calculus for a few years in the late 1970s. I also often consulted
several 19th-century calculus textbooks that I had found. These books typically had few
diagrams, instead featuring exercise sections with amazingly long lists of problems.
Part of the calculus education landscape has changed considerably since my teaching
days. Students can use graphing calculators or computers to solve calculus problems and to
explore many different kinds of mathematical behavior. It's easy to obtain pictures of
what's going on.
Software products such as Calculus WIZ are advertised as homework solvers for
students. "Are you worried that calculus will sabotage your GPA or, even worse, that
you might fail it? Calculus WIZ actually does the calculus for you—and shows
its work."
At the same time, leaders of a movement to reform calculus teaching have advocated a
shift in emphasis from problem solving, which computers can do much faster and more
accurately, to developing an understanding of what calculus can do and building an
awareness of the richness and elegance of the subject.
Is there still a place for Calculus Made Easy? "Curiously, Thompson's first
edition, with its great simplicity and clarity, is in a way closer to the kind of
introductory book recommended today by reformers who wish to emphasize the basic ideas of
calculus," Gardner notes. In addition to teaching his readers how to differentiate
and integrate simple functions, Thompson explains the "philosophy of the
subject."
Thompson's compact book also stands as a rebuke to the hefty, overstuffed volumes
lugged around by today's college calculus students. One of the few current textbooks that
actually gets right to the point is the slim volume Calculus Lite, written by Frank
Morgan of Williams College.
Other antidotes to the contemporary norm are also available. Colin Adams of Williams
College and Joel Hass and Abigail Thompson of the University of California, Davis have
written How to Ace Calculus: A Streetwise Guide. A breezy, cheerful, conversational
tone and humor, via outrageous puns and ridiculous jokes, sugarcoat the neatly packaged
nuggets of calculus wisdom dispensed by the book. It's funny and irreverent, but it also
tends to treat calculus as an unfortunate hurdle that must somehow be surmounted.
David Berlinski's A Tour of the Calculus is another sort of antidote. A cross
between a textbook and a romance novel, it gleefully plunges into the sort of calculus
taught in a beginning course. From a mathematical point of view, there's nothing new here.
The book's appeal stems from its passionate voice and its sense of wonder at the amazing
intellectual achievement that calculus represents.
In the end, calculus isn't easy. It doesn't automatically seep into the mind. It
requires thought and hard work. The best guides—whether teachers or
books—illuminate the way |
Using interactive manipulations created with Mathematica, the Illinois State Water Survey studies groundwater recharge and discharge, as deemed critical by the National Research Council. Hydrogeologist Yu-Feng Lin explains the advantages gained from using Mathematica in this videoMathematica gives students the power to manipulate interactive graphics and develop complex data models. High-school teacher Abby Brown shares the success she experiences by using Mathematica in her classroom.
Mathematica gives students the power to manipulate interactive graphics and develop complex data models. High-school teacher Abby Brown shares the success she experiences by using Mathematica in her classroom. Includes Spanish audio Includes Spanish audio.
Paul Abbott, a faculty member in the school of physics at the University of Western Australia, uses Mathematica to build courseware, from lectures to exams. His students visualize surfaces, explore concepts interactively, hypothesize results, and check their work—all in Mathematica. |
MAA Review
[Reviewed by Allen Stenger, on 06/22/2010]
This is a very modest revision of the already-excellent second edition. It in an inquiry-based text and has what is probably a unique approach to a math appreciation course: rather than focusing on fun math or useful math, it tries to teach how mathematicians think and approach problems.
Although this third edition is 200 pages longer than its predecessor, much of the increase is due to reformatting, with about 80 pages of new material. Most of the book is completely unchanged. There is a new section in Chapter 5 on the Koenigsberg Bridge problem and Eulerian circuits, and Chapter 6 has been rearranged. The old Chapter 7, "Taming Uncertainty," has been split into separate chapters on probability and on statistical analysis of data and statistical inference. Most of the book's new material is in this new statistics chapter. This chapter adds a number of interesting real-world problems, such as "what exactly does 30% chance of rain mean?" and a look at the 1969 Vietnam draft lottery, where statistical data makes it clear that the draws were not randomized enough.
Bottom line: An improvement over an already-great text, but the improvements are fairly far along in the text and most courses will not get that far. Unfortunately, the existence of a new edition makes obsolete (in the eyes of booksellers) the previous perfectly-good edition.
Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.com, a math help site that fosters inquiry learning. |
UAF Core Curriculum in Mathematics
The goals of the mathematics core curriculum are to ensure that students develop basic numeracy skills, are able to employ problem solving strategies, can communicate mathematical concepts, and are able to construct and evaluate mathematical arguments. |
Linear Algebra is concerned with solving systems of algebraic linear equations. In introductory linear algebra, this is done using the technique of elimination which works for systems of two or three equations. However, when more than three equations need to be solved simultaneously, one needs to begin using arrays and matrices. |
*It is recommended that students earn at least a C in algebra before enrolling in Algebra 2-Trigonometry.Integrated Math and/or Math Technology are recommended for students who earned below a "C."
This is the third course in a sequence of courses preparing a student for college admission eligibility.It is also the first course in the sequence which requires average or above proficiency in the previous two courses.The student strengthens and extends the algebraic skills begun in the Algebra 1 course and continues a study of more advanced algebraic skills and applications with mathematical arguments.He/she also begins a study of trigonometry. |
Bob the terrorist wrote:If you got a C in maths GCSE, I wouldn't do maths A levelHah. Nah, AS physics is just an easier version of maths with some added splainin to do★ Economic Left: 91.2% Social Libertarian: 90.3%
We are convinced that freedom without Socialism is privilege and injustice, and that Socialism without freedom is slavery and brutality.
Bob the terrorist wrote:Agreed. It's when you look back at a gcse paper lieing about and can do a whole page with about 10 marks on in less than 30 seconds (the page i looked at was surds and powers), but in Alevel you are expected to know that stuff inside out - if you're lucky you might get a 1 marker for them.
Chris Kettle wrote:I only got a C in my Maths GCSE. I am hoping to do maths A Levels next year but I need to brush up on it, I can barely remember pythagoras theorem and quadratic equations. :/
ghqwerty wrote:I agree that Chris may struggle with the A-level course, but IIRC, you get a quick refresher in some of the stuff covered in GCSE (surds, quadratics etc.) anyway. To be completely honest, Core 1 - the first paper I took as part of AS maths - is basically just an extension of the topics from GCSE (for example, solving polynomials would probably replace quadratics, but the process is not too dissimilar).
In terms of the grades at GCSE, the grade boundaries are completely off what you'd expect from other subjects (as far as I know). IIRC, an A* for GCSE maths is about 60-70%, so you only need to get just over half of each paper correct to get into the top tier. I guess this has something to do with sixth forms/colleges only accepting students wanting further education to A-Level having at least a 'C' in GCSE maths and English.
To put your mind at ease Chris, some of the people I did maths with were around the B/C boundary at GCSE, and they didn't find AS too much of a chore. After doing a few mocks, you realise quite a lot of it is just repetition; so if you struggle, it may be worth trying to get the processes nailed so you can apply it again and again for a similar question with different values.
jimbojoy wrote:Never got round to doing it, I'd assumed it was just formulas/graphs?
LOL no.
Actually I guess graphs yes, but not really mathematical graphs. Most of them won't even need values on the axes to answer any given question. There are also some "divide one number by another" formulas too. But it's mainly just reasoning and saying why things should happen, and the worst thing is that it's completely subjective and you can't really be wrong. |
MATH P##-Series: Introductory Mathematics
When offered, courses in the MATH P##-series are used by
students who have a very weak high school background in Mathematics.
MATH P06/3.0 Introduction to Calculus
MATH P06/3.0 can only be taken by students who have not completed any Grade 12 Mathematics
course. It is not always available.
MATH P10/3.0, MATH P13/3.0, and MATH P14/3.0
These courses examine elementary concepts in mathematics for
students who are intending to teach at the primary/junior level. They are usually taken as electives by
upper-year Concurrent Education students teaching in the Primary/Junior
level. These courses do not prepare students
for any further courses in Mathematics or Statistics.
MATH 11#-Series: Linear Algebra
MATH 110/6.0
MATH 110/6.0 is an advanced course in linear algebra,
primarily designed for those students who intend to pursue a Mathematics or
Statistics Plan. Even if they are not
intending to study Mathematics or Statistics at an upper-year level, students
with a strong interest or background in mathematics (particularly those
planning to study Physics or Computing) are encouraged to consider this
course. Any student intending to pursue
a Plan in Mathematics or Statistics should choose this course, or MATH
111/6.0. It is also a good elective for
any Arts or Science student.
MATH 111/6.0
MATH 111/6.0 is a course in linear algebra, primarily
designed for students who intend to pursue a science discipline other than
Mathematics or Statistics. Students who
are planning to pursue a Plan in Physics or Computing in upper-years should
take this course, or MATH 110/6.0.
Students intending to pursue studies in Chemistry may wish to consider
this course in lieu of MATH 112/3.0. If
you are undecided as to what Plan you will pursue in upper-years at this time,
you should choose this course. It may
also be of particular interest to students in Economics who have a strong
mathematical background. It is a good
elective for any student in Arts or Science.
MATH 112/3.0
MATH 112/3.0 is an introductory course in linear
algebra. Students intending to pursue a
Plan in Chemistry should take this course, or one of the full-year linear
algebra courses noted above. It may also
be of particular interest to students in Economics, Geography, Political
Studies, Psychology, or Sociology, as it will help prepare students for the
second-year courses in statistics required in these Plans. It is a good elective for any student in Arts
or Science.
MATH 12#-Series: Calculus
MATH 120/6.0
MATH 120/6.0 is an advanced course in calculus, primarily
designed for those students who intend to pursue a Mathematics or Statistics
Plan. Even if they are not intending to
study Mathematics or Statistics at an upper-year level, students with a strong
interest or background in mathematics (particularly those planning to study
Physics, Chemistry, Geology or Computing) are encouraged to consider this
course. It is also a good elective for
any Arts or Science student.
MATH 121/6.0
MATH 121/6.0 is a course in calculus, primarily designed for
students who intend to pursue a science discipline other than Mathematics or Statistics. Students who are planning to
pursue a Plan in Physics, Chemistry, Computing, Geology or Environmental
Science in upper-years should take this course, or MATH 120/6.0. If you are undecided as
to what Plan you will pursue in upper-years at this time, you should choose
this course. It may also be of
particular interest to students in Economics who have a strong mathematical
background, instead of MATH 126/6.0. It
is a good elective for any student in Arts or Science.
MATH 122/6.0(NOTE: This course will not be offered during the 2012/2013 academic year)
MATH 124/3.0
This course in Calculus is designed
primarily for students who hold advanced standing (IB, AP or GCSE-level) in
differential calculus. The combination
of the TRansfer credit you receive (MATH 123/3.0) and this course (MATH 124/3.0) are equivalent to MATH 121/6.0 for all academic purposes. Students who are eligible will receive
transfer credit for MATH 123/3.0 (Differential Calculus, which is only available as a transfer credit) and will register
in MATH 124/3.0 (Integral Calculus) for the Winter Term. They will join the MATH 121/6.0 classroom in
January and continue their integral calculus training.
MATH 126/6.0
This is an introductory course in calculus, primarily
designed for students in Arts who have not previously taken calculus at the
Grade 12 level. Science students should not register in this course. Students who are planning to pursue a Plan in
Economics should take this course, or MATH 121/6.0. It is also a good elective choice for any
Arts student. It may also be of particular
interest to students in Geography, Political Studies, Psychology, or Sociology,
as it will help prepare students for the second-year courses in statistics
required in these Plans.
REGISTRATION: This
course is open only to Arts students If a course is offered in more than one section. When you register in the course, you must
choose the section that best suits your timetable. |
With the same design and feature sets as the market leading Precalculus, 8/e, this addition to the Larson Precalculus series provides both students and instructors with sound, consistently structured explanations of the mathematical concepts. Designed for a two-term course, this text contains the features that have made Precalculus a complete solution for both students and instructors: interesting applications, cutting-edge design, and innovative technology combined with an abundance of carefully written exercises. In addition to a brief algebra review and the core precalculus topics, PRECALCULUS WITH LIMITS covers analytic geometry in three dimensions and introduces concepts covered in calculus.
This market-leading text continues to provide both students and instructors with sound, consistently structured explanations of the mathematical concepts. Designed for a one- or two-term course that prepares students to study calculus, the new Eighth Edition retains the features that have made PRECALCULUS a complete solution for both students and instructors: interesting applications, cutting-edge design, and innovative technology combined with an abundance of carefully written exercises.
Get a good grade in your precalculus course with PrecalculusMike Sullivanís time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. In the Ninth Edition, Precalculus has evolved to meet todayís course needs, building on these hallmarks by integrating projects and other interactive learning tools for use in the classroom or online.
Get a good grade in your precalculus course with PRECALCULUSClear explanations, an uncluttered and appealing layout, and examples and exercises featuring a variety of real-life applications have made this text like you. The book also provides calculator examples, including specific keystrokes that show you how to use various graphing calculators to solve problems more quickly. Perhaps most important-this book effectively prepares you for further courses in mathematics.
Precalculus, Fifth Edition, by Lial, Hornsby, Schneider, and Daniels, engages and supports students in the learning process by developing both the conceptual understanding and the analytical skills necessary for success in mathematics. With the Fifth Edition, the authors adapt to the new ways in which students are learning, as well as the ever-changing classroom environment. integrating projects and other interactive learning tools for use in the classroom or online.
Suitable for either one or two semester college algebra with trigonometry or precalculus courses, Precalculus introduces a unit circle approach to trigonometry and includes a chapter on limits to provide students with a solid foundation for calculus concepts. The large number of pedagogical devices employed in this text will guide a student through the course. Integrated throughout the text, students and instructors will find Explore-Discuss boxes which encourage students to think critically about mathematical concepts. In each section, the worked examples are followed by matched problems that reinforce the concept being taught. In addition, the text contains an abundance of exercises and applications that will convince students that math is useful. A MathZone site featuring algorithmic exercises, videos, and other resources accompanies the text.
Get a good grade in your precalculus course with Cohen's PRECALCULUS: A PROBLEMS-ORIENTED APPROACH and it's accompanying CD-ROM! Written in a clear, student-friendly style and providing a graphical perspective so you can develop a visual understanding of college algebra and trigonometry, this text provides you with the tools you need to be successful in this course. Preparing for exams is made easy with iLrn, an online tutorial resource, that gives you access to text-specific tutorials, step-by-step explanations, exercises, quizzes, and one-on-one online help from a tutor. Examples, exercises, applications, and real-life data found throughout the text will help you become a successful mathematics student! |
Latest Polls
Mathematics
All students in Years 10 and 11 follow a course in Mathematics appropriate to their ability and needs. For the majority of students this will lead to a final GCSE examination.
In formulating the courses on offer to the students, regard has been taken of three main principles:-
1. That the methods of teaching and assessment aim to develop the full potential of the individual.
2. That the methods of teaching and assessment should enable each student to demonstrate what they know rather than what they do not know.
3. That the examination and coursework should not undermine the confidence of the candidate.
Students are taught in sets comparable to their ability. Movement between sets is possible at various times during the year. Students cover the following courses, depending upon which set they are placed.
Our overall intention is to develop the Mathematical ability of the individual to its full potential. Further information on the various courses on offer is available from any Mathematics teacher.
Any students deemed to be near the C/D border potentially will be allocated an extra period of "Study Plus" Mathematics to help ensure they reach the desired C grade |
Saxon Homeschool Teacher Lesson and Test CDs
The Saxon Teacher CDs provide your student with instruction for every lesson in the latest editions of
Saxon Math. In addition, the instructor shows how to work
every problem in the text. For those of you who want the "teacher" instruction for Saxon, this is the solution for you and your student. The
CDs play on your computer and is compatible with both Windows and Mac. It is formatted with a customized player that has helpful navigation tools.
The Saxon Teacher Math 5/4 CDs includes instruction for every part of every lesson. It has complete solutions for every example problem, practice
problem, problem set, and test problem in Saxon Math 5/4.
The Saxon Teacher Math 65 CDs includes instruction for every part of every lesson. It has complete solutions for every example problem, practice
problem, problem set, and test problem in Saxon Math 6/5.
The Saxon Teacher Math 7/6 CDs includes instruction for every part of every lesson. It has complete solutions for every example problem, practice
problem, problem set, and test problem in Saxon Math 7/6.
The Saxon Teacher Math 8/7 CDs includes instruction for every part of every lesson. It has complete solutions for every example problem, practice
problem, problem set, and test problem in Saxon Math 8/7.
Saxon Teacher Algebra ½ 3rd Edition Lesson and Test CDs
Publisher: Saxon Homeschool
The Saxon Teacher Algebra ½ CDs contain over 130 hours of
Algebra ½ content. Instruction for every part of every lesson and complete solutions for
every example problem, practice problem, problem set, and test problem in Saxon Algebra 1 is included.
There are 6 CDs in the set which cover 124 lessons and the test solutions.
The Saxon Teacher Algebra 1 CDs contain over 130 hours of Algebra 1 content. Instruction for every part of every lesson and complete solutions for every example problem, practice problem, problem set, and test problem in Saxon Algebra 1 is included.
There are 6 CDs in the set which cover 124 lessons and the test solutions.
The Saxon Teacher Algebra 2 CDs contain over 110 hours of Algebra 2 content. Instruction for every part of every lesson, as well as complete solutions for every example problem, practice problem, problem set, and test problem in Saxon Algebra 2 is included.
There are 5 CDs in the set which cover 129 lessons and the test solutions.
The Saxon Teacher Advanced Math CDs contain over 100 hours of Advanced Math content. Instruction for every part of every lesson, as well as complete solutions for every example problem, practice problem, problem set, and test problem in Saxon Advanced Math is included.
There are 5 CDs in the set which cover 125 lessons and the test solutions. |
Graphs In Discrete Mathematics
posted on: 25 May, 2012 | updated on: 29 Aug, 2012
Discrete mathematics is a distinct mathematical term rather than being continuous term. Graph, integers, etc. are the part of discrete mathematics it excludes the topics such as of Calculus and analysis, etc. or in short we can say discrete mathematics deals with the countable Sets. As such there is no specified definition of discrete mathematics.
Graph in discrete mathematics can be studied with the help of graph theory which is also considered as the part of combinatorics, but in the present era it is a separate branch of mathematics first investigated by D.König in the year 1930.
Also graphs are considered to be the prime subject in the discrete mathematics. graph theory discrete mathematics is considered among the omnipresent model of both the natural and the structures which are made by man. They can mold many type structures and Relations such as method dynamics in physical, social and biological system. They have their several uses in many fields like in computer science they represent communication network, organization of data, help in the flow of computation, data organization, etc. in the field of mathematics, they can be used in the Geometry and also in many areas of topology. Also the group theory has a close link with the algebraic graph theory.
Discrete mathematics is also known as finite mathematics and the decision mathematics. As it is given above that it studies the countable Sets but it is different from continuous graph, we must not mix continuous graph with the graph theory. The graphs in discrete mathematics are of the many types few of them are simple graph, multi graph, directed graph, pseudo graph and many more. Now we will see brief description about these graphs:
1. The simple graphs are un- weighted and not in the particular direction and they have no loops but they have multiple edges.
2. The graphs which have multiple edges are multiple graphs.
3. The graphs which are connected with the Set of nodes and with its edges are directed graph.
4. Pseudo graph has the multiple edges and the graph loops connect them.
Topics Covered in Graphs In Discrete Mathematics
In field of science, graph theory is one of the very important concepts which describes that how a graph models different type of mathematical structures and also it can be used for all those structures which are created by human beings.
Also graphs are ubiquitous models which may be useful for various Relations.
Graphs has wide use due to their practical im...Read More
Path can be defined as distance traveled by an object from one Point to another. Points are called vertices of the path. Let there be two vertices A and B, then path between these two vertices is called A – B path. The distance between these two points or vertices is known as edge. Hence a path may include several vertices and edges. The Set of vertices and edges ac...Read More
Cycle graph can be defined as a graph which is comprised of single cycle. In other words, if vertices in given graph are connected in a closed form then graph is called as cycle graph. A cycle graph may can also be referred to circular graph. In a cycle graph, if there are 'n' vertices then cycle graph will be denoted by C n and number of vertices (nodes) in C n is...Read More
Connectivity is related to the network flow problems. It is used to find out the minimum number of vertices or edges which can be used to disconnect the remaining nodes from each other. Connectivity of a graph actually shows the robustness of the graph. If there are two nodes or vertices A and B, then they will be said connected if there is a path from A to ...Read More |
CLEP - Trigonometry
Item# trigonometry1
$109.00
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The Trigonometry examination covers material usually taught in a one-semester college course in trigonometry with primary emphasis on analytical trigonometry. More than half the exam is made up of routine problems requiring basic trig skills; the remainder involves solving nonroutine problems in which students demonstrate an understanding of the concepts. A calculator is not permitted on the first part of the exam, but an online non-graphing calculator is available during the second part of the test. This computer software contains all the topics necessary for success on the CLEP-Trigonometry exam.
(25% of the exam) Trigonometric functions and their relationships: Cofunction relationships; Reciprocal relationships; Pythagorean relationships; Functions of two angles such as sin(x+y); Functions of double angles such as cos 2x; Functions of half angles; Identities
(15% of the exam) Evaluation of trig functions of angles with terminal sides in the various quadrants or on the axes, including positive and negative angles greater than 360 degrees.
(10% of the exam) Trigonometric equations
(15% of the exam) Interpreting graphs of trig functions
(15% of the exam) Trigonometry of the triangle including the law of sines and the law of cosines
(20% of the exam) Miscellaneous topics such as Inverse functions (arcsin, arccos, arctan) and Polar coordinates. This trigonometry computer software program contains 26 learning sections (30-60 minutes each) and two practice tests with explanations and solutions. Graphing calculator instruction is also included. |
The following computer-generated description may contain errors and does not represent the quality of the book: In the preparation of this book, the aim of the authors has been to give the student a working knowledge of the elementary processes of algebra, with a conviction of the truth of principles through illustrations and particular examples. Each principle, or method, is therefore first clearly illustrated by numerous and simple exercises worked in the text. But the student is not left to assume that the principles are thereby proved. Even a beginner should not be encouraged, by textbook or teacher, to accept an illustrative example as a proof, or he will lose much of the educational value of the study. Particular attention has been paid to the grading of the exercises. The introductory chapter extends the familiar processes of arithmetic to the corresponding processes of algebra. The pupil is led by simple exercises, similar to those in arithmetic, to understand the use of letters to represent general and unknown numbers. Negative numbers are naturally introduced in connection with the extension of subtraction of arithmetical numbers. The meaning and use of positive and negative nimibers, in the fundamental operations, are properly emphasized. Equations and problems are distributed throughout the book. The importance of equivalent equations is not overlooked, but is very briefly and simply considered in Chapter IV. Until that chapter is reached, the solutions of equations should be checked. |
Book Description: For all intermediate Microeconomics courses at the undergraduate or graduate level. Understand the practical, problem-solving aspects of microeconomic theory. Microeconomics: Theory and Applications with Calculus uses calculus, algebra, and graphs to present microeconomic theory using actual examples, and then encourages students to apply the theory to analyze real-world problems. The second edition has been substantially updated and revised, and is now offered with MyEconLab–the online tutorial and assessment solution that personalizes both the teaching and learning experience. |
Excursions in Classical Analysis
Hongwei Chen
Excursions in Classical Analysis will introduce students to advanced problem solving and undergraduate research in two ways: it will provide a tour of classical analysis, showcasing a wide variety of problems that are placed in historical context, and it will help students gain mastery of mathematical discovery and proof.
The author presents a variety of solutions for the problems in the book. Some solutions reach back to the work of mathematicians like Leonhard Euler while others connect to other beautiful parts of mathematics. Readers will frequently see problems solved by using an idea that might at first glance, not even seem to apply to that problem. Other solutions employ a specific technique that can be used to solve many different kinds of problems. Excursions emphasizes the rich and elegant interplay between continuous and discrete mathematics by applying induction, recursion, and combinatorics to traditional problems in classical analysis.
The carefully selected assortment of problems presented at the end of the chapters includes 22 Putnam problems, 50 MAA Monthly problems, and 14 open problems. These problems are not related to the chapter topics, but connect naturally to other problems and even serve as introductions to other areas of mathematics.
The book will be useful in students' preparations for mathematics competitions, in undergraduate reading courses and seminars, and in analysis courses as a supplement. The book is also ideal for self study, since the chapters are independent of one another and may be read in any order. |
More About
This Textbook
Overview
Discrete Mathematics, Second Edition is designed for an introductory course in discrete mathematics for the prospective computer scientist, applied mathematician, or engineer who wants to learn how the ideas apply to computer sciences. The choice of topics-and the breadth of coverage-reflects the desire to provide students with the foundations needed to successfully complete courses at the upper division level in undergraduate computer science courses.
This book differs in several ways from current books about discrete mathematics. It presents an elementary and unified introduction to a collection of topics that has not been available in a single source. A major feature of the book is the unification of the material so that it does not fragment into a collection of seemingly unrelated |
All Students are required to complete three credits in Mathematics, two credits in Algebra and one credit of Geometry or Geometry & Trigonometry. Students earn .5 credit each semester for full-year courses.
COURSE DESCRIPTIONS
BASIC MATH SKILLS .25 credit This course is a review of basic math skills. It includes addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals. Students will also work with percents and develop basic problem solving skills. The class will meet twice a week with homework assignments due at each class meeting. Calculators will not be used. The course is designed for 9th grade students who need to improve basic skills and will be required of students with low computation scores. Other students may register for the course, if they feel they would benefit from the additional drill and practice. PREREQUISITE: Department Recommendation or Department Approval. CLASS STATUS: Freshmen
AL The course is designed for students who have an average ability in mathematics. It differs from Algebra 1, Level A, in depth of subject matter and in problem difficulty. PREREQUISITE: Department Recommendation CLASS STATUS: Freshmen
HONORS AL This course is designed for students who are interested in mathematics and who have shown above-average ability. Students may accelerate by testing out of previously learned material, working ahead of the class (with teacher help) and starting Advanced Algebra as soon as this course is completed. Students may use the entire year to complete this course and then accelerate (with department recommendation) by taking Advanced Algebra and Honors Geometry and Trigonometry sophomore year. PREREQUISITE: Department Recommendation CLASS STATUS: Freshmen
ALGEBRA, PART 1 1 credit This course is an introductory Algebra course for students who have had difficulty in the study of mathematics. It includes a review of arithmetic skills when necessary. The course then introduces operations with signed numbers, properties of real numbers, linear equations, and some factoring of polynomials. PREREQUISITE: Department Recommendation CLASS STATUS: Freshmen
HONORS ALGEBRA 2 1 credit This course further develops the principles of Algebra 1 and, in general, deepens understanding of mathematical concepts. These concepts include operations in the real number system, equations and inequalities, arithmetic and geometric sequences and series, systems of equations in two and three variables, and complex numbers. The course also includes higher degree equations, matrices, and determinants, and logarithms. PREREQUISITE: Algebra 1 and Department Recommendation CLASS STATUS: Sophomore
ALGEBRA 2 1 credit This course reviews and further develops the principles of Algebra 1. These concepts include operations in the real number system, equations and inequalities, systems of equations, arithmetic and geometric sequences and series, and quadratic equations. The course also introduces matrices and determinants, higher degree equations, and complex numbers. PREREQUISITE: Algebra 1 and Department Recommendation CLASS STATUS: Sophomore
ALGEBRA, PART 2 1 credit This course reviews and develops the principles of Algebra, Part 1 and introduces new concepts. These include operations in the real number system, equations and inequalities, systems of equations and quadratic equations. PREREQUISITE: Algebra, Part 1 and Department Recommendation CLASS STATUS: Sophomore
*HONORS GEOMETRY & TRIGONOMETRY 1 credit This first part of this course attempts to develop basic reasoning patterns, an understanding of important geometric concepts, and the ability to write simple proofs. Concepts included are: points, lines and planes, angles, parallel and perpendicular lines, similar and congruent triangles, right triangles, polygons and quadrilaterals, and circles. The second part of the course introduces the study of trigonometric functions from both a right triangle and a circular function Honors Algebra 2 and Department Approval CLASS STATUS: Junior & Sophomore with Department Recommendation
GEOMETRY & TRIGONOMETRY 1 credit The first part of this course attempts to develop basic reasoning patterns and an understanding of geometric concepts. The course includes a study of points, lines and planes, angles, parallel and perpendicular lines, similar and congruent triangles, right triangles, polygons and quadrilaterals, and circles. The second part of the course introduces the study of trigonometric functions from a right triangle Algebra 2 and Department Recommendation CLASS STATUS: Junior
GEOMETRY 1 credit This course attempts to develop basic reasoning ability and an understanding of geometric concepts. Both inductive and deductive reasoning methods are used. Concepts included in the course are: points, lines and planes, angles, parallel and perpendicular lines, similar and congruent triangles, right triangles, polygons and quadrilaterals, circles, perimeter, area and volume, and a brief look at coordinate geometry. PREREQUISITE: Algebra 2 or Algebra, Part 2 and Department Recommendation CLASS STATUS: Junior
*HONORS TR with above-average math ability, who have already completed a full-year geometry course and 2 years of algebra, but still need trigonometry in order to take higher level honors math courses. PREREQUISITE: Geometry and Department Recommendation CLASS STATUS: Junior & Senior
TR who have already completed a full-year geometry course and 2 years of algebra, but still needs trigonometry in order to take higher level math courses. PREREQUISITE: Geometry and Department Recommendation CLASS STATUS: Junior & Senior
STATISTICS .5 credit Statistics is a branch of mathematics dealing with the collection, analysis, interpretation and presentation of data. Statistics is used in all the sciences, in business, in medicine, and in many other fields. This course is recommended for college bound students, even those entering fields not directly involving mathematics. PREREQUISITES: Geometry & Trigonometry and Department Recommendation CLASS STATUS: Senior
DISCRETE MATH .5 credit Discrete mathematics deals with topics that have a step-by-step, or discrete, nature (rather than a continuous nature). Topics include logic, probability, math induction, graphs and trees, circuits, counting techniques, and other modern algebra topics. These subjects have important applications in the physical, engineering, management, computer, and social sciences. The importance of computer science in other disciplines is making discrete mathematics an essential course in many college programs. PREREQUISITE: Geometry & Trigonometry and Department Recommendation CLASS STATUS: Senior
*HONORS ANALYTIC GEOMETRY .5 credit This course starts with a review of the Cartesian coordinate system, the slope, midpoint and distance formulas, and systems of equations. Students learn to use these familiar formulas to prove geometric properties analytically. New topics include distance from a point to a line, linear programming, graphing techniques, polar coordinates, and the conic sections. PREREQUISITE: *Honors Geometry & Trigonometry and Department Recommendation CLASS STATUS: Junior & Senior
ANALYTIC GEOMETRY .5 credit This course reviews and continues the study of linear relations and functions, and the nature of graphs. It also introduces coordinate geometry and proofs, polar coordinates, and complex numbers. The final unit includes a study of the conic sections: circle, parabola, ellipse, and hyperbola.. PREREQUISITE: Geometry & Trigonometry and Department Recommendation CLASS STATUS: Senior
SENIOR MATH TOPICS 1 credit This course will include four areas of study: - Right Triangle Trigonometry will include trigonometric functions, Law of Sines and Cosines. Emphasis will be on learning to use trigonometry to solve triangles. - Math Applications – Students will explore various problem solving strategies and the application to real-world situations. - Statistics will cover basic statistics concepts, terms, and applications such as displaying data (graphs and frequency distributions), mean, median, mode, range, standard deviation. - Discrete Math will deal with topics that have a step-by-step, or discrete, nature like group-ranking, graphs and trees, and circuits. These topics have applications in business and social sciences. PREREQUISITE: Geometry and Department Recommendation CLASS STATUS: Senior
*ACC CALCULUS 1 credit (Saint Louis University title: MTX142: Calculus I) This course continues the development of advanced mathematics and encompasses a first course in the differential and integral calculus of functions of a single variable. Topics covered are real numbers, analytic geometry and their functions, limits and continuity, the derivative, the differential, anti-differentiation, and the definite integral. The course may be taken for high school and college credit or high school credit only. Upon completion of course requirements, a student receives 1 high school credit and/or four credit hours of college mathematics from Saint Louis University. PREREQUISITE: *Honors Pre-calculus and Department Recommendation CLASS STATUS: Senior |
Math
Department Mission The Mathematics Department course offerings provide learning opportunities for every student and their educational needs, experiences, and goals. The purpose of our curriculum is to provide students an opportunity to develop problem-solving skills and techniques for theoretical and applied practice. The Mathematics Department strives to create a learning environment that motivates the students of Riverside Brookfield High School to achieve to their fullest potential. Technology will be used to promote student engagement and understanding within learning activities. Graphing calculators are used as an integral part of concept development. The skills and techniques the students learn in the Mathematics Department will motivate and prepare them to become life-long learners of mathematics. |
Finite Mathematics For Business, Economics, Life Sciences And Social Sciences - 11th edition
Summary: This book covers mathematics of finance, linear algebra, linear programming, probability, and descriptive statistics, with an emphasis on cross-discipline principles and practices. Designed to be reader-friendly and accessible, it develops a thorough, functional understanding of mathematical concepts in preparation for their application in other areas. Each chapter concentrates on developing concepts and ideas followed immediately by developing computational skills a...show morend problem solving. Two-part coverage presents a library of elementary functions and finite mathematics. For individuals looking for a view of mathematical ideas and processes, and an illustration of the relevance of mathematics to the real world. Illustrates relevance of mathematics to the real worldThis book has a light amount of wear to the pages, cover and binding. Blue Cloud Books ??? Hot deals from the land of the sunGood
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Schaums Outline of Tensor Calculus
Summary
This lucid introduction for undergraduates and graduates proves fundamental for pactitioners of theoretical physics and certain areas of engineering, like aerodynamics and fluid mechanics, and exteremely valuable for mathematicians. This study guide teaches all the basics and efective problem-solving skills too.
Table of Contents
The Einstein Summation Convention.Basic Linear Algebra for Tensors.General Tensors.Tensor Operations.Tests for Tensor Character.The Metric Tensor.The Derivative of a Tensor.Further Riemannian Geometry.Riemannian Curvature.Spaces of Zero Curvature.Tensors in Differential Geometry.Tensors in Mechanics.Tensors in Special Relativity.Tensors Without Coordinates.Introduction to Tensor Manifolds. |
Algebra (pdf)
A branch of mathematics in which symbols represent numbers of a specified set of numbers and are related by operations that hold for all numbers in the set.
College Algebra
An understanding of the general concepts of relation and function and specifically of polynomial, exponential, and logarithmic functions. The ability to solve practical problems using algebra. |
Integrated Algebra
Integrated Algebra is a high school level mathematics course which provides opportunities for students to develop the math skills needed for success in their career and Algebra II or its equivalent. In this course, students will explore and solve mathematical problems, think critically, work cooperatively with others, and communicate ideas clearly. Selected topics from algebra will be interwoven with geometry, logical reasoning, measurement, statistics, and probability.
Integrated Algebra II
Integrated Algebra II is a high school level mathematics course which provides opportunities for students to develop the math skills needed for success in their career and in Advanced Algebra or Pre-Calculus. In this course, students will explore and solve mathematical problems, think critically, work cooperatively with others, and communicate ideas clearly. Selected topics from algebra and trigonometry will be interwoven with geometry, logical reasoning, measurement, statistics, and probability.
Advanced Algebra
Advanced Algebra is a high school level mathematics course which provides opportunities for students to develop the math skills needed for success in their career and in Pre-Calculus, Calculus, or other Post-Secondary mathematics courses. In this course, students will explore and solve mathematical problems, think critically, and communicate mathematical ideas clearly. Selected topics from algebra and trigonometry will be interwoven with geometry, logical reasoning, measurement, statistics, and probability.
Geometry
Geometry is the mathematical study of our physical world. Taken after Algebra I, Geometry includes the study of points, lines, planes, circles, angles, triangles, rectangles, area, and volume. Geometry helps to develop the ability to think critically while concepts are applied to real life situations.
Algebra II
Algebra II reinforces most of the concepts of Algebra I and includes relations and functions, polynomial functions, and exponential and logarithmic functions. An emphasis will include applications of algebra in problem solving. Students taking this course are encouraged to continue their study of math in Geometry or Pre-calculus.
Pre-Calculus
Pre-Calculus is designed for the college-bound student who wishes to eventually continue their study in calculus. This course allows students to explore elements of trigonometry, functions, series and sequences, logarithms, algebra, and geometry in preparation for advanced coursework in calculus at either the high school or college level. Students are strongly encouraged to obtain a graphing calculator.
College Pre-Calculus (college credit available)
This dual credit course is offered in partnership with Ohio University-Lancaster (OU-L) on the Eastland and Fairfield campuses. Students who meet the qualification requirements may enroll and will earn high school credit for math as well as 4 semester hours of credit from OU-L. This course follows an accelerated Pre-Calculus curriculum. Prerequisite: B average in Algebra II and placement at the appropriate college level on the COMPASS test.
Calculus
Calculus is a college level course in introductory calculus which includes concepts in elementary functions. This course provides opportunities for students to receive college credit as well as high school credit. It is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, geometry, trigonometry, and pre-calculus. A graphing calculator is required for this course.
College Calculus (college credit available)
This dual credit course is offered in partnership with Hocking College on the Eastland and Fairfield campuses. Students who meet the qualification requirements may enroll in this dual academic course. Successful students will earn high school credit for math as well as 3 semester hours of credit from Hocking College. This course follows an accelerated Calculus curriculum. Prerequisite: C or better average in Pre-Calculus or College Pre-Calculus |
MATH 155: Mathematics, A Way of Thinking
Course Description: An investigation of topics, including the history of mathematics, set theory, logic, number systems, basic algebra concepts, linear graph functions, geometry, counting methods, basic probability and statistics, consumer mathematics. There is an emphasis throughout on problem solving. Recommended for general education requirements, B.S. degree.
CORE SKILL OBJECTIVES: These skills are related to the General Education core abilities document. They are also written to refer to the various INTASC standards for the purposes of the Elementary Education program. Thinking Skills: The students will engage in the process of inquiry and problem solving that involves both critical and creative thinking. Students will (a) ...explore writing numbers and performing calculations in various numeration systems.
(b) ... solve simple linear algebraic equations.
(c) ... explore a few major concepts of Euclidean Geometry, focusing especially on the axiomatic-deductive nature of this mathematical system.
(d) ... develop an ability to use deductive reasoning, in the context of the rules of logic and syllogisms.
(e) ... explore the basics of probability.
(f) ... learn descriptive statistics, including making the connection between probability and the normal distribution table.
(g) ... learn the basics of financial mathematics, including working with the formulas for compound interest, annuities, and loan amortizations.
(h) ... solve a variety of problems throughout the course which will require the application of several topics addressed during the course.
Life Value Skills: The students will analyze, evaluate and respond to ethical issues from informed personal, professional, and social value systems.
Students will
(a) ... develop an appreciation for the intellectual honesty of deductive reasoning.
(b) ... understand the need to do one's own work, to honestly challenge oneself to master the material.
Communication Skills: The students will communicate orally and in writing in an appropriate manner both personally and professionally.
Students will
(a) ... write a mathematical autobiography.
(b) ... do group work (labs and practice exams), involving both written and oral communication.
(c) ... turn in written solutions to occasional problems.
Cultural Skills: The students will understand their own and other cultural traditions and respect the diversity of the human experience.
Students will
(a) ... explore a number of different numeration systems used by other cultures, such as the early Egyptian and the Mayan peoples.
(b) ... develop an appreciation for the work of the Arab and Asian cultures in developing algebra during the European "Dark Ages".
(c) ... explore the contribution of the Greeks, especially in the areas of Logic and Geometry.
It is also worth mentioning the NCTM (National Council of Teachers of Mathematics) "standards" for mathematics education, because they are also a list of some overall goals we strive for in this course:
The students shall develop an appreciation of mathematics, its history and its applications.
The students shall become confident in their own ability to do mathematics.
The students shall become mathematical problem solvers.
The students shall learn to communicate mathematical content.
The students shall learn to reason mathematicallyMATHEMATICAL AUTOBIOGRAPHY: Due: Monday, January 31 85% or more, "B" = 80% or more, "BC" = 75% or more, "C" = 70% or more, "CD" = 65% or more, and "D" = 60% or more. My advice is simple: if you wish to earn a satisfactory grade, make sure that you keep up with your work and that you turn in ALL the papers which are to be graded. The surest way to receive less than a "C" is to miss some classes and fail to turn in all your work! See the testing schedule included in the course schedule. The number of tests should give an adequate sampling of your understanding of course content.
ATTENDANCE POLICIES: Attendance is important in this class. There is really never a "good day" to miss because we will either be covering new material or working in groups on some problems. You will be give one point for each class you attend and these will be added to your point totals for this course,third floor, Murphy Center. I also want you to consider arranging to see me if you have a problem with some material. Sometimes we can resolve in a few minutes a difficulty that can cause problems for weeks. Don't wait to get the help you need. I want you to be successful in this class. Get involved. This can be a rewarding experience for you classmates(MC 320, 796-3085) within ten days to discuss your accommodation needs. |
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