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Textbook Experiencing Geometry: Euclidean and
Non-Euclidean with History (Third Edition), David W. Henderson and
Daina Taimina
Purposes
To develop a deep and personal understanding of
Euclidean, spherical and hyperbolic geometries and how they relate to
measuring the universe in which we live.
Overview
This course will take a more philosophical perspective on
geometry rather than a computational or result-based perspective. In
this class we will use several different methods to analyse
geometries. We will rarely have traditional lectures. More
frequently will be times for individual work, group work, and class
discussion. While there will be some familiar looking homework
exercises, there will mostly be more personal discussions of homework
problems.
Reading
I have intentionally chosen Henderson'€™s book as an
exploratory and philosophical text. In addition to planning time to do
homework, please take time to carefully read the chapters in the book.
Notice use of the words '€œtime'€ and '€œcarefully'€. Read the
sections slowly. Read actively, that is while writing and with models
at hand. If you do not understand some statement reread it, think of
some potential meanings and see if they are consistent, and if all else
fails, ask me. If you do not believe a statement, check it with your
own examples. Finally, if you understand and believe the statements,
consider how you would convince someone else that they are true, in other
words, how would you prove them?
Learning Outcomes
Upon successful completion of Math 335 a student will be
able to
'€Ę Compare and contrast the geometries of
the Euclidean and hyperbolic planes.
'€Ę Analyze axioms for the Euclidean
and hyperbolic planes and their consequences.
'€Ę Use transformational and axiomatic
techniques to prove theorems.
'€Ę Analyze the different consequences
and meanings of parallelism on the Euclidean and hyperbolic planes.
'€Ę Demonstrate knowledge of the
historical development of Euclidean and non-Euclidean geometries.
Grading
Your grade in this course will be based upon your
performance on two styles of homework, a project, an in-class exam and a
final experience. The weight assigned to each is designated below:
Homework Problems 3/5
Project
1/5
Final Experience
1/5
Homework Problems
Throughout the course you will write up discussions of
'€œProblems'€ from Henderson'€™s book. Before these papers are handed
in, I strongly suggest somehow submitting drafts to me for comments.
These drafts are not required, but will strengthen your understanding and
your final products. Drafts can either be submitted in paper or via
email. Either way I will return them with comments and
suggestions. The end goal of writing each problem will be presenting
your complete understanding of the question in a well-written
discussion. These discussions will be graded on a ten point decile
scale based on completeness, accuracy and writing.
These problems will be evaluated similarly to evaluating
papers in an English class.
0 missing or plagiarised
3 question copied, nothing written
6 something written that appears that it was only written
to take up space
7 substantially incomplete. Something written, but
does not really answer the main questions. Major errors.
Very poor writing
8 mostly complete. maybe a few minor errors
9 complete, no errors, some personal insight,
well-written
10 wonderful (includes concise, and to the the
point directly)
Solutions and Plagiarism
There are plenty of places that one can find all kinds of
solutions to problems in this class. Reading them and not referencing
them in your work is plagiarism, and will be reported as an academic
integrity violation. Reading them and referencing them is not quite
plagiarism, but does undermine the intent of the problems. Therefore,
if you reference solutions you will receive 0 points, but you will *not* be
reported for an academic integrity. Simply 'ۦ please do not read any
solutions for problems in this class.
Projects
Each student is responsible for completing a project as
part of a pair. A project will consist of reading one of chapters
11,14-22 from Henderson'€™s book or a similar portion of another book not
discussed in class (I have several options you may examine). The
materials for the projects must be chosen by February 22. Each project
will include a write-up of all the problems in the chosen part.
Finally, each of the projects will be presented in the last two weeks of
class.
Final Experience
The final experience will include extensive writing and
focused on summarizing the experience of different aspects of the
course. This product will be due at the time of the scheduled
final exam, May 12, 12-3p, when we will also meet to discuss the topic and
the course as a whole.
Geometer'€™s Sketchpad
We may occasionally using Geometer'€™s Sketchpad as a
method of gaining intuition for geometry. Details for working with
this software will be described in class no later than February 4 of
plans to observe the holiday.
Schedule
January 25 '€" February 13 Discuss Chapters
1-5 of Henderson
February 4
As a homework exercise,
show a model of a hyperbolic plane
February 18 - March 10 Discuss
Chapters 6, 7, 9 of Henderson
February 22
Final write
up of Chapters 1-5 '€œProblems'€ due
February 22
Projects
must be chosen by this date.
March 11 - 29
Discuss Chapters
8, 10 of Henderson
March 15
Drafts of Chapters 6, 7, 9 will not be accepted after
March 29
Final write up of Chapters 6, 7, 9 '€œProblems'€ due
April 1 '€" 18
Discuss Chapters 11, 12 of
Henderson, and Constructions
April 5
Drafts of Chapters 8, 10 will not be
accepted after
April 12
Final write up of Chapters 8, 10 '€œProblems'€ due
April 21
Drafts of Chapters 12, 13 will not be accepted
after
April 26 '€" May 6
Project presentations
May 6
Written projects due. Final write up of
Chapters 12, 13 "Problems" due
Wednesday May 15, 12-3p Final
experience - leftover presentations. | 677.169 | 1 |
Share and embed TI-Nspire documents online: create homework for the class or lesson ideas for colleagues. Create a new Web page in a few simple steps or add playable TI-Nspire documents to your Web page or blog – ideal for sharing your ideas with users who don't yet have TI-Nspire software installed.
TI-Nspire Student Software provides you with the same functionality as the handheld: Calculator, Graphs, Geometry, Lists & Spreadsheet, Data & Statistics, Notes, Programming and Vernier DataQuest™. Download the full software as either a .exe or zip file for Windows, or a Mac App. Fully functional for 30 days. Buy a permanent licence key below.
TI-Nspire Teacher Software provides additional functionality to help manage content, create documents that include Questions and deliver lessons with an on-screen handheld emulator. One software package now includes CAS and numeric functionality. Download the full software as either a .exe or zip file for Windows, or a Mac App. Fully functional for 30 days. Buy a permanent licence key in our online store.
TI-Nspire™ Software Features Summary
TI-Nspire™ Computer Software for Maths and Science has the same functionalities
as the TI-Nspire handheld device, offering a unique parallel learning experience.
Thanks to TI-Nspire Software, seamless creation and transition of classroom
materials between teacher and learner is possible:
• Teachers can use the software
to create materials for learners using handheld devices and/or the software.
•
Learners can easily transfer their work from the handheld device to the teacher's
computer for assessment - Assessment for Learning in practice!
FREE
online video tutorials now available from Atomic Learning
Already own TI-Nspire
Computer Software?
Get the free download for the latest TI-Nspire Computer
Software release.
Now compatible with Windows® Vista (Home Premium/Ultimate/ Business) and Mac®
OS, with added enhancements to programming functionality, Data & Statistics
and the addition of Polar Graphing.
Download the Latest Release | 677.169 | 1 |
Fort Worth Precalculus both steps are meaningless if you don't know or don't understand what's going on. You need to understand what you're doing and why. In another word, what you do should make sense to you | 677.169 | 1 |
This "book" isn't an explanation of mathematics at all; sure, I can accept that. My biggest qualm is that it isn't even written in Pushtu; sure, it has the same letters. Sure, the vocabulary could be bloody freaking accurate, but this book is written with English grammar, AND from LEFT to RIGHT! (This is a right to left language BTW.) Its like trying to read something below.
.is stupid above book The (the book above is stupid) ~This is written with Pushtu grammar BTW. .think is it I (I think it is)
Get the picture? Its an absolute waste of time, effort and money. Go elsewhere and don't even spend time considering this worthless book. There wasn't any effort put into it despite the notion otherwise. | 677.169 | 1 |
This is a free, online textbook offered by American Mathematical Society (AMS). "The sescond semicentennial volume contains brief treatises on eight representative subjects and a historical summary of American contributions of mathematics during the past fifty years." | 677.169 | 1 |
Math 0306 Sections
1.1 Introduction to Whole Numbers 1.2 Addition and Subtraction of Whole Numbers 1.3 Multiplication and Division of Whole Numbers 1.4 The Order of Operations Agreement
2.1 LCM and GCF 2.2 Introduction to Fractions 2.3 Addition and Subtraction of Fractions 2.4 Multiplication and Division of Fractions 2.5 Introduction to Decimals 2.6 Operations on Decimals 2.7 The Order of Operations Agreement
3.1 Introduction to Integers 3.2 Addition and Subtraction of Integers 3.3 Multiplication and Division of Integers 3.4 Operations with Rational Numbers 3.5 The Order of Operations Agreement
12.1 The Rectangular Coordinate System 12.2 Linear Equations in Two Variables 12.3 Intercepts and Slopes of Straight Lines 12.4 Equations of a Straight Line
13.1 Solving System of Linear Equations by Graphing 13.2 Solving System of Linear Equations by the Substitution Method 13.3 Solving System of Linear Equations by the Addition Method 13.4 Application Problems in Two Variables
MATH 2413 - Calculus I, 4 Credits
Textbook
Math 2413 Sections
2.1 The Tangent and Velocity Problems 2.2 The Limit of a Function 2.3 Calculating Limits Using the Limit Laws 2.4 The Precise Definition of the Limit 2.5 Continuity 2.6 Limits at Infinity 2.7 Derivatives and Rates of Change 2.8 The Derivative as a Function
3.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions 3.4 The Chain Rule 3.5 Implicit Derivatives 3.6 Derivatives of Logarithmic Functions 3.7 Rates of Change in the Natural and Social Sciences
11.1 Sequences 11.2 Series 11.3 The Integral Test and Estimates of Sums 11.4 The Comparison Tests 11.5 Alternating Series 11.6 Absolute Convergence and the Ratio and Root Tests 11.7 Strategy for Testing Series 11.8 Power Series 11.9 Representations of functions as Power Series 11.10 Taylor and Maclaurin Series 11.11 Applications of Taylor Polynomials | 677.169 | 1 |
Math 300: Mathematical Computing
Math 300 Syllabus
Welcome to Math 300 - Mathematical Computation. The goal of this course
is to make you more sophisticated in your knowledge of computing in
mathematics. Anyone can use a browser and a word processor, but mathematicians
and teachers need an array of more specialized techniques to do and communicate
mathematics in myriad formats. Mathematicians need unique powerful tools
to analyze their problems, and use multiple platforms for those ends.
To that end, we try to familiarize you with some of the most common
aspects of operating systems, networking, typesetting, and applications
that mathematicians use.
Instructor:
Kevin Cooper
Office:
Neill 322
Office Hours:
3-5 MWF: these will ordinarily be in room 120
Phone:
5-4771
Email:
[email protected]
Tests:
There will be two tests worth a total of 200 points.
Assignments:
There will be several assignments worth about 400 points. These will
typically involve solving a problem and writing about the solution,
and then typesetting that writing in some way. Several of the assignments
in this course include substantial writing components. You will be graded
on writing as well as computational understanding. Thus, technical proficiency
alone will not suffice to do well in the class.
Text:
This is it. There are some HTML text pages available at this site,
as well as somewhat more complete notes in portable document format.
There are other resources available on the Web to which we provide links.
Academic Integrity:
Because much of the work in this class is done electronically, some
students find it too tempting to copy the work of others. While we encourage
collaboration and helpfulness among students, ultimately students must
demonstrate that they have learned something by turning in their own
work. Assignments or exams that show clear evidence of plagiarism (copying)
will receive scores of zero, or in egregious cases might
lead to a failing grade in the class.
This can apply regardless of whether the
student in question was the one copying, or the one copied. Protect
your own work.
Topics:
Working Remotely
Operating Systems - especially Unix
HTML, MathML, XML
Tex and Latex2html - document formatting
Python - including programming
Students with disabilities
Reasonable accommodations are available for students with a documented disability. If you have a disability and need accommodations to fully participate in this class, please either visit or call the Access Center (Washington Building 217; 509-335-3417) to schedule an appointment with an Access Advisor. All accommodations MUST be approved through the Access Center. | 677.169 | 1 |
Apprenticeship & Workplace Mathematics 12
Prerequisite: Apprenticeship & Workplace Mathematics 11
This course includes the following topics: purchasing vehicles, small business liability, polygons, transformations, puzzles, precision and accuracy of instruments, probability, linear relations, central tendency, sine and cosine law.
This is a course for students who will be going directly into the work force or into some trades. | 677.169 | 1 |
Schaum's Outline Of Trigonometry - 3rd edition
Summary: Updated to match the emphasis in today's courses, this clear study guide focuses entirely on plane trigonometry. It summarizes the geometry properties and theorems that prove helpful for solving trigonometry problems. Also, where solving problems requires knowledge of algebra, the algebraic processes and the basic trigonometric relations are explained carefully. Hundreds of problems solved step by step speed comprehension, make important points memorable, and teach p...show moreroblem-solving skills. Many additional problems with answers help reinforce learning and let students gauge their progress as they goGoodwill BookWorks Austin, TX
No comments from the seller | 677.169 | 1 |
Contemporary's Number Power: Real World Approach to Math (The Number Power Series)
Book Description: Number Power is the first choice for those who want to develop and improve their math skills. Every Number Power book targets a particular set of math skills with straightforward explanations, easy-to-follow, step-by-step instruction, real-life examples, and extensive reinforcement exercises. Use these texts across the full scope of the basic math curriculum, from whole numbers to pre-algebra and geometry. Number Power: Review builds critical-thinking skills and reviews computational skills from whole numbers to beginning algebra and geometry | 677.169 | 1 |
Product Description
The Algebra 1: The Complete Course DVD Series will help students build confidence in their ability to understand and solve algebraic problems.
In this episode, students will learn about the history of problem solving and the derivation of the algebraic equation by functional exploration and by symbolic manipulation. Grades 5-9. 30 minutes on DVD. Finally learn the language you've always wanted to learn with the Living Language Method! | 677.169 | 1 |
determine if integrating a unit on functions would benefit students. Previous studies have shown that integrating science and mathematics increases students' understanding of certain topics in science. TypicallyEach year thousands of students are tracked into mathematics classes. In these particular classes, students may struggle or find their mathematics skills less academically able than their classmates and give up on the tasks that are introduced to | 677.169 | 1 |
Revise for MEI Structured Mathematics - FP1
Catherine Berry, Sophie Goldie, Richard Lissaman, Charlie Stripp
Summary: Revise for MEI Structured Mathematics has been written by experienced authors and examiners especially for A Level mathematics students and provides the ideal preparation for their exam. The series accompanies the MEI Structured Mathematics textbooks. This Revision Guide covers the full content of the FP1 module. Each topic is put into context in terms of its general application, and its links to other modules in the course. It also contains handy reminders of related topics covered previously, whilst worked solutions guide students through all the necessary steps in solving typical questions.
Features to help students to improve their grades and to ensure exam success include:
'Key Facts' - a summary of the essential points to remember 'Caution' - a guide to the most common exam pitfalls students can avoid.
This Revision Guide also has an accompanying website featuring:
'Test Yourself' - interactive multiple choice questions on every topic, with diagnostic answers which identify any weaknesses or common errors Exam-style questions - covering every topic, these audio-visual 'Personal Tutor' worked examples explain exactly how each type of question should be tackled.
This Revision Guide and website can be used throughout the course, but are also perfect for students to use at home on study leave. These ground-breaking Revision Guides will ensure that students go in to their exam with confidence.
written by experienced authors and examiners especially for MEI A Level mathematics students
ideal preparation for the MEI A Level exam
covers the full content of the Further Pure 1 module
worked solutions show students how to solve typical questions
'Key Facts' summarise the essential points to remember
'Caution' indicates the most common exam pitfalls students can avoid
accompanying website contains audio-visual 'Personal Tutor' worked examples explaining exactly how each type of question should be tackled
can be used throughout the course, but perfect for students to use at home on study leave | 677.169 | 1 |
Never worry about battery running down in a test. ? Easy to read clear function keys combined with the assistance of a step-by-step instruction manual to make learning scientific calculations almost painless! | 677.169 | 1 |
Whether
teaching calculus at the introductory or AP level, at a high school or
college, there is no better way to explore this rich study of movement
and change than through dynamic animation. Calculus In Motion™ animations are packaged on a CD and perform equally well on
either the Windows or Macintosh platform. An instruction booklet
is included. The animations described below must be opened by
The Geometer's Sketchpad v4 or v5 (no prior versions),
owned and sold by Key Curriculum Press ( on either
Windows or Macintosh platforms.
Although a detailed instruction manual is included on the CD-ROM (PDF
format), most of the animations can be run successfully using only the
on-screen information.
ARC LENGTH
Develop the idea of arc length using any f(x), parametric, or polar
curve & any number of partitions.
AREA BETWEEN 2 CURVES Sweeping horizontally or vertically, the first animation explains the main idea, then 8 specific examples
follow with changeable intervals, and finally, 2 animations (one for vertical sweeps and one for horizontal)
you can enter any desired curves as well as the boundaries of integration.
DEF. OF A DERIVATIVE
DEF.
OF INTEGRATION
INVERSE FUNCTIONS
Drag h to 0 to see PQ become the
tangent line. See the limit process in action. Also, create the
numerical derivative.
Sweep left or right
to accumulate the integral using standard changeable geometric
shapes. Also vary the start and stop points.
Using animated tangent lines,
compare the derivatives of inverse functions. "Morph" the curves
using sliders.
(*also for precalculus)
GRAPHERS Explore slope using animated tangent lines.
See any desired combination of f ', f '', area, and F. "Morph" each graph using
sliders. A 7th animation (not shown below) allows the user to
enter any
desired function and applies all of the same animated features
to it. (*also for precalculus)
RELATED RATES A click of a button advances time to commence the
action to these classic problems.
Other buttons reveal the values
and graphs of the rates.
RIEMANN SUMS Choose rectangles using left endpoints, right
endpoints, or midpoints; or trapezoids to approximate an
integral for any number partitions from 1 to 80!
Functions can be morphed by dragging sliders, or use the first
page to type in any desired function for f(x).
VOLUMES ON A BASE Visualize these shapes one step at a time. Start
by rotating the xy-plane to horizontal. View a few stationary
slices, then a sweeping slice, and finally, an accumulating slice.
Rotate the solid any time for other viewing angles. Choose from an
assortment of bases and cross-sections.
VOLUMES BY REVOLUTION These animations cover both the disk/washer
technique and the cylindrical shell technique.
Develop the process
by first revolving one lone rectangle. Next, revolve several
rectangles in a region and stack or nest the results.
Finally,
revolve any desired region (bounded by 1 or 2 functions of choice)
on an interval of choice, about any horizontal or vertical axis.
SLOPE FIELDS + EULER'S METHOD To introduce what a slope field is, use the graph
of f ' to see its values controlling a gliding dynamic "slope
column". Snapshots of this column are the
slope field. A tangent segment "pilots" the field to draw f.
Once understood, a different animation allows any differential
equation to be entered and generates the slope field.
Manually follow the field to draw f or use Euler's Method (includes
explanation of E.M. and numerical table of data). Easily adjustable.
LIMITS Explore the ε, ∂ definition of limits.
Evaluate the limits (full, left-hand or right-hand) of any
function (including piece-wise defined) as x →a or as x→±∞
MACLAURIN & TAYLOR SERIES Enter any f(x). Overlay a Maclaurin or
Taylor Series polynomial of degree n & use it to approximate
the value of f(x) at any point t. Vertical gray bands show
where the power series is within a chosen tolerance to f(x).
As n increases, the band widens. | 677.169 | 1 |
Find a SoutheasternMajor topics studied include: probability, combinatorics, set theory and graph theory. Set theory is the study of sets, both infinite and finite. Some basic operations of set theory include the union and intersection of sets | 677.169 | 1 |
Math 125 - Intermediate Algebra with Applications
Course Description
This course is designed for the intermediate algebra student who plans to continue on to MATH 300, 310, 320, 325, STAT 300, 301, or complete an associate degree. It does not fulfill the prerequisite for MATH 315, 330, or higher numbered math courses. Topics include linear functions, models, systems, and graphs, as well as polynomial, exponential, logarithmic, and quadratic functions. The course emphasizes authentic applications and mathematical models using real-world data.
Student Learning Outcomes
Upon completion of this course, the student will be able to:
identify and solve various types of equations and systems of equations.
factor a variety of polynomials.
collect like terms in simplifying polynomial, exponential, and logarithmic functions. | 677.169 | 1 |
About The Cartoon Guide to Calculus
Master cartoonist Larry Gonick has already given readers the history of the world in cartoon form. Now, Gonick, a Harvard-trained mathematician, offers a comprehensive and up-to-date illustrated course in first-year calculus that demystifies the world of functions, limits, derivatives, and integrals. Using clear and helpful graphics--and delightful humor to lighten what is frequently a tough subject--he teaches all of the essentials, with numerous examples and problem sets. For the curious and confused alike, The Cartoon Guide to Calculus is the perfect combination of entertainment and education--a valuable supplement for any student, teacher, parent, or professional.
About The Cartoon Guide to Calculus | 677.169 | 1 |
Boost your students understanding of Saxon Math with DIVE's easy-to-understand lectures! Each lesson in Saxon Math's textbook is taught step-by-step on a digital whiteboard, averaging about 10-15TAlgebra 2 covers traditional second year algebra topics as well as a semester of geometry, real world problems, linear and nonlinear equations, statistics and probability, graphing and basic trigonometry. This DIVE CD can be used with Saxon Algebra 2's 2nd and 3rd Editions; the CLEP Professor College Algebra CLEP Exam prep course is also included.
The Dive CD presents the material in an easy to understand format. Using the Dive CD with the textbook will allow my 9th grader to do the work almost completely on his own.
Share this review:
0points
0of0voted this as helpful.
Review 2 for Saxon Math Algebra 2 2nd & 3rd Edition DIVE CD-Rom
Overall Rating:
5out of5
DIVE CD Algebra 2 w/ CLEP Professor
Date:November 4, 2010
Chea
Location:Sacramento
Quality:
5out of5
Value:
5out of5
Meets Expectations:
5out of5
I've used the DIVE CD, since 76 series, and find them to be a wonderful additional tool to teach my child lessons.
First off; DIVE CD's were meant to be used 'WITH' Saxon Books, not separate, it was design to moves along with each lesson. If you don't have the books you will NOT get the full benefit..period.
It pains me to hear bad reviews about Saxon Math books or this DIVE CD, when not all the materials are being purchased to save money. You can not simply buy a CD and expect to get the results of the entire book series.
My son was able to move into College level math and beyond with this CD and the Saxon math series. He's planning on majoring in math, even though he was failing in the public school systems books. When I switched him to Saxon he excelled and is now three years ahead of his classmates. Something four years ago I never thought would happen.
I'm thank full for the option Saxon and DIVE CD's have provided.
Share this review:
+2points
2of2voted this as helpful.
Review 3 for Saxon Math Algebra 2 2nd & 3rd Edition DIVE CD-Rom
Overall Rating:
5out of5
Date:September 9, 2010
Christine Roth
The DIVE CD's are the best investment one can make when teaching math. Our children are enjoying math so much more and having an easier time learning. The ability to review anything they don't understand is priceless. Highly recommended, especially for those with several math students at different levels. CR
Share this review:
+3points
3of3voted this as helpful.
Review 4 for Saxon Math Algebra 2 2nd & 3rd Edition DIVE CD-Rom
Overall Rating:
3out of5
Date:August 12, 2009
Angela Rochester
I'm sure this cd would be a great help if you are already using Saxon Math, as I am told that Saxon builds on itself through the years. We had never used Saxon and found that there was not enough instruction to complete the problem sets. | 677.169 | 1 |
Introduction
American secondary mathematics education has been accused of it for years;
breadth without depth, and lack of connections to anything meaningful.
Certainly the problem isn't that mathematics doesn't naturally connect to other
things, but rather that we've not put great effort into teaching about those
meaningful connections. Confounding this problem is that some of the most
impressive applications are not necessarily supported by traditionally
"important" curriculum topics (those that allow students to score well on
standardized tests), so they are often considered "enrichment" and put off until
such time as when everything else has been adequately covered. The silver
lining in this cloud is that meaningful (and digestible) applications for
traditionally important topics in secondary level mathematics are actually
plentiful for anyone who cares to do a bit of research… so, here is a bit of
research. Additionally, since the evolution of these mathematical applications
is often as interesting as the applications themselves, it is perhaps
appropriate to share some of that as well, particularly when it provides insight
into unique uses of a concept.
For now, we will leave specific applications unstated, and instead begin with a
simple curve sketching example using straight lines, a concept which will become
increasingly more relevant as we progress. Equations of lines and their
respective graphs are commonly seen in a variety of applications from unit
conversions to inferential statistics, and although these applications are most
certainly important, the frequency of their use, both in classrooms and
otherwise, makes them appear somewhat contrived and generally not very
interesting. There are, however some interesting applications in the graphing
of lines and other functions that are not so well known. We will begin by
examining some numeric patterns which translate to geometric patterns when they
are graphed.
Anyone who has ever investigated straight line geometry knows that curves can be
created with a series of straight lines. These lines can be considered tangents
to an actual curve at given points if you wish, but primarily we just want to
look closely at the transformational coefficients, those values that provide
information about the location, shape, and direction of curves. In this
example, we will limit our graph to points only in the first quadrant. To create
the geometric pattern we will predictably adjust the slope variables up and down
in a series of lines, and simultaneously decrease the y-axis intercepts. The
result looks like a curve. Consider the following equations:
Lines:
Pattern Graph:
The Evolution of Practical Connections with a Rich
History In the last example (which can be easily shown with a spreadsheet
graphing option or graphing calculator), predictable manipulation of the slope
coefficient and the y-axis intercept constant creates a neat overlapping
spider-web pattern. These patterns are fun to look at maybe, but not really
applicable to much. So what is this all leading up to? Well, oddly enough this
kind of graphing is a first stage in some very complex and useful functions that
produce what are known as Guilloché patterns. The word Guilloché (pronounced by
some as Ga-Lowsh', and by others as Gee'-o-shay) is
actually a French word for a painted or carved kind of ornament. The patterns
usually consist of a series of circles that are intricately overlapping and
woven together to create some rather unique "spirograph" type patterns. These
overlapping curved patterns can be observed in Greek, Assyrian, Roman, French,
and English architecture and art. The more advanced and contemporary
definitions and applications of Guilloché patterns however, are a little more
subtle, and quite a bit more complicated. In point of fact, you've probably
touched one recently. Can you guess what it is?
While you're thinking about where you may have encountered a Guilloché pattern,
I'll give you some additional background about how they became popular in the
United States. In 1962, a mechanical engineer from England named Denys Fischer
was designing bomb detonators for NATO, and in the process invented
spriograph, a concept that became one of the most popular toys in America in
the late 1960's. Certainly the transition in thinking that takes a person from
bomb detonators to spirograph is quite a leap; but the truth is, spirograph is
the geometric manifestation of some very complex mathematics. The patterns the
toy creates are called hypotrochoids, which fall into a class of functions known
as roulettes… indicating functions not unlike a roulette wheel. Are you ready
for the application? The wheel within a wheel function of the spirograph, which
is used to inscribe an overlapping curve, is exactly what is used to create the
patterns on paper money (only there are more wheels used). Did you guess that
money was what contained Guilloché patterns? Look at a dollar bill and you will
see the intricate Guilloché patterns near the perimeter on both the front and
back.
These patterns can be seen on the paper currency in virtually every country in
the world. According to the United States Bureau of Printing and Engraving,
there was a time that anyone with $50,000 to spare could start a bank and issue
banknotes. Of course, if the bank failed, the notes they issued would become
worthless, so it was necessary for the banks to protect their currency… enter
the Guilloché patterns. As it happened, the larger (and I'm sure richer) banks
could employ more talented artists, who in turn, could produce more
sophisticated Guilloché patterns on the money. Why? Because more complex
patterns were more difficult to replicate, thus reducing the possibility of
forgery. Today, the colored watermark, ultraviolet, and infrared printing
techniques add another layer of security that make unauthorized duplication of
the bills very difficult.
Let's now take a look at the transformational coefficients that affect the
shape, direction, and vertex points of another common algebraic function. By
doing so, we will create patterns slightly more like those seen on the dollar
bill. Using the same basic idea of predictably changing the coefficients as was
done in the example using lines, see if you can determine what each coefficient
affects for the base parabolic function:
Parabolic
Curves Pattern Graph:
In this example, only two of the coefficients were
manipulated, but the pattern created is a little more interesting than if we had
just used lines. What would happen if the 'h' value were to be manipulated as
well… perhaps in a pattern that changed from positive to negative each time?
The geometric patterns emerging from creative manipulation of the variables 'a',
'h', and 'k' could produce virtually limitless options for a security pattern or
document decoration. We also know that these coefficients act similarly for
different kinds of functions, from rational to trigonometric. Trigonometric
functions in particular allow for the types of designs that represent truer
Guilloché patterns because of the natural curves. You will find yourself
closer yet to the patterns on the dollar bill if you try manipulating the
variables from the base function:
Now, because they tend to better represent the patterns we want to
investigate, those on the dollar bill, let's look at some trigonometric
patterns. One of the most popular, but probably over simplified,
representations of a sine function is to roll a disk along a straight edge while
mapping the curve that follows a fixed point somewhere between the center and
edge of the rolling disk. Though this is not actually a sine wave, it does
illustrate the oscillation factor of many trigonometric functions, and in
particular those that create our Guilloché patterns. This curve is actually a
cycloid-type curve. The more complex patterns are then created by rolling the
same disk along a curve, circle, or ellipse… or at least some figure other than
a straight edge. The most complicated patterns are created by having several
different disks of varying size rolling along or inside each other
simultaneously. These types of Guilloché patterns were, at one time,
constructed with very complicated machinery; the most notable application
perhaps being the decorating of the famous Fabergé Eggs.
In many Eastern European cultures, eggs were decorated as a celebration of the
onset of Spring. For instance, in Russia during the late 19th and
early 20th centuries, Czar Alexander III and then Nicholas II, who
continued the tradition, annually commissioned jeweled eggs to be fashioned by
Karl Fabergé for the Czars. The decoration technique used by Fabergé included
Guilloché machining which turned the egg on a lathe-type device in order to
engrave the design on the metallic surface. The complexity of the pattern was
determined by calibrating the size and rotational coefficients for the gears.
Basically, calibrating the gear size on the lathe is analogous to how we have
changed the formula coefficients in our examples to create unique designs on a
flat surface. The difficulty in Fabergé's process is that etching a pattern on
an ellipsoidal surface is somewhat different than the patterns we've been
producing on a plane. The calculations necessary for Fabergé's work can be best
described with the construction of cycloid patterns in spherical geometry. I'll
bet you had never thought of Karl Fabergé as a mathematician!
Let's now take another step forward by looking at some other cycloid patterns.
The kinds of cycloid curves that can be graphed on planes can typically be
modeled mathematically by functions that add trigonometric terms of the type a sin (bt) and c cos (dt) and where t is an iterative variable. For example, points (x, y) on a
cycloid curve can be parametrically represented as follows:
Note that by incrementing 't', each successive (x, y) point
is modified slightly even when the translational, amplitude, or wavelength
coefficients 'a' through 'h' are held constant. This is generally true with any
planar function, though in our previous examples we graphed a series of
functions rather than adjusting a 't' value. This allowed us to follow more
closely the differences in the coefficients. If we graduate to a more advanced
parametric function for determining each successive (x, y) point as 't'
increases, we may create an example such as the following:
Conclusion
The Guilloché pattern above is entitled "The Slinky" and
can be seen along with others on the web at
These types
of dynamic geometric patters are actually fairly predictable once one becomes
comfortable with how the various transformational coefficients affect the shape
of a given equation's graph. Like anything else, practice producing and
interpreting the graphs that emerge from manipulating transformational
coefficients makes understanding come more quickly.
Secondary level mathematics students will probably never produce patterns that
are as sophisticated as those seen on paper money, but by looking at the various
geometric patterns a base function can produce, one should be able to identify
how the coefficients are being manipulated. Students should also be encouraged
to create their own patterns, and by experimenting with the coefficients, be
able to bring their own flavor to the patterns they generate. Because of the
consistency in how these coefficients affect the shape, location, and direction
of various base functions, students learning about pre-calculus mathematics
should begin to gain an excellent sense of curve sketching in a very short
time. Who knows, they may even learn something about connecting other
mathematical topics to the real world through creative outlets like Guilloché
patterns. | 677.169 | 1 |
Citations with the tag: MATHEMATICS -- Bibliography
Results 1 - 22
Presents a specialist reviewers' guide to books for students on mathematics. `Mathematics Recovered: For the Natural and Medical Sciences,' by Dennis Rosen; `Discrete Mathematics for New Technology,' by Rowan Garnier and John Taylor; `Introduction to the Galois Correspondence,' by Maureen...
Introduces `The Nth Degree,' a secondary level mathematics journal for students published by students Nichols School in New York state. Call for general math-related articles; Release of first issue in November 1991.
Presents a plan to make learning mathematics easier for children. Lack of interest in children to be numerate and adult attitudes serving to legitimize them; `Math Curse,' book by Jon Scieszka; Development of ideas for elementary and preschool math mathematicians; Bibliography.
Introduces pre-math picture books for children between 2 to 7 years old. Includes `Who's Counting?' by Nancy Tafuri; `Up to Ten and Down Again,' by Lisa Campbell Ernst; `Eating Fractions,' by Bruce McMillan.
Focuses on publications pertinent to the teaching of mathematics. 'Geometry at Work: Papers in Applied Geometry,' edited by Catherine A. Gorini; 'The Heart of Mathematics: An Invitation to Effective Thinking,' by E.B. Bruger and M. Starbird.
Focuses on the publication principles of the journal 'Educational Studies in Mathematics.' Illustration of issues of principle, policy and practice in mathematics education; Development of coherent bodies of theorized knowledge; Basis of an explicit theoretical and methodological framework of...
Reports on the errors of fact found in middle school physical science textbooks in the United States. Impact of the errors on the performance of students on international tests in science and mathematics; Number of mistakes found by reviewers; Suggestion for science and mathematics teaching.
In this paper we calculate certain chiral quantities from the cyclic permutation orbifold of a general completely rational net. We determine the fusion of a fundamental soliton, and by suitably modified arguments of A. Coste , T. Gannon and especially P. Bantay to our setting we are able to...
Provides information on books about mathematics and computers. "The Power of Picture Books in Teaching Math & Sscience: Grades Prek-8," by Lynn Columba; "A Tour Through Mathematical Logic," by Robert S. Wolf"; "A to Z of Mathematicians,' by Tucker McElroy; "Understanding Mathematics and Science...
The article presents a bibliography of books related to mathematics and computers. The books include "The Art of Conjecturing: Together With His Letter to a Friend on Sets in Court Tennis," by Jacob Bernoulli, "Handbook of Parallel Computing and Statistics," John Kontoghiorghes and "A Concise...
The article presents a list of forthcoming books on science, math and medicine, including "Thomas Kuhn's Revolution: An Historical Philosophy of Science," by James Marcum, "Multimedia and Security Workshop: Proceedings", "Computer Science and Computing: A Guide to the Literature," by Michael...
Presents several books related to mathematics and computers. "Pseudodifferential Analysis on Conformally Compact Spaces," by Robert Lauter; "A Guide to Classical and Modern Model Theory," by Annalisa Marcja and Carlo Toffalori; "An Introduction to Mathematical Logic and Type Theory: To Truth... | 677.169 | 1 |
In years 10 and 11, set movement occurs usually because of a change of tier of entry ( Higher or Foundation) or after early entry if this happens to accommodate individual needs for further progression or studying for a different mathematical award.
Students currently in Year 9 and all future students will be enrolled onto the 3 year course for GCSE Mathematics. The syllabus outline can be downloaded below.
The Mathematics syllabus is broken down into the following areas: Number and Algebra, Shape and Measures and Handling Data. Using and Applying Mathematics will be assessed in the context of the above subject areas.
The course encourages students to:
a) consolidate their understanding of mathematics
b) be confident in their use of mathematics
c) extend their use of mathematical vocabulary, definitions and formal reasoning.
d) develop the confidence to use mathematics to tackle problems in the work place and everyday life.
e) realise the application of mathematics in the world around them and in a cross-curricular dimension within subjects studied in school
f) develop and ability to think and reason mathematically
g) learn the importance of precision and rigour in mathematics
h) make connections between different areas of mathematics
i) realise the application of mathematics in the world around them and in a cross-curricular
dimension within subjects studied in school
j) develop a firm foundation for appropriate study.
Assessment
The Scheme of Assessment consists of 2 exams at the end of Year 11. A calculation paper and a non-calculator paper (each 50% weighting). Pupils are assessed at Higher Level (grades A*- D available) or Foundation Level (grades C-G available).
Some years, early entry has been an option but this depends on the exam board and changes year on year. Correspondences will be sent between the individual student and their Maths Tutor/Head of Mathematics.
The Maths Department subscribe to the website which is an excellent resource if your child needs help in remembering how to answer a type of question or for practice and revision purposes. | 677.169 | 1 |
Lie algebras have many varied applications, both in mathematics and mathematical physics. This book provides a thorough but relaxed mathematical treatment of the subject. Proofs are given in detail and the only prerequisite is a sound knowledge of linear algebra. A detailed Appendix is included. more... | 677.169 | 1 |
The aim of this syllabus has been to produce a course which, while challenging, is accessible and enjoyable to all students. The course develops ability and confidence in mathematics and its applications, together with an appreciation of how mathematical ideas help in an understanding of the world and the society in which we live. It also extends the GCSE teaching and assessment methods into the sixth form.
Requirements
We would hope that students starting A-level or AS-level Maths had obtained a grade of A* or at G.C.S.E at Higher Level. Students who achieve B grade at Higher level will be considered, though they are likely to find the course difficult.
What could this lead to?
This A-level is an essential element for further study in mathematical areas and computer studies. The core elements in particular are highly desirable for those going on to study scientific, engineering and design related courses. Discrete maths gives a good background to a solving a range of problems in the modern world from the best route to take to grit roads in winter to understanding the processes involved in programming a computer. The statistical element is valuable for potential psychologists, geographers and biologists. Because passing Mathematics A-level demonstrates an ability to think logically and analytically it is also well regarded as a good qualification in all other areas. | 677.169 | 1 |
This lesson consists of providing you with a Self-Tutorial on what is algebra, what are variables, constants, coefficients, terms, and expressions. I explain the use of proper notation, how to... More...
This lesson consists of providing you with a Self-Tutorial on what is algebra, what are variables, constants, coefficients, terms, and expressions. I explain NOTE: This is only the first 11 minutes of the video. Complete movie is on my web site | 677.169 | 1 |
Main menu
You are here
AlgebraGenie is Launched!
Finally, our flagship Next-Generation Interactive Textbook is released! Check it out if you haven't already here. You will be guided magically to the appropriate App Store if you are
Breadth
It wasn't easy! This content is made up of 14 topics and a total of 250 lessons. At 4 minutes per lesson, that's a 1000 minutes or 17 hours of continuous instruction. No Algebra electronic course we know of covers so much.
Journey
We first started developing this course over three years ago. At the time, our technology and standards were not mature yet (and those of you who have been with us that long, will notice that the voice is much better now). It takes a lot to get to this point of maturity.
We launched our free version in 2011 to see if it gets enough interest, and our website got overwhelmed! We upgraded our servers, fixed up the content and technology, we even launched the apps on iPad / iPhone, Android, and Kindle. In many app stores, we are the #1 Algebra App.
Now fast-forward to end of 2012, we now have improved our technology substantially, learned from our users and teachers, and added many of the missing lessons. The App is now updated on iOS and Android with In-App Purchase per topic (launch price at $0.99 per topic).
What's next
Now we have to tell the whole world that it's ready. Many schools are starting to use it in the next school year, this will get more people to hear about it. We will reach out to more educational institutions and key thought leaders to share with them the good news and get their feedback. | 677.169 | 1 |
2.1SOLUTIONSNotes: The definition here of a matrix product AB gives the proper view of AB for nearly all matrix calculations. (The dual fact about the rows of A and the rows of AB is seldom needed, mainly because vectors here are usually written
3.1SOLUTIONSNotes: Some exercises in this section provide practice in computing determinants, while others allow thestudent to discover the properties of determinants which will be studied in the next section. Determinants are developed through
4.1SOLUTIONSNotes: This section is designed to avoid the standard exercises in which a student is asked to check ten axioms on an array of sets. Theorem 1 provides the main homework tool in this section for showing that a set is a subspace. Stude
5.1SOLUTIONSNotes: Exercises 16 reinforce the definitions of eigenvalues and eigenvectors. The subsection oneigenvectors and difference equations, along with Exercises 33 and 34, refers to the chapter introductory example and anticipates discuss
6.1SOLUTIONSNotes: The first half of this section is computational and is easily learned. The second half concerns theconcepts of orthogonality and orthogonal complements, which are essential for later work. Theorem 3 is an important general fac
7.1SOLUTIONSNotes: Students can profit by reviewing Section 5.3 (focusing on the Diagonalization Theorem) beforeworking on this section. Theorems 1 and 2 and the calculations in Examples 2 and 3 are important for the sections that follow. Notespace of P2 : The neutral element f (t) = 0 (for all t) is in V .
Chapter 14CHAPTER 14 Oscillations 1. In one period the particle will travel from one extreme position to the other (a distance of 2A) and back again. The total distance traveled is d = 4A = 4(0.15 m) = 0.60 m. (a) We find the spring constant from
Chapter 17CHAPTER 17 Temperature, Thermal Expansion, and the Ideal Gas Law 1. The number of atoms in a mass m is given by N = m/Mmatomic. Because the masses of the two rings are the same, for the ratio we have NAu/NAg = MAg/MAu = 108/197 = 0.548.
Chapter 22 p. 1CHAPTER 22 Gauss's Law 1. Because the electric field is uniform, the flux through the circle is = ? E dA = E A = EA cos . (a) When the circle is perpendicular to the field lines, the flux is = EA cos = EA = (5.8 102 N/C)p(0.15 m)2
Chapter 25 p. 1CHAPTER 25 Electric Currents and Resistance 1. 2. 3. 4. The rate at which electrons pass any point in the wire is the current: I = 1.50 A = (1.50 C/s)/(1.60 1019 C/electron) = 9.38 1018 electron/s. The charge that passes through the
Chapter 27 p. 1CHAPTER 27 Magnetism 1. (a) The maximum force will be produced when the wire and the magnetic field are perpendicular, so we have Fmax = ILB, or Fmax/L = IB = (7.40 A)(0.90 T) = 6.7 N/m. (b) We find the force per unit length from F/
Chapter 28 p.1CHAPTER 28 Sources of Magnetic Field 1. The magnetic field of a long wire depends on the distance from the wire: B = (0/4p)2I/r = (107 T m/A)2(65 A)/(0.075 m) = 1.7 104 T. When we compare this to the Earth's field, we get B/BEarth
Chapter 30, p. 1CHAPTER 30 Inductance; and Electromagnetic Oscillations 1. The magnetic field of the long solenoid is essentially zero outside the solenoid. Thus there will be the same linkage of flux with the second coil and the mutual inductance
Ch. 35 p. 1CHAPTER 35 The Wave Nature of Light; Interference 1. We draw the wavelets and see that the incident wave fronts are parallel, with the angle of incidence 1 being the angle between the wave fronts and the surface. The reflecting wave fro
Chapter 38 p. 1CHAPTER 38 Early Quantum Theory and Models of the Atom Note: At the atomic scale, it is most convenient to have energies in electron-volts and wavelengths in nanometers. A useful expression for the energy of a photon in terms of its
Chapter 39 p. 1CHAPTER 39 Quantum Mechanics Note: At the atomic scale, it is most convenient to have energies in electron-volts and wavelengths in nanometers. A useful expression for the energy of a photon in terms of its wavelength is E = hf = hc
Chapter 40 p. 1CHAPTER 40 Quantum Mechanics of Atoms Note: At the atomic scale, it is most convenient to have energies in electron-volts and wavelengths in nanometers. A useful expression for the energy of a photon in terms of its wavelength is E
Chapter 41p. 1CHAPTER 41 Molecules and Solids Note: At the atomic scale, it is most convenient to have energies in electron-volts and wavelengths in nanometers. A useful expression for the energy of a photon in terms of its wavelength is E = hf | 677.169 | 1 |
Help
There is a substantial research literature that suggests learning in mathematics can be achieved by reading worked-out examples. WebGraphing.com goes one step further: it strives to jump-start students to learn mathematics by reading worked-out examples of their own choosing.
Unlike other web sites dedicated to mathematics, WebGraphing.com delivers real-time, step-by-step answers to challenging mathematics problems. There are a number of unique, patented features that make our calculators easier to use and more powerful than other graphing calculators. In comparison, our calculators take more of the grunt work out of demanding computations that contribute very little either to student learning or teacher productivity.
WebGraphing.com began operations in 2003. On average, we receive over 8,000 daily visitors from over 100 countries. We currently have over 150,000 members comprised of students, teachers and parents. This represents a lot of learning of mathematics, checking answers, copying publication-quality graphs, and mathematics exploration.
WebGraphing.com is the brainchild of Barry Cherkas (also known as pskinner on the Forum), a Professor of Mathematics holding a joint faculty appointment with the Department of Mathematics & Statistics at Hunter College and the Ph.D. Program in Urban Education at the City University of New York Graduate Center.
Professor Cherkas has received numerous grants and written many articles in mathematics and mathematics education, including an article related to graphing: "Finding polynomial and rational function turning points in precalculus," which appeared in the International Journal of Computers for Mathematical Learning, Vol. 8, No. 2, 2003, 215-234 Computer Math Snapshots Section. He has also written a book on using technology to learn precalculus: "Precalculus: Anticipating Calculus Using Mathematica® Labs," 2002, Jamaica, New York: Euler Press. More recently, he is a coauthor (with Dr. Rachael Welder) of the chapter Interactive Web-based Tools for Learning Mathematics: Best Practices appearing in the 2011 IGI Global publication, Teaching Mathematics Online: Emergent Technologies and Methodologies (edited by Dr. Angel A. Juan, Maria A. Hertas, Sven Trenholm and Cristina Steegman.)
Professor Cherkas welcomes any feedback and suggestions through the contact form.
Just like a math textbook, every once in a while we publish an error. If you think you've come across an error, please let us know. We'll get back to you with the correct solution. | 677.169 | 1 |
College Algebra and Trigonometry that include highlights, exercise hints, art annotations, critical thinking exercises, and pop quizzes, as well as procedures, strategies, and summaries. This text is designed for a variety of students with different m... MOREathematical needs. for those students who will take additional mathematics, the text will provide the proper foundation of skills, understanding, and insights necessary for success in further courses. for those students who will not pursue further mathematics, the extensive emphasis on applications and modeling will demonstrate the usefulness and applicability of mathematics in the world today. Many of the applied problems in this text are actually real problems that people have had to solve on the job. With an emphasis on problem solving, this text provides students with an excellent opportunity to sharpen their reasoning and thinking skills. With increased critical thinking skills, students will have the confidence they need to tackle whatever future problems they may encounter inside and outside the classroom. This text is technology optional. With this approach, teachers will be able to offer either a technology-oriented course or a course that does not make use of technology. for departments requiring both options, this text provides the advantage of flexibility. | 677.169 | 1 |
02056
Requirements
Prerequisites
Algebra IA graphing calculator is recommended but not required. A graphing program called Gcalc will be available throughout the courseIn this course students will use their prior knowledge from previous courses to learn and apply
Algebra II skills. This course will include topics such as functions, radical functions, rational
functions, exponential and logarithmic functions, trigonometry, geometry, conic sections, systems of
equations, probability, and statistics. Students will apply the skills that they learn in this course to
real world situations.
I think that the Algebra II class that I am taking is fantastic! I love that I don't have to actually be in a classroom to take it. The main problem for me, though, is keeping up with everything. It is hard to not put off doing the work because you are busy or tired.
Kingston High School Student - 01/14/08
This has been a great program to work with. The teachers and tutors are so helpful and encouraging. They truly want you to succeed in your subject! They have many ways of explaining something to you and are great about getting back to you quickly. It does take a lot of commitment and effort on the student's part, though. The student has to want this for a reason, not just because they think it will be an easy way to get out of a class at school. The work they give you is truly challenging. Good Luck! | 677.169 | 1 |
6SAM_M : AS/A level Mathematics - Mechanics
Course description:
This course is particularly suited for students studying AS/A Level Physics and Technology. The Mechanics units (MI and M2) in particular, complement these subjects.
Course content:
You will study both Pure Maths (which includes algebra, calculus, trigonometry and geometry) and Applied Maths modules. Pure Maths (the "Core" modules) gives you the tools needed for solving problems while the Applied Maths allows you to use these in real world contexts. What you learn in Maths can be used in many other subjects. Mechanics 1 and 2 are a very useful support in Physics.
Teaching methods:
In addition to topics being explained and examples worked through on the board, you will be expected to participate fully in class by contributing ideas, working in small groups on worksheets or working through questions. There will be a variety of learning styles including use of graphic calculators and computer software. You will be expected to do a significant amount of work outside class including being set regular homework.
Maths workshops are available for students to use on a drop-in basis to sort out any problems you have.
Course assessment:
AS level Mathematics comprises of 3 modules (C1, C2 and M1), which will be examined at the end of your first year.
A level Mathematics comprises of 6 modules: these include the 3 AS modules taken at the end of the first year, with two further Pure Modules C3 and C4 and an Applied Module (either M2 or S1)in the second year.
All modules contain an exam. A second year module contains a piece of assessed coursework.
Entry requirements:
Minimum GCSE Maths grade required: AGCSEs at mostly A/B grade.
Progression opportunities:
At the end of the first year students take AS level Maths and on successful completion can then decide to continue on to A2 Maths to gain the full A level.
Additional information:
Students are required to pay for textbooks and resources, which include revision material and past papers. The total cost for the AS course is about £40. | 677.169 | 1 |
Mathematical Olympiad Challenges
This significantly revised and expanded second edition of Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory from numerous mathematical competitions and journals have been selected and updated. The problems are clustered by topic into self-contained sections with solutions provided separately. Historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on creative solutions to open-ended problems.
New to the second edition: * Completely rewritten discussions precede each of the 30 units, adopting a more user-friendly style with more accessible and inviting examples * Many new or expanded examples, problems, and solutions * Additional references and reader suggestions have been incorporated Featuring enhanced motivation for advanced high school and beginning college students, as well as instructors and Olympiad coaches, this text can be used for creative problem-solving courses, for professional teacher development seminars and workshops, for self-study, or as a resource for training for mathematical competitions | 677.169 | 1 |
05.0 MATHEMATICS
05.0.1.9.1
-- Students will use real-life experiences, physical materials and technology to construct meanings for rational and irrational numbers, including integers, percents and roots
05.0.1.9.2
-- Students will use number sense and the properties of various subsets of real numbers to solve real-world problems
05.0.2.9.2
-- Students will apply and explain procedures for performing calculations with whole numbers, decimals, factions and integers
04.2 LRIT - COMPUTER TECHNOLOGY
04.2.2.9.1
-- Students will identify capabilities and limitations of contemporary and emerging technology resources and assess the potential of these systems and services to address personal, lifelong learning, and workplace needs What roles do variables play in C++?
2. What roles do data structures play in C++?
3. How do basic math operations perform in C++?
4. How do mixed data types perform in C++?
5. What problems can occur in can occur when performing calculations as a result of the limitations of data types? | 677.169 | 1 |
Description—
Features
Diverse applications both in the exercises and the examples help students see how mathematics is applied to everyday and work-related situations. Many use real-world data to increase their relevance to students' lives.
More than 5,000 exercises provide a wide variety of quality problems that are sorted in increasing order of difficulty, starting with basic skills and applications and progressing to increasingly challenging exercises.
More than 850 examples are worked out in detail. Many examples include strategies that are specifically designed to guide students through the logistics of the solution before finding the solution.
"Now Work" exercises follow every example, suggesting an end-of-section exercise that is similar in style and concept to the example. This gives the student the opportunity to test and confirm their understanding. Answers to the "Now Work" exercises are found in the Answers section in the back of the text.
Apply It exercises (formerly titled Principles in Practice) are located in the margins next to examples to provide an opportunity for students to apply and check their understanding of the mathematics in the corresponding example.
Reviews
Very good
3 Oct 2011
By Yousef- | 677.169 | 1 |
Geometric Sequences
We already know that an arithmetic sequence is one where the difference between successive terms is constant. The distance each term is the same. A geometric sequence is a lot like an arithmetic sequence, but it is completely different at the...
Please purchase the full module to see the rest of this course
Purchase the Sequences Pass and get full access to this Calculus chapter. No limits found here. | 677.169 | 1 |
Mathematical modelling modules feature in most university undergraduate mathematics courses. As one of the fastest growing areas of the curriculum it represents the current trend in teaching the more complex areas of mathematics. This book introduces mathematical modelling to the new style of undergraduate - those with less prior knowledge, who require more emphasis on application of techniques in the following sections: What is mathematical modelling?; Seeing modelling at work through population growth; Seeing modelling at work through published papers; Modelling in mechanics.
Written in the lively interactive style of the Modular Mathematics Series, this text will encourage the reader to take part in the modelling process. | 677.169 | 1 |
Academic Wellness
Be prepared to be a better student and achieve your academic goals
Math.com: This website will help you with math concepts from Basic Math, Algebra, Trigonometry, Statistic, and Calculus
Math Lessons - Looking to understand a subject better or maybe you don't understand what your textbook is trying to tell you? We have a collection of algebra and geometry lessons that you can view online right now.
How to Study: Get tips on how to stay organized, time management, learning styles, procrastination, and how to listen better. This site also gives you a break-down by subject! | 677.169 | 1 |
Course Description:
Relations and functions, equations and inequalities, complex numbers; polynomial, rational, exponential and logarithmic functions; systems of equations, and matrices. Prereq: MATH 102 with a grade of C or better or placement. | 677.169 | 1 |
Project Based Learning Pathways - David Graser
A blog about real life projects suitable for college math courses such as algebra, finite math, and business calculus. Most of these applied math projects include handouts, videos, and other resources for students, as well as a project letter. Graser,
...more>>
Public Domain Materials - Mike Jones
A collection of public domain instructional and expository materials from a US-born math teacher who teaches in China. Microsoft Word and PDF downloads include a monthly circular consisting of short problems, "The Bow-and-Arrow Problem," and "Twinkle
...more>>
A Recursive Process - Dan Anderson
Anderson's blog, which dates back to June of 2010, has included posts such as "Robocode & Math," "Standards Based Grading," "Cake:Frosting (A look into a proper ratio of real math:cool tech)," "Paper Towels WCYDWT (What Can You Do With This?)," "TwoShelley Walsh
Syllabi and notes for math courses from arithmetic review to beginning calculus. Download MathHelp a tutorial program with problem sets for Mac or PC, or learn how to use MathHelp to create your own tutorials. Brief Mathematics Articles present concepts
...more>>
Sites with Problems Administered by Others - Math Forum
Problems of the week or month: a page of annotated links to weekly/monthly problem challenges and archives hosted at the Math Forum but administered by others, and to problems and archives elsewhere on the Web, color-coded for the level(s) of the problemsStella's Stunners - Rudd Crawford
More than 600 non-routine mathematics problems named in honor of the Dutch baroness Ecaterina Elizabeth van Heemsvloet tot Schattenberg. Each collection in the Stella Library contains five subsets, one for each course of Pre-Algebra, Algebra I, Geometry,
...more>>
studymaths.co.uk - Jonathan Hall
Free help on your maths questions. See also the bank of auto-scoring GCSE maths questions, games, and resources such as revision notes, interactive formulae, and glossary of terms.
...more>>
Success for All
Curriculum driven by co-operative learning that focuses on individual pupil accountability, common goals, and recognition of team success, all with the aim of getting learners "to engage in discussing and explaining their ideas, challenging and teachingaching Mathematics - Daniel Pearcy
Pearcy has used this blog, subtitled "Questions, Ideas and Reflections on the Teaching of Mathematics," as a "journal of ideas, lessons, resources and reflections." Posts, which date back to October, 2011, have included "New Sunflower Applet: Fibonacci
...more>>
ThinkQuest
An international contest designed to encourage students from different schools and different backgrounds to work together in teams toward creating valuable educational tools on the Internet while enhancing their ability to communicate and cooperate in
...more>>
Ti 84 Plus Calculator
Instructional videos include using the parametric function to construct a pentagram, hypothesis testing, sketching polynomial functions, finding critical points of a function, and using the TVM (Time Value of Money) Solver method. The site also offers
...more>>
TI-89 Calculus Calculator Programs
TI-89 calculator programs for sale. Enter your variables and see answers worked out step by step: a and b vectors, acceleration, area of parallelogram, component of a direction u, cos(a and b), cross product, curl, derivative, divergence of vector field,
...more>> | 677.169 | 1 |
Introduction to MathematicaSeth F. Oppenheimer The purpose of this handout is to familiarize you with Mathematica. The Mathematics and Statistics Department computer lab is on the fourth floor of Allen Hall and is open most afternoons and evenings.
(* Content-type: application/mathematica * Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing s
(* Content-type: application/mathematica * CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook start
Chapter 1Sections 1.1-1.9 Fluid Mechanics EM 3313Sec. 1.1-1.91What's the Point? Context Fluids have many characteristics that make them different from solids. That's why we are in this class. Motivation We are unfamiliar with many importa
Sections 2.1-2.11Fluid Mechanics EM 3313Sec. 2.1-2.111What's the Point? Context In the previous chapter, we learned that fluids at rest must have zero shear stress. We called the nonzero normal stress the hydrostatic pressure. Motivation
Sections 4.1-4.2Fluid Mechanics EM 3313Sec. 4.1-4.21What's the Point? Context Fluid kinematics is concerned purely with the motion of fluid without regard for the forces acting on the fluid. Motivation We need to understand these concepts
Sections 4.3-4.4Fluid Mechanics EM 3313Sec. 4.3-4.41What's the Point? Context We can relate system behavior (Lagrangian) to behavior of fluid in region of space (Eulerian) called control volume. Motivation We need to understand these conc
Hydrostatic Pressure in Compressible Fluids (Gases pg. 45-46)We know that in the case of a fluid at rest (or a fluid moving as a solid body at constant velocity) with gravity being the only body force (acting in the z direction), Newton's second la
ME 3533: Thermodynamics Assignment #1.1: General Introduction I. 1. Familiarization Tasks E-mail: this is the most convenient means for communicating essential/urgent information to the class. Check your e-mails daily. Test e-mail will be sent out on
ME 3533: ThermodynamicsAssignment #1.2: Applications and Basic Modeling Due date: Wednesday, January 16, 2008Review Exercises/Group Activities on Section 1.21.Choose a major area of thermodynamic application (such as Steam Power Plants, Gasoli
Thermodynamics(For Assignment #1.1) Energy Fun Facts This really is good for anyone in a Thermodynamics class. Refer to the following web page: http:/ Click on unit of measure link .For a
Domain Bacteria Prokaryotic Reproduction by cell division Lack membrane bound organelles Asexual reproduction N2 Bacteria Nitrogen fixing bacteria Can't be used directly, must be fixed into a form that is usable Rhizobium and other soil bacteria Prot
Plant Growth Principles of Biology II- GSU LeegePlant Growth: Overview Annual vs. biennial vs. perennial - annual blooms once a year, then dies -biennial blooms once after 2 years then dies, or blooms once, then again in 2 years, and dies -annual | 677.169 | 1 |
courses in secondary or middle school math. This text focuses on all the complex aspects of teaching mathematics in today's classroom and the most current NCTM standards. It demonstrates how to creatively incorporate the standards into teaching along with inquiry-based instructional strateg... | 677.169 | 1 |
Mr. Mark Pierce Trig/College Math
[email protected]
(480) 472-5844
Room 616
Office Hours:Before School, B Lunch
Course Description:
This course is an accelerated course preparing students for enrollment in pre-calculus.Algebra 2 and Trigonometry are studied in-depth.Application of mathematics to the physical world will be stressed.Problem solving skills are also emphasizes throughout the course.Students will also continue to learn to use technology (TI-83 calculators) to aid them in problem solving.
Textbook:
Algebra and Trigonometry by Houghton Mifflin. 40% of the 1st quarter grade, 40% of the 2nd quarter grade, and 20 | 677.169 | 1 |
Algebra is one of the building blocks of Mathematics in IIT JEE examination. While preparing for IIT JEE, it is this portion where an aspirant begins. Though Algebra begins with Sets and Relations but we seldom get any direct question from this portion. Functions can be said to be a prerequisite to Calculus and hence it is critical in IIT JEE preparation. Sequence and series is one other section which is mixed with other concepts and then asked in the examination. Quadratic equation fetches direct questions too and is also easy to grasp. Binomial Theorem is also a marks fetching topic as the questions on this topic is quite easy. Permutations and Combinations along with Probability is the most important section in Algebra. IIT JEE exam fetches a lot of questions on them. Those who get good IIT JEE rank always do well in this section. Complex Numbers are also important as this fetches question in the IIT JEE exam almost every year. Matrices and Determinant mostly give direct question and there are no twist and turns in the questions based on them.
askIITians covers following topics in Algebra for IIT JEE, AIEEE and other engineering exams syllabus. | 677.169 | 1 |
Place into MATT 133 with approved and documented math placement scores or by successfully completing MATT 132.
NOTES:
COURSE OBJECTIVES / GOALS:
The student in this course must have facility in the fundamentals of Algebra. This course is designed to provide the student with the skill in the practical application of trigonometry in the industrial technology disciplines.
Given radicals, students will learn to change them to a simple form so that basic arithmetic operations the group can be reduced to simplest form.
The use of a personal electronic calculator in performing operations required in solving right triangles will be demonstrated so that students will develop the ability to substitute the calculator for the menial arithmetic tasks formerly required in fulfilling course objectives.
Given second degree equations, students will solve by factoring or by quadratic formula.
Given angles in any quadrant, the student will learn the trig functions and apply them in any polygon situation.
Given any angle, the student will learn radian measurement and apply radians in linear, area, and velocity problems.
Given vector components, the student will learn to solve for the resultants by trig.
TOPICAL OUTLINE
Use of electronic calculator in multiplying, dividing, and finding roots.
Trig functions of any angle or number.
Radians
Vectors
TEXTBOOK / SPECIAL MATERIALS:
Technical Mathematics, John C. Peterson
EVALUATION:
(8)Hour Exams-(Competency based-must obtain a grade of "C" or better on each exam) | 677.169 | 1 |
David Cohen's PRECALCULUS, WITH UNIT-CIRCLE TRIGONOMETRY, Fourth Edition, focuses on teaching mathematics, using a graphical perspective throughout to provide a visual understanding of college algebra and trigonometry. The author is known for his clear writing style and the numerous quality exercises and applications he includes in his respected texts. In this new edition, graphs, visualization of data, and functions are now introduced much earlier and receive greater emphasis. Many sections now contain more examples and exercises involving applications and real-life data. While this edition takes the existence of the graphing calculator for granted, the material is arranged so that one can teach the course with as much or as little graphing utility work as he/she wishes.
This best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, ...
Practitioners in the helping professions make life-affecting judgements and decisions. This new integrated learning package seeks to improve practice reasoning through principles of logical thinking ... | 677.169 | 1 |
School Search
Mathematics
JUNIOR INSTITUTE Students learn mathematics by focusing on real world applications and exploring key concepts from the New York State math standards in depth. Units are based around hands on projects. Students learn how to use math concepts to become critical thinkers. The curriculum content follows the 6th, 7th, and 8th grade New York State Content Standards.
SENIOR INSTITUTE Students study Algebra, Geometry, and Algebra 2 consecutively for grades 9-11. Students learn math by focusing on real world applications and exploring in depth key concepts from the New York State math standards. Units are based around hands on projects, while learning how to use math concepts to become critical thinkers. The curriculum content follows the New York State Content Standards. | 677.169 | 1 |
Meshoppen AlgebraOnce these rules are learned, the equations become a jigsaw puzzle and can be quite fun to solve. Pre-algebra is the first step on the path to higher mathematics for most students. Pre-algebra courses introduce students to mathematical concepts beyond that of basic arithmetic. | 677.169 | 1 |
Listed below are most of the courses that mathematics majors take either as required courses or electives in mathematics. The variety of courses offered allows students to design programs to meet their individual needs. The department also teaches a number of additional courses students in the liberal arts or business take to meet general requirements.
The department also offers courses at the graduate level, which mathematics majors may take in their senior year as electives. In some cases, mathematics seniors obtain dual enrollment with the MU Graduate School and receive graduate credit for some courses taken in their final undergraduate year.
All prerequisite courses listed must be passed with a C- or better (whether specifically indicated or not).
MATH _0110-Intermediate Algebra (3). Mathematics [MATH] 0110 is a preparatory course for college algebra that carries no credit towards any baccalaureate degree. However, the grade received in Mathematics [MATH] 0110 does count towards a student's overall GPA. The course covers operations with real numbers, graphs of functions, domain and range of functions, linear equations and inequalities, quadratic equations; operations with polynomials, rational expressions, exponents and radicals; equations of lines. Emphasis is also put on problem-solving. Prerequisites: Elementary College Algebra or equivalent. Placement in Mathematics [MATH] 0110 based on the student's ACT math score or equivalent, in addition to other criteria.
MATH 1100-College Algebra (3). A review
of exponents, order of operations, factoring, and
simplifying polynomial, rational, and radical expres
sions. Topics include: linear, quadratic, polyno
mial, rational, inverse, exponential, and logarithmic
functions and their applications. Students will solve
equations involving these functions, and systems of
linear equations in two variables, as well as inequali
ties. Prerequisite: Mathematics [MATH] 0110 or a
sufficient score on the ALEKS exam. This course
is offered in both 3 day and 5 day versions. See the
math placement website for specific requirements. A
student may receive at most 5.0 credit hours among
the Mathematics courses 1100, 1120, 1140, and 1160.
MATH 1300-Finite Mathematics (3). A selections
of topics in finite mathematics such as: basic financial
mathematics, counting methods and basic prob
ability and statistics, systems of linear equations and
matrices. Prerequisites: Math [MATH] 1100, or Math
[MATH] 1160, or both a College Algebra exemp
tion and sufficient ALEKS score. Warning: without a
College Algebra exemption, a sufficient ALEKS score
will not suffice unless it is a proctored exam (for Math
[MATH] 1100 credit).
MATH 1320-Elements of Calculus (3). Introduc
tory analytic geometry, derivatives, definite integrals.
Primarily for Computer Science BA candidates,
Economics majors, and students preparing to enter
the College of BUS. No credit for students who
have completed a calculus course. Prerequisite: Math
[MATH] 1100, or Math [MATH] 1160, or sufficient
ALEKS score. A student may receive credit for Math
[MATH] 1320 or 1400, but not both. A student may
receive at most 5 credit hours among the Mathemat
ics courses 1320 or 1400 and 1500.
MATH 1400-Calculus for Social and Life Sci
ences I (3). The real number system, functions,
analytic geometry, derivatives, integrals, maximum-
minimum problems. No credit for students who have
completed a calculus course. Prerequisite: grade of C-
or better in Mathematics [MATH] 1100 or 1160, or
sufficient ALEKS score. A student may receive credit
for Mathematics [MATH] 1320 or 1400 but not both.
A student may receive at most 5 units of credit among
the Mathematics [MATH] 1320 or 1400 and 1500.
Math Reasoning Proficiency Course.
MATH 1800-Introduction to Analysis I (5). This course will cover the material taught in a traditional first semester calculus course at a more rigorous level. The focus of this course will be on proofs of basic theorems of differential and integral calculus. The topics to be covered include axioms of arithmetic, mathematical induction, functions, graphs, limits, continuous functions, derivatives and their applications, integrals, the fundamental theorem of calculus and trigonometric functions. Students in this class will be expected to learn to write clear proofs of mathematical assertions. Some previous exposure to calculus is helpful but not required. No credit for Mathematics [MATH] 1800 and 1320, 1400 or 1500. Prerequisites: ACT mathematics score of at least 31 and ACT composite of at least 30 or instructor's consent. Graded on A/F basis only.
MATH 1900-Introduction to Analysis II (5). This course is a continuation of Mathematics [MATH] 1800. In this course we shall cover uniform convergence and uniform continuity, integration, and sequences and series. The topics will be covered in a mathematically rigourous manner. No credit for Mathematics [MATH] 1900 and 1700 or 2100. Prerequisite: Mathematics [MATH] 1800 or instructor's consent. Graded on A/F basis only.
MATH 2100-Calculus for Social and Life Sciences II (3). Riemann integral, transcendental functions, techniques of integration, improper integrals and functions of several variables. No credit for students who have completed two calculus courses. Prerequisites: Mathematics [MATH] 1320 or 1400 or 1500. Math Reasoning Proficiency Course.
MATH 4150-History of Mathematics (3). This is a history course with mathematics as its subject. Includes topics in the history of mathematics from early civilizations onwards. The growth of mathematics, both as an abstract discipline and as a subject which interacts with others and with practical concerns, is explored. Pre- or Co-requisite: Mathematics [MATH] 2300 or 2340.
MATH 4335-College Geometry (3). Euclidean geometry from an advanced viewpoint. Synthetic and coordinate methods will be used. The Euclidean group of transformations will be studied. Prerequisite: Mathematics [MATH] 2300.
MATH 4340-Projective Geometry (3). Basic ideas and methods of projective geometry built around the concept of geometry as the study of invariants of a group. Extensive treatment of collineations. Prerequisite: Mathematics [MATH] 2300.
MATH 4370-Actuarial Modeling I (3). This course covers the concepts underlying the theory of interest and their applications to valuation of various cash flows, annuities certain, bonds, and loan repayment. This course is designed to help students prepare for Society of Actuaries exam FM (Financial Mathematics). It is oriented towards problem solving techniques applied to real-life situations and illustrated with previous exam problems. Prerequisites: grade of C-or better in Mathematics [MATH] 2300.
MATH 4371-Actuarial Modeling II (3). This course covers the actuarial models and their applications to insurance and other business decisions. It is a helpful tool in preparing for the Society of Actuaries exam M (Actuarial Models), and it is oriented towards problem solving techniques illustrated with previous exam problems. Prerequisites: Mathematics [MATH] 2300 and 4320 or Statistics [STAT] 4750. Students are encouraged to take Mathematics [MATH] 4355 prior to this course.
MATH 4540-Mathematical Modeling I (3). Solution of problems from industry, physical, social and life sciences, economics, and engineering using mathematical models. Prerequisites: 3 semesters of calculus and some exposure to ordinary differential equations or instructor's consent.
MATH 4580-Mathematical Modeling II (3). Solution of problems from industry, physical, social and life sciences, economics, and engineering using mathematical models. More general classes of problems than in Mathematics 4540 will be considered. Prerequisites: 3 semesters of calculus and some exposure to ordinary differential equations or instructor's consent. Mathematics [MATH] 4540 is not a prerequisite.
MATH 4800-Advanced Calculus for One Real Variable II (4). Continuation of Advanced Calculus for functions of a single real variable. Topics include sequences and series of functions, power series and real analytic functions, Fourier series. Prerequisites: Mathematics [MATH] 4700/7700 or permission of the instructor.
MATH 4900-Advanced Multivariable Calculus (3). This is a course in calculus in several variables. The following is core material: Basic topology of n-dimensional Euclidian space; limits and continuity of functions; the derivative as a linear transformation; Taylor's formula with remainder; the Inverse and Implicit Function Theorems, change of coordinates; integration (including transformation of integrals under changes of coordinates); Green's Theorem. Additional material from the calculus of several variables may be included, such as Lagrange multipliers, differential forms, etc. Prerequisite: Mathematics [MATH] 4700.
MATH 4970-Senior Seminar in Mathematics (3). Seminar with student presentations, written projects, and problem solving. May be used for the capstone requirement. Prerequisite: 12 hours of mathematics courses numbered 4000 or above. | 677.169 | 1 |
Mathematics is the foundation of the sciences and is at the core of a liberal arts education. Many great ideas in human history are mathematical in nature or are easily understood by viewing them mathematically. The idea of infinity was first explained by mathematicians, for example, although originated by philosophers and theologians. While mathematics has practical applications to many academic disciplines, including business, computer science, psychology, political science, music, chemistry and physics, most mathematicians do not study mathematics because it is useful. Instead, they study mathematics for the same reason that other people study art, music or literature – because it interests them.
The math major
Berry's broad-based mathematics major is designed to prepare you for graduate study or a professional career. You also can earn a degree to teach mathematics in grades 6-12. In your first two years as a math major you'll get a solid foundation of calculus, differential equations and linear algebra, as well as an introduction to proof. Then you'll study abstract algebra, real and complex analysis, and other electives. Faculty members also teach "special topics" courses. Subjects that have been offered or are under consideration include topology, combinatorics, knot theory, differential geometry, chaos theory, fractal geometry, graph theory and functional analysis. In addition, you'll have the opportunity to take directed-readings courses in areas that are of particular interest to you. Students have studied partial differential equations, number theory and topology. They also have prepared to take the mathematics GRE subject test and the first actuarial exam.
Students who are declaring a major in mathematics should use the documents to the right of the screen to work with their advisor to build an appropriate plan of study. The information represents tentative degree plans for students majoring in mathematics. It presupposes that the students decide to be mathematics majors at the beginning of their academic careers.
Working with faculty members on research projects. Recent subject areas have included number theory, dynamical systems, geometry and complex analysis.
Working in the mathematics tutoring lab, earning extra money as you explain mathematics to others.
Helping to plan and implement regional mathematics competitions for middle-school and high-school students.
Joining mathematics professional organizations and honor societies, including a chapter of the Kappa Mu Epsilon mathematics honor society and a student chapter of the Mathematical Association of America.
Joining the Georgia Council of Teachers of Mathematics, if you are a mathematics-education major.
Attending annual professional meetings with members of the faculty.
Scholarships are available
Outstanding upper-class students are eligible for special mathematics scholarships, including the:
Barton Mathematics Award.
Hubert McCaleb Memorial Scholarship.
Mary Alta Sproull Scholarship.
The faculty
Berry College's mathematics faculty members have a diverse range of teaching and research interests. In addition, they simply enjoy working with students – inside and outside of the classroom. You'll find that it is common to see students talking with their professors. You'll also discover that there is a real sense of community among the mathematics faculty and students.
Graduate study
Berry College mathematics students have gone on to graduate school at such places as Duke University, the University of Virginia, the University of North Carolina at Chapel Hill, Georgia Tech, Georgia State, the University of Georgia, Auburn University, Syracuse University, Tulane, Clemson and Harvard. | 677.169 | 1 |
Quick Overview
M
Details
A child with a strong foundation takes much less time to understand a subject as compared to other students. M The book covers a very broad syllabus so as to build a strong base. The USP of the book is its style and format. The book is supplemented with Do You Know, Knowledge Enhancer, Checkpoints and Idea Box. Another unique feature is the Exercise Part which is divided into 2 levels. The broad variety of questions covered are Short, Very Short, Long, Fill in the Blanks, True/ False, Matching, HOTS, Chart/ Picture/ Activity Based, MCQ's - one option correct, multiple options correct, Passage based, Assertion-Reason, Multiple Matching etc. Solutions to selected questions has been provided at the end of each chapter.
Why Buy AIETS IIT Foundation MATHEMATICS Class IIT Foundation MATHEMATICS Class 10 at KOOLSKOOL. Get unmatched deals and discounts when you buy AIETS IIT Foundation MATHEMATICS Class IIT Foundation MATHEMATICS Class | 677.169 | 1 |
Learn about Mathematical Modeling
The solution to a mathematical equation can be feasible or infeasible. There can be mathematical models with boundaries as well. Such models are termed as optimization models where the solution resides within a set of values. Usually such models are expressed with a set of constraints. For example, the classical functions of pricing the supply and demand for products, both these functions together create a fixed value for the price.
Here is a sample mathematical model
Objective: Maximize Profits from selling two products P1 and P2 at Price $3 and $4 respectively.
If you carefully notice the system of equations above, the first equation constantly increases for any value of P1 and P2. But the increase is restricted by equation number 2 which enforces a boundary on the system. Hence the solution set returns feasible values.
Equations can be both deterministic as well as stochastic. Stochastic systems are systems that do not have fixed values such as USD 3 as cost of product or labor hours as 2 hours per product. The expected values can be specified as a probability distribution. An Example of a probability distribution is the arrival rate of automobiles in a junction. One cannot determine the exact rate as the source would be dependant upon a lot of factors.
Simulation is an extended technique of analyzing variations of input and output using expected values for a large number of trials. Many contrasting system conditions can be specified and the simulation can be run for a large number of trials.
Math models are common place and are used to describe physical phenomena, astronomical phenomena and population growth. They are also used in production planning, manufacturing etc. In synopsis a mathematical model can create unbounded values or bounded values. A system with boundaries can be used to study extreme objectives such as profit maximization, time minimization etc.,
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If this technique fails, Pólya advises: "If you can't solve a problem, then there is an easier problem you can solve: find it." Or: "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?"
First principle: Understand the problem
"Understand the problem" is often neglected as being obvious and is not even mentioned in many mathematics classes. Yet students are often stymied in their efforts to solve it, simply because they don't understand it fully, or even in part. In order to remedy this oversight, Pólya taught teachers how to prompt each student with appropriate questions, depending on the situation, such as:
What are you asked to find or show?
Can you restate the problem in your own words?
Can you think of a picture or a diagram that might help you understand the problem?
Is there enough information to enable you to find a solution?
Do you understand all the words used in stating the problem?
Do you need to ask a question to get the answer?
The teacher is to select the question with the appropriate level of difficulty for each student to ascertain if each student understands at their own level, moving up or down the list to prompt each student, until each one can respond with something constructive.
Second principle: Devise a plan
Pólya mentions that there are many reasonable ways to solve problems. The skill at choosing an appropriate strategy is best learned by solving many problems. You will find choosing a strategy increasingly easy. A partial list of strategies is included:
Guess and check
Make an orderly list
Eliminate possibilities
Use symmetry
Consider special cases
Use direct reasoning
Solve an equation
Also suggested:
Look for a pattern
Draw a picture
Solve a simpler problem
Use a model
Work backward
Use a formula
Be creative
Use your head/noggin
Third principle: Carry out the plan
This step is usually easier than devising the plan. In general, all you need is care and patience, given that you have the necessary skills. Persist with the plan that you have chosen. If it continues not to work discard it and choose another. Don't be misled; this is how mathematics is done, even by professionals.
Fourth principle: Review/extend
Pólya mentions that much can be gained by taking the time to reflect and look back at what you have done, what worked and what didn't. Doing this will enable you to predict what strategy to use to solve future problems, if these relate to the original problem.
The book contains a dictionary-style set of heuristics, many of which have to do with generating a more accessible problem. For example:
The technique "have I used everything" is perhaps most applicable to formal educational examinations (e.g., n men digging m ditches) problems.
The book has achieved "classic" status because of its considerable influence (see the next section).
Russian inventor Genrich Altshuller developed an elaborate set of methods for problem solving known as TRIZ, which in many aspects reproduces or parallels Pólya's work.
From Yahoo Answers
Question:I am searching the WWW but I can't find what I need. I need a site that breaks down how to slove this arithmetic reasoning problems found on the Officer Aptitude Rating exam given by the navy to Qualify for OCS. I'm math eliterate!!!!!
Answers:Well, I was unable to find a site as well. I do have a suggestion.... In doing research, I came across the description of the math portion of the exam....
"The math skills assessed by the ASTB subtests include arithmetic and algebra, with some geometry. The assessments include both equations and word problems. Some items require solving for variables, others are time and distance problems, and some require the estimation of simple probabilities. Skills assessed include basic arithmetic operations, solving for variables, fractions, roots, exponents, and the calculation of angles, areas, and perimeters of geometric shapes."
Given each of these topics, maybe will be a good place to start, looking under algebra and geometry primarily. From browsing the site, it looks like it provides enough information necessary to help you learn the steps needed to work most problems on the exam.
Hope this was of some help to you. Best wishes on your exam.
Question:I've been trying to convince my parents to let me do online high school and they just wont give in! I have solid reasons as to why I want to study at home and I'm wondering why they're so stubborn about it.
If you were a parent, would you think that these are good reasons to let your child do online schooling?
- I'm originally from California but my family moved to Switzerland. The school system is so different here and they focus on shoving French down my throat before any other subject. I've studied at the public school here for a year and counting, and they teach me things that I already know. I don't feel like I'm up-to-par with the things the kids my age are studying back in the US. For example: Before I left, I was in the 8th grade and in Algebra. I actually felt challenged in all of my classes. When I got here, the teacher was teaching our class how to add fractions.
- I also don't want to end up like my brother, who was told that he can't go to "college" (the high school here) if he doesn't perfect his French by June. My brother is supposed to be in his senior year of high school in the US, yet they won't even let him start the first year of "college" here because he can't speak French. I feel like I'm cracking under the pressure to learn this language and not have to repeat grades.
- I'm harassed at school on a daily basis to the point where I can't even go through the same hallways anymore. I've changed my routes to all my classes just to avoid being bullied. I feel THAT threatened at school. Because of the bullying, I constantly feel stressed and scared. I can't defend myself either because I still have a ton of French to learn and I'll end up looking like even more of an idiot.
I'm being reasonable, right? It's not like I want to do online schooling just to sit at home and rot. I feel like it's the best thing to do if I want to stay sane. The only problem is that my mom is extremely old-fashioned and thinks that anything out of the ordinary should be shunned by society! She doesn't realize how bad of an influence public school has on me because I'm so good at controlling myself at home.
Answers:You can easily compare info about these schools in this site - schools.iblogger.org
Question:how does it benefit us to know other peoples learning styles?
Answers:Numero Uno: If I know your preferred way of learning, then I can adjust my training/teaching in such a way to make it easier for you to learn
Question:Scientists can now determine the complete DNA sequences of organisms, including humans. Now that this milestone has been reached, is there a reason to continue to learning about Mendel, alleles, and inheritance patterns.
Answers:Just because you have a few million base pairs of code doesn't mean you have a clue about how the genes are regulated and interact in order to fashion an organism. When you selectively breed and make crosses you can study the interactions of combinations of alleles.
Basic introduction to mendelian genetics shows you a maximum of three or four gene interactions with no linkage but an organism is the cascading series of interactions of thousands of genes.
Looking at restricted breeding experiments can give insight in how the the allelic combinations respond. This is done to link a variation in phenotype with actual genotypes. This often how specific desirable alleles that influence predisposition to disease resistance are found.
More Reasons NOT to Believe in God - 2 :More Reasons NOT to Believe in God: Reason #2: Arrogance To quote douglas adams: Space... is big. Really big. You just won't believe how vastly hugely mindboggingly big it is... -We, are just one species of many on this tiny planet. -There are 9 planets, (give of take pluto) orbiting this average star we call the sun. -there are over 200 billion stars in our average galaxy we call the milky way. -traveling at 186000 miles per second it would take 100000 years to travel from one side of our galaxy to the other. -There are hundreds of BILLIONS of galaxies in the universe. -the Universe existed 9.1 billion years before earth was ever even formed. -The earth existed for almost 1 billion years before primitive life even began to emerge -microbes didn't even exist on land until 2.7 billion years ago. -245 million years ago the earth was populated by giant dinosaurs and prehistoric beasts (Dinosaurs lived on earth for 180 million years, homosapiens have lived on Earth for less than 1 million years) -over the course of 2.5 million years our primate species evolved from the genus: homo into the homosapiens we are now. -for hundreds of thousands of years mankind told stories and developed folklore. only recently, within the past ten thousand years have we learned to sustain our culture through written language. And to be certain, based on nothing but personal intuition, that in this TINY TINY TINY fragment of a blink in time, on this TINY TINY spec of dust we call home, and out of ... | 677.169 | 1 |
Basic Mathematics: A Text/Workbook, 7th Edition
Pat McKeague's seventh edition of BASIC MATHEMATICS is the book for the modern student like you. Like its predecessors, the seventh edition is clear, concise, and patient in explaining the concepts. This new edition contains hundreds of new and updated examples and applications, a redesign that includes cleaner graphics and images (some from Google Earth) that allow you to see the connection between mathematics and your world. This includes references to contemporary topics like gas prices and some of today's most forward thinking companies like Google | 677.169 | 1 |
...Robert Moses calls math and algebra the ticket to 21st century citizenship, and I would agree. It is the foundation upon which all other secondary and college math and science success will be built, so it is of strategic importance to every student. I focus on working with students to understand the "why" not just the "how", so the "how" will stick.
...But the simple fact of the matter is that algebra is NOTHING but arithmetic without the numbers. If you can add, subtract, multiply, and divide numbers, then there is very little in public school algebra that one doesn't already know. It really is a shame that Algebra 1 is the topic that turns so many students off to math, when it ought to be a cakewalk | 677.169 | 1 |
To create mathematically, scientifically and technologically literate and functional learners who will be successful in a business world that relies on calculators, computers, scientific and mathematical procedures, rapidly growing and extensively applied in diverse situations. | 677.169 | 1 |
by Virtual Dynamics Org Visual Mathematics, is a Mathematical Visualizer (containing -at least- 67 modules) to learn more and better in less time. Enjoy learning!!! . Get to really Understand what you Study !!!
by Virtual Dynamics Org Panageos is oriented to the intensive solution of problems on Plane Analytic Geometry.
The main feature of Panagoes is its power to read the user's equations and interpret them, for this reason the data input is exclusively through the keyboard.
by Virtual Dynamics Org Curvilinear: Easy Learning Plane Analytic Geometry
An Intuitively-Easy-To-Use visual interactive software, oriented to overcome the abstraction that exists in the Plane Analytic Geometry (PAG), this is a tool that makes it easy to master PAG.
by SolidLearning, Inc. mBasics makes math worksheets for addition, subtraction, multiplication and division. Generate worksheets and assign them to students for testing. Automatic grading and customizable
by RomanLab Software Powerful yet easy-to-use graph plotting and data visualization software. You can plot and animate 2D and 3D equation and table-based graphs. The unlimited number of graphs can be plotted in one coordinate system using different colors and lighting. | 677.169 | 1 |
The goal of this series is to provide readers with a strong foundation in Algebra. Each book is designed to develop readers' critical thinking and problem-solving capabilities and prepare readers for subsequent Algebra courses as well as "service" math courses. Topics are presented in an interesting and inviting format, incorporating real world sourced data and encouraging modeling and problem-solving. The Real Number System. Linear Equations and Inequalities in One Variable. Problem Solving. Linear Equations and Inequalities in Two Variables. Systems of Linear Equations and Inequalities. Exponents and Polynomials. Factoring Polynomials. Rational Expressions. Roots and Radicals. Quadratic Equations and Functions. For anyone interested in introductory and intermediate algebra and for the combined introductory and intermediate algebra. | 677.169 | 1 |
Gambrills CalculusIt has amazing plotting capabilities with both 2-D and 3-D plots. It also provides a vast array of statistical functions including means, variances, medians, and modes of data sets. It can also generate random data from uniformly distributed and normally distributed random variables for use in monte carlo simulations.
...My method of tutoring is mostly "hands on" with the use of a personal-sized white board. With the white board, the students are able to display to me their knowledge of the concept and topic in order for me to assist if they understand. I am also able to display the mathematical concept and topic pictorial to them. | 677.169 | 1 |
Course Outline
Rationale:
This course line was developed in response to the changing mathematical requirements in the work place. The increased use of technology and the way information is communicated has changed significantly in the last 20 years. This course was developed to give students practical hands on mathematics that they will use in the jobs that they work at after high school.
Units:
Unit A: Systems of Inequalities
Unit B: Quadratic Functions
Unit C: Scale
Unit D Trigonometry
Unit E: Statistics
Unit F: Proofs
Unit G: Problem Solving
Unit H: Personal Finacne
The units may not be taught in the order listed above. Each unit will be allotted approximately two weeks. This means there will be a test about every two weeks. | 677.169 | 1 |
Algebra Placement Exam - Study Guide
1 Purpose of this document
There are currently four ways to become eligible to enroll
in any of th 100 level math classes
at The University of Montana Western
1. Pass MATH 007 with a C- or better.
2. Earn a score of 520 or higher on the math section of
the SAT or 22 or higher on the
math section of the ACT.
3. Earn a C- or better on a transferrable course from
another university. This course
must be equivalent to MATH 007 or any of the 100 level math classes offered at
the
University of Montana Western.
4. Pass the math placement exam with a score of 70% or
higher.
The primary purpose of this document is to provide you
with an inventory of the skills you
should become proficient in in order to pass the placement exam. However, it
also should
serve as a reasonable study guide for MATH 007. With this in mind, pages from
Prealgebra
and Algebra, by Daniel D. Benice (the MATH 007 textbook) will be cited in this
document.
A broad description of the skills you should posess before
taking a 100 level math class
follows.
1. You should be able to state what an algebraic
expression is, know the mathematical
operations you may apply to it without changing its value, and demonstrate
skills at simplifying or manipulating algebraic expressions that involve monomials,
polynomials,
fractions, exponents, and roots and various combinations of these.
2. You should be able to solve single linear equations for
an unknown variable (or root).
This includes equations that are obviously linear and equations that must be
transformed
or simplified first.
3. you should be able to solve a system of two linear
equations in two independent variables
by employing either the method of elimination or the method of substitution . In
addition, you should be able to demonstrate the connection between the solution
of a
system of linear equations and the graphs of the lines described by the two
equations.
4. You should be able to take an equation for a line,
interpret its slope and x and y
intercepts , and graph the line. Similarly, you should be able to look at the
graph of
a line and be able to come up with its equation. Finally, you should be able to
write
down the equation of a line if you are given two points on the line or one point
on the
line and the slope of the line.
5. You should be able to solve quadratic equations by
factoring them or by employing
either "completing the square" or the quadratic formula.
3 Course of study for preparing for the placement exam
If you are looking for a more general course of study that
should cover the topics you will
need to master in order to pass the placement exam, or, if you simply want to
have an
overview of what you will most likely be studying in Math 007, then read on.
1. Expressions are introduced in section 11.1 of
Prealgebra and Algebra, pages 134 and 135.
2. Elementary simplification problems first appear in
sections 11.1–11.4 of Prealgebra
and Algebra, pages 135–153. These problems involve, combining like terms,
elementary
manipulation of expressions involving exponents, use of the FOIL method, and
division
of polynomials and monomials .
3. Linear equations are first introduced and defined in
section 12.1 of Prealgebra and
Algebra, on page 154.
5. A strategy for solving slightly more general linear
equations appears in sectin 12.6,
pages 165–169. These are mostly just linear equations that ought to be
simplified
before you solve them, but they are good practice.
6. You can learn what it means to graph a straight line in
chapter 14. The basic idea of
how to graph anything in a two-dimensional, Cartesian coordinate system is
intoduced
in 14.1, pages 197–201.
7. Techniques for graphing straight lines appear in
sections 14.2–14.4, pages 201–221.
You need to be familiar with how to graph lines by plotting points, and using
slope
intercept method. In addition, you need to be able to write down the equation
for a
line if you are given (1) two points on the line, or (2) a point on the line and
the slope
of the line.
8. Be sure that you can explain the relationship between
the x-intercept of a line and the
solution to the equation of the line.
9. Systems of linear equations are first introduced and
defined in section 15.1 on pages
222 and 223.
10. You need to demonstrate an ability to solve a system
of two linear equations (in
two independent variables) using both the method of elimination and the method
of
substitution. These appear in sections 15.2 and 15.3, respectively (pages
223–230.)
11. You should be able to explain the relationship between
the graphs of the two equations
in the system and the solution to the system.
12. The skill of factoring simple mathematical expressions
is first developed in section 17.1,
pages 248–251.
14. Once you can factor simple quadratic expressions that
have rational roots, use this
skill to solve simple quadratic equations. This skill is developed in section
17.4, pages
251–268.
15. You need to be able to manipulate and simplify
expressions involving fractions. Fractional
expressions are introduced in section 18.1, pages 269–271. However, there are
some very specific skills you need to develop. In particular,
(a) you can learn how to apply your factoring and
elementary simplification skills
in order to simplify fractions that involvemonomials and polynomials in the numerator and denomenator in section 18.2, pages 271–276;
(b) you can learn how to simplify expressions that involve products and
quotients of
fractional expressions in sections 18.3 and 18.4, respectively (pages 276–281);
(c) you can learn how to simplify expression involving sums and
differences of fractions
in section 18.5, pages 281–285. This requires you to develop an ability to
find a common denomenator between two fractions;
(d) you can learn how to mix and match some of these skills and apply them
to some
slightly more complex fractional expressions in section 18.6, pages 286–289.
16. Once you have mastered the skills for manipulating and
simplifying fractional expressions,
you can apply these to solving equations that involve fractional expressions.
Generally this means simplifying the equations until you have reduced them to
either
linear or quadratic equations. Once you've done that, you can solve them as
before.
Section 18.7, pages 289-294, addresses this.
17. Many expressions involve exponents. The laws of
exponents are reviewed in section
20.1, pages 313–317. You should be able to use these laws to simplify and
manipulate
expressions that involve exponents when appropriate.
18. Exponents need not be positive numbers (or even
integers!). You can find out an
interpretation of what negative and fractional exponents mean in sections 20.2
and
20.5. (Section 20.4 tells you what it means to raise a quantity to the power of
0). Be
sure that you understand the relationship between fractional exponents and
radicals!
19. Since radicals are intimitely related to exponents,
your ability to manipulate and simplify
expressions that involve radicals will depend on your ability to work with
exponents.
Some basic skills are developed in sections 21.1–21.2, pages 336–341.
20. You can learn how to combine two or more like radicals
in section 21.3, pages 341–342.
21. You can learn how to take a fractional expression that
involves radicals in both the
numerator and denomenator and simplify it in a way that leaves the radicals only
in
one position (but not both). This is called rationalization, and it can be found
in
section 21.4, pages 342–346.
22. Once you have mastered the skills for manipulating and
simplifying expressions that
involve radicals, you can apply these to solving equations that involve
radicals. Generally
this means simplifying the equations until you have reduced them to either
linear
or quadratic equations. Once you've done that, you can solve them as before.
Section
21.5, pages 346–351, provides instruction on this subject.
23. Finally, it is important that you recognize that not
all quadratic equations have integer
or rational roots. Many have irrational roots. It is not easy to factor these
equations
"by inspection," so a more general technique is needed. One is called completing
the
square and the other is called the quadratic equation. Both methods are related
and
knowing either one will do. You can learn about them in sections 22.1–22.3,
pages
353–362.
4 Practice exam
Have you studied the concepts in the previous section
hard? Do you feel like you are ready
for the placement exam? If so, read on. There is a practice exam (with a key)
immediately
fol lowing this document . You should take it under conditions similar to the ones
you will
find on the the test day. In particular take it in during a quiet, fifty minute
period, use
only a pencil or something else to write with, and put away all books, notes,
calculators,
and other mathematical aids. You can miss no more than 6 out of the 20 problems
on the
practice exam in order to earn a pass. Please note that this exam should be
representative
of the actual placement exams, but it is not the same exam you will see. Actual
placement
exams may seem harder (or easier), but they will address similar topics.
IMPORTANT: The test consists of 20 problems. You
will have 50 minutes to
complete the problems. You are not allowed to use calculators, books or any
other aids during the test. Calculations may be done on provided scratch paper,
but you must turn this scratch paper in with your test. All answers must be
complete, legible and simplified to lowest terms. Record only final answers in
the blanks after the problems.
1. Simplify:
3(2x + 1) − 5
2. Find the equation of the line through point (1, 2) and
(3, 8). (The equation should be
in a slope-intercept form y = mx + b.)
3. Solve the equation for x. Express your answer as a
common fraction.
4. Solve an equation for x. Express your answer as a
common fraction.
5. Solve the equation:
2x + 1 = 3x + 7
6. Solve the following system of equations for x and y:
7. Solve the following system of equations for x and y:
8. Simplify:
9. Simplify:
10. Simplify:
11. Solve the equation:
12. Solve the equation:
13. Solve the equation:
14. Solve the equation for x. Express your answer as a
common fraction. | 677.169 | 1 |
Search Journal of Online Mathematics and its Applications:
Journal of Online Mathematics and its Applications
Power Maths
by Sidney Schuman
Power Maths is a pre-calculus investigation designed to enable students to discover the integral and differential power rules numerically. The investigation leads the student to conjecture a simple ratio of areas, from which the rules are then deduced for the restricted domain [0,x].
A hardcopy version of Power Maths includes calculator/graph-based investigations for both power rules. If you would like a copy, or if you have any comments, please click the Worksheet link on the Investigation page.
Power Maths (both parts) appeared originally as a booklet used while teaching at Lewisham College, London UK.
Editor's note, 11/04: When published, this investigation included only the integral power rule, and there was a separate investigation for the differential power rule. The author has since combined these in the present version.
Acknowledgements: Grateful thanks to David A. Smith for his encouragement and to Lana Holden for the applet. | 677.169 | 1 |
Modelling with Fourier series
This unit shows how partial differential equations can be used to model...
This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations.
After studying this unit you should be able to:
understand how the wave and diffusion partial differential equations can be used to model certain systems;
determine appropriate simple boundary and initial conditions for such models;
find families of solutions for the wave equation, damped wave equation, diffusion equation and similar homogeneous linear second-order partial differential equations, subject to simple boundary conditions, using the method of separating the variables;
combine solutions of partial differential equations to satisfy given initial conditions by finding the coefficients of a Fourier series.
Contents
Modelling with Fourier series
Introduction
This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations | 677.169 | 1 |
The book is the first to give a comprehensive overview of the techniques and tools currently being used in the study of combinatorial problems in Coxeter groups. It is self-contained, and accessible even to advanced undergraduate students of mathematics. The primary purpose of the book is to highlight approximations to the difficult isomorphism problem... more...
The book introduces readers in the often-overlooked math-related fields to the ideas of writing-to-learn (WTL) and writing in the disciplines (WID). It offers a guide to the pedagogy of writing in the mathematical sciences, and gives theoretically grounded means by which writing can be used to help undergraduate students to understand mathematical... more... | 677.169 | 1 |
Mammoth, AZ SAT Math modern Algebra we most frequently use "x" to represent "the thing". Start any word problem with labeling the unknown, "Let x = the number of ...." It is this great art that has so greatly advanced all the modern sciences. Think of it as the art that supports the sciences! | 677.169 | 1 |
Welcome to Chapter Three of Math Planet
Algebra Crash Course. In this chapter, we will talk about polynomials.
Polynomials are the essentail parts of algebra, and they have many uses, and we will
mainly talk about their basic concepts and the most common manipulations of
polynomials. But before you continue, you should learn the terms below so that you
can have a better understanding of the lesson afterward. Different parts of the
lesson are also provided so that you can go to the section of your choice. | 677.169 | 1 |
College Algebra Essentials CourseSmart eTextbook, 4th Edition
Description
Bob Blitzer has inspired thousands of students with his engaging approach to mathematics, making this beloved series the #1 in the market. Blitzer draws on his unique background in mathematics and behavioral science to present the full scope of mathematics with vivid applications in real-life situations. Students stay engaged because Blitzer often uses pop-culture and up-to-date references to connect math to students' lives, showing that their world is profoundly mathematical.
With the Fourth Edition, Blitzer takes student engagement to a whole new level. In addition to the multitude of exciting updates to the text and MyMathLab® course, new application-based MathTalk videos allow students to think about and understand the mathematical world in a fun, yet practical way. Assessment exercises allow instructors to assign the videos and check for understanding of the mathematical concepts presented.
Table of Contents
P. Prerequisites: Fundamental Concepts of Algebra
P.1 Algebraic Expressions, Mathematical Models, and Real Numbers
P.2 Exponents and Scientific Notation
P.3 Radicals and Rational Exponents
P.4 Polynomials
Mid-Chapter Check Point
P.5 Factoring Polynomials
P.6 Rational Expressions
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER P TEST
1. Equations and Inequalities
1.1 Graphs and Graphing Utilities
1.2 Linear Equations and Rational Equations
1.3 Models and Applications
1.4 Complex Numbers
1.5 Quadratic Equations
Mid-Chapter Check Point
1.6 Other Types of Equations
1.7 Linear Inequalities and Absolute Value Inequalities
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 1 TEST
2. Functions and Graphs
2.1 Basics of Functions and Their Graphs
2.2 More on Functions and Their Graphs
2.3 Linear Functions and Slope
2.4 More on Slope
Mid-Chapter Check Point
2.5 Transformations of Functions
2.6 Combinations of Functions; Composite Functions
2.7 Inverse Functions
2.8 Distance and Midpoint Formulas; Circles
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 2 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-2)
3. Polynomial and Rational Functions
3.1 Quadratic Functions
3.2 Polynomial Functions and Their Graphs
3.3 Dividing Polynomials; Remainder and Factor Theorems
3.4 Zeros of Polynomial Functions
Mid-Chapter Check Point
3.5 Rational Functions and Their Graphs
3.6 Polynomial and Rational Inequalities
3.7 Modeling Using Variation
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 3 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-3) 410
4. Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Properties of Logarithms
Mid-Chapter Check Point
4.4 Exponential and Logarithmic Equations
4.5 Exponential Growth and Decay; Modeling Data
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 4 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-4)
5. Systems of Equations and Inequalities
5.1 Systems of Linear Equations in Two Variables
5.2 Systems of Linear Equations in Three Variables
5.3 Partial Fractions
5.4 Systems of Nonlinear Equations in Two Variables
Mid-Chapter Check Point
5.5 Systems of Inequalities
5.6 Linear Programming
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 5 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-5)
Appendix: Where Did That Come From? Selected Proofs
Answers to Selected Exercises
Subject Index
Photo Credits | 677.169 | 1 |
Mathematics in our world by Robert E Eicholz(
Book
) 64
editions published
between
1976
and
1983
in
English
and held by
160
libraries
worldwide
Elementary school mathematics by Robert E Eicholz(
Book
) 13
editions published
between
1963
and
1971
in
English
and held by
108
libraries
worldwide
This series of braille mathematics textbooks for primary and intermediate grades uses the Nemeth Code and provides material for mastering the basic math facts and computation techniques. Basic strands extending throughout the series stress the structure of mathematics. Attention is focused upon the fact that a few fundamental concepts compose the foundation from which the entire structure rises in logical sequence. | 677.169 | 1 |
Stewartstown ACT also learn about rational numbers, polynomials, roots, quadratic and exponential functions. Algebra II is a continuation of Algebra I, and will cover many of the same topics, but with more depth. Equations and inequalities become standard, and are used regularly in other topics | 677.169 | 1 |
How I Teach Calculus: A Comedy (Optimization)
This post is a part a larger series documenting the changes I am making to my calculus course. My goals are to implement standards-based grading and to introduce genuine applications of the concepts being taught. I'm not suffering any delusions that any of this is all that ground-breaking, I just want to log the comedy that ensues:
What does this map of Middle-Earth do for me? Other than indulging my current obsessions with Tolkien, it gets at the inherent inelegance and drudgery of guess and check.
At this point my kids have been working with related rates. They've been doing things with water jugs, as well as working the traditional book style problems. Kids tend to be frustrated by "word" problems. This is because they can't memorize and repeat a process. Most people love to be told exactly what to do — whether they'll admit that or not — if the process has enough complicated steps, but not too many, then they'll feel like they're getting something done, but it was easy because the task had already been planned out with an explicit end in mind. Word problems piss kids off because they have to try and piece together information and frame it mathematically in a form that will allow them to apply the appropriate technique. That is not a fun process for someone who has no idea what that technique actual does or means. This is why you must generate context before content. The changes to my calculus class have brought me a lot of work, but they've also brought on a whole lot more student conceptual understanding. Cornally is happier.
So, in a pretty large breach of calculus etiquette, I skip most of the material about critical points, extrema, 1st and 2nd derivative tests, and what have you, and I move straight to optimization. How can they do optimization, if they don't know all that other stuff?! Easily, optimization is really only about using your noggin and finding critical points. So, what better way to introduce a whole chapter of "Applications of the Derivative," as Larson so deftly puts it, than by starting with the most useful application itself!
A word about text book structure. Why, oh WHY, do we always put "applications" after abstract content? Don't you get it? The only thing I'm trying to do here is switch that order. You have to be very very judicious in how you do this so as not to burn the children, but why would anyone give two shakes about critical points until they know why they'd want to find them? So, optimization we must do first. Aside of an aside: do not pretend that the "real world applications" your book gives you are sufficient. They just put those in there as a buzz word to sell more books. I blame Texas.
So, I spent a lot of this winter reading Tolkien's Lord of the Rings. I've never gotten through all three in a row, and I felt it was about time. I didn't anticipate how engrossing they would be, and when they started showing up in my lessons, I knew I had a problem. See above.
I presented the kids this map, and asked them what's the shortest distance to Mordor? I accompanied this question with a little set-up from the book. I won't reproduce it here, but I read an excerpt from Two Towers Book 4 Chapter 3. I also showed the complementary part from the movie (Two Towers DVD Chapter 15 The Black Gate is Closed). The story is that Gollum leads Sam and Frodo to the gates of Mordor, but they are shut. Gollum then leads the two hobbits on a crazy hike through the mountains north of the gate.
This is an exercise in implicit differentiation, orthogonal trajectories, and — nominally — optimization; however, the task becomes very daunting very quickly. The kids start drawing lines. Some quickly realize that each step down requires use of the Pythagorean theorem to find the actual distances covered. Many students eventually raise the important question, "Aren't there an infinite number of ways to check?" Yes. They become sad at the thought that I might make them do this. Of course, we don't.
The point has been made; we need to develop some mathematics that gets at optimization.1
So where from here? We now need to learn how to optimize. A discussion of critical points occurs. I don't say those words; vocab always comes last. We draw some graphs, what's common about all the highest points? My slope-minded students easily point out that the slope there is nothing. So, if only we could get a function, find its derivative, and then set it to zero, perhaps then we've built a process here? Yup.
We then launch into the very classic open-topped-box-from-sheet-of-paper example. I tell a story about camping and chili and having limited tin foil with which to make a chili holding vessel. This kind of contrived problem really rubs me the wrong way, but I'm OK with it now that the kids have context, we're using it to learn process.
I have the kids build boxes the boxes by cutting out the edges and taping them up. They then measure the length, width, and height of the box and find its volume. Many students realize that there was really no point in making the box, but hey a lot don't.
Fold on the grey lines!
They then graph their data on the board making a graph of Volume vs. Cut-out length. It comes out a little shaky but pretty much looks like this plot: (from 0 up to 4.25 anyway…)
f(x) = x(8.5-2x)^2
The 8.5 is the dimension of our paper. A great discussion of domain ensues, I'm sure you already see it. In fact, I am suffering absolutely no delusions that this is at all unique. In fact this is about as traditional as I get. Sometimes you just do what works best, even if it smacks of pretense.
All that's left to do is develop the math for this model. We get to work out a fairly simple example to show how to combine two equations that relate the same idea:
An equation in one variable for single-variable calculus, it must be Christmas! Derivatives ensue, zeroes get thrown around, and optimum values get found. In case you're trying to learn from this:2 we need to use the product then chain rule (or you could distribute first)
Again, my goal is always to motivate the necessity for a new technique. I am not Mr. Wizard.
1. I don't usually give impossible/extremely difficult tasks, but I planned this map bit in response to a conversation about the method of guess and check: A student told me that he prefers guess and check because he can usually get the right answer to a problem, and sometimes it's even faster. He likes the method mostly because he doesn't have to learn anything new. This should strike some of you, I know it hit me hard. He recognized the inherent ridiculousness of many math lessons; the techniques taught aren't always the best way to do it. SO WHY ARE YOU TEACHING IT? What does this map of Middle-Earth do for me? Other than indulging my current obsessions with Tolkien, it gets at the inherent inelegance and drudgery of guess and check.
2. I never intended for this blog to teach content, but I've noticed a that a lot of the Google searches that lead to my site are from students looking for help. If you want to learn calculus, you can attend my high school and take my course. Otherwise there are about six trillion other sites that attempt to teach you calculus.
I didn't at all get the impression that you don't do math. I just want for math people to consider the benefits or ramifications of stressing "real-world" applications before context and theory.
The more we examine this topic in our own classrooms, the better our knowledge will be about it. I know certainly that I've had lots of supervisory "help" that essentially said that "real-life" is the only thing I should teach and that students will be able to construct the theory to match. I'd really like to be able to point to more than one set of research on it.
One reason to put abstract teaching before real world applications is that students may learn better that way. I had always felt that it was easier to learn a simplified version before trying to analyze a complicated real-world situation but I didn't really have more than an anecdotal sense of this until I found this article.
I read this article when it was published in 2008. As much as I'd love to argue the merits of the study, I guess I don't feel that the article is clear enough about what was taught, how, and then how the assessments were given. For me, it's not about "real-world" it's about context. I've seen the data in my own students that show that concise context building scaffolds the rigorous symbolic math.
I hope I haven't given the impression that I don't do hard math. I definitely spend my fair share of time at the board working examples. Hopefully my posts haven't obfuscated that.
I think you may be contesting my use of a complicated introduction, which, as I footnoted, I rarely do. I actually try to be as clear and to the point as possible with any non-direct instruction. Do you think I should be clearer about that when I write? Thanks for the comment | 677.169 | 1 |
Few would argue that, through its development of science and technology, the human species has been more successful than any other in taking control of the environment and using the resources of the earth to its own advantage. It is probably equally clear that this dramatic development of science and technology is only possible because of our ability to think creatively, consistently and logically. Indeed, there seems to be a parallelism, a consistency, between the rules that govern logical thought and the rules that govern the functions of the physical universe. The physical universe is quite logical and consistent. It reveals its secrets to those who study it using creative, consistent and logical thought. And for the development of one's ability to exercise this very useful way of thinking there is probably no better approach than through the study of mathematics.
So welcome to the Department of Mathematics where you will have the opportunity to hone your thinking skills by taking some of our twenty four courses in algebra, statistics, trigonometry, calculus and differential equations. In addition to improving your ability to think clearly, you will also learn about many of the astounding mathematical discoveries that have been made throughout the centuries and how they can be used for practical applications in science, engineering, business and the health fields.
I encourage you to humbly and enthusiastically place yourself in the hands of our experienced and capable faculty who are fully devoted to teaching you mathematics. If you do this, you will be taken on an intellectual journey to fascinating places that you cannot easily imagine. You will come away not only well prepared with the technical knowledge you need for your chosen career or field of study, but with an enhanced ability to think more clearly, more deeply, more rigorously, more analytically and more precisely about yourself and everything you encounter. Welcome to the world of mathematics! | 677.169 | 1 |
CAT in Mathematics
The CUNY Assessment Test in Mathematics (also known as the CAT in Mathematics, or the COMPASS Math test) is an untimed, multiple-choice, computer-based test designed to measure students' knowledge of a number of topics in mathematics. The test draws questions from four sections: numerical skills / pre-algebra,
algebra, college algebra, and trigonometry. Numerical skills / pre-algebra questions range from basic math concepts and skills (integers, fractions, and decimals) to the knowledge and skills that are required in an entry-level algebra course (absolute values, percentages, and exponents). The algebra items are questions from elementary and intermediate algebra (equations, polynomials, formula manipulations, and algebraic expressions). The college algebra section includes questions that measure skills required to perform operations with functions, exponents, matrices, and factorials. The trigonometry section addresses topics such as trigonometric functions and identities, right-triangle trigonometry, and graphs of trigonometric functions. No two tests are the same; questions are assigned randomly from the four sections, adapting to your test-taking experience.
Placement into CUNY's required basic math courses is based on results of the numerical skills/pre-algebra and algebra sections. The test covers progressively advanced topics with placement into more advanced mathematics or mathematics-related courses based on results of the last three sections of the test.
Students are permitted to use only the Microsoft Windows calculator while taking the test. CAT in Mathematics Practice Materials
Below are some sample tests and websites containing more samples and information about the CAT in Mathematics and related materials. Special software may be needed to view some of these files; check under our Software section to get them.
Emmy Noether, the German algebraist that Albert Einstein called the most important woman in mathematics. | 677.169 | 1 |
Shmoop Launches Calculus Guide for Students and Teachers
Shmoop's new calculus guide breaks down the important concepts in engaging ways in a portable digital medium.
Calculus Exercises
Mountain View, CA (PRWEB) September 20, 2012
One of the most common questions that flits across a math student's mind is, "Why does this matter?" Understandably, it may be difficult to see at a glance how finding a solution to the derivative of an expression might directly correlate to one being able to tie their shoelaces.
Thank goodness for calculus. Admittedly, some of the concepts are tough, but along the way you begin to see its wicked practical applications. Rather than simply juggling numbers and variables, you are beginning to apply the mathematical concepts you have picked up along the way to solve real-world problems. Suddenly, math has a purpose! Huzzah!
Shmoop, a publisher of digital curriculum and online test prep, is proud to announce the launch of its new Calculus Guide. Here, students can learn that "dy is over dx." (Or is it in denial? It does still keep dx's photo in a frame on its desk…)
Hundreds of examples, exercises, and sample problems. The best way to learn is by example. Which is how Jack Osbourne got to be such a phenomenal singer.
3 quizzes per chapter. Students master the skills, train with Newton's weapons, and climb towards that black belt of calculus.
Shmoop's "In the Real World" section will fill students in on how calculus is used in STEM fields. These are not meadows where the tops of wildflowers have been chopped off.
Graphs galore to help visualize calculus terms and functions. Let these axes be students' allies.
Check out Shmoop's Calculus Guide and start making sense of the world.
About Shmoop
Shmoop is a digital curriculum and test prep company that makes fun, rigorous learning and teaching materials. Shmoop content is written by master teachers and Ph.D. students from Stanford, Harvard, UC Berkeley, and other top universities. Shmoop Learning Guides, SAT Prep, and Teacher's Editions balance a teen-friendly, approachable style with academically rigorous materials to help students understand how subjects relate to their daily lives. Shmoop offers more than 7,000 titles across the Web, iPhone, Android devices, iPad, Kindle, Nook, and Sony Reader. The company has been honored twice by the Webby Awards and was named "Best in Tech" for 2010 and 2011 by Scholastic Administrator. Launched in 2008, Shmoop is headquartered in a labradoodle-patrolled office in Mountain View, California. | 677.169 | 1 |
Accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Regardless of the software system used, the book describes and gives examples of the use of modern computer software for numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, factorisations, matrix and vector norms, and other topics in linear algebra. The book is essentially self- contained, with the topics addressed constituting the essential material for an introductory course in statistical computing. Numerous exercises allow the text to be used for a first course in statistical computing or as supplementary text for various courses that emphasise computations. [via]
More editions of Numerical Linear Algebra for Applications in Statistics: | 677.169 | 1 |
Mathematics A Discrete Introduction
9780534398989
ISBN:
0534398987
Edition: 2 Pub Date: 2005 Publisher: Thomson Learning
Summary: With a wealth of learning aids and a clear presentation, this book teaches students not only how to write proofs, but how to think clearly and present cases logically beyond this course. All the material is directly applicable to computer science and engineering, but it is presented from a mathematician's perspective | 677.169 | 1 |
Unlike most engineering maths texts, this book does not assume a firm grasp of GCSE maths, and unlike low-level general maths texts, the content is tailored specifically to the needs of engineers. The result is a unique book written for engineering students that takes a starting point below GCSE level. Basic Engineering Mathematics is therefore ideal for students of a wide range of abilities, especially for those who find the theoretical side of mathematics difficult.
Now in its fifth edition, Basic Engineering Mathematics is an established textbook, with the previous edition selling nearly 7500 copies. All students that require a fundamental knowledge of mathematics for engineering will find this book essential reading. The content has been designed primarily to meet the needs of students studying Level 2 courses, including GCSE Engineering, the Diploma, and the BTEC First specifications. Level 3 students will also find this text to be a useful resource for getting to grips with essential mathematics concepts, because the compulsory topics in BTEC National and A Level Engineering courses are also addressed. less | 677.169 | 1 |
0321652797
9780321652799
Using and Understanding Mathematics: Using and Understanding Mathematics: A Quantitative Reasoning Approach, Fifth Edition increases readers' mathematical literacy so that they better understand the mathematics used in their daily lives, and can use math effectively to make better decisions every day. Contents are organized with that in mind, with engaging coverage in sections like Taking Control of Your Finances, Dividing the Political Pie, and a full chapter about Mathematics and the Arts. Note: This is the standalone book, if you want the book with the Access Card please order the ISBN below: 0321727746 / 9780321727749 Using and Understanding Mathematics: A Quantitative Reasoning Approach with MathXL (12-month access) * Package consists of 0201716305 / 9780201716306 MathXL -- Valuepack Access Card (12-month access) 0321652797 / 9780321652799 Using and Understanding Mathematics: A Quantitative Reasoning Approach «Show less
Using and Understanding Mathematics: Using and Understanding Mathematics: A Quantitative Reasoning Approach, Fifth Edition increases readers' mathematical literacy so that they better understand the mathematics used in their daily lives, and can use math effectively to make... Show more»
Preface
xi
Acknowledgments
xviii
Prologue: Literacy for the Modern World
PART ONE Logic and Problem Solving
Thinking Critically
Activity Bursting Bubble
Recognizing Fallacies
Propositions and Truth Values
Sets and Venn Diagrams
A Brief Review: Sets of Numbers
Analyzing Arguments
Critical Thinking in Everyday Life
Approaches to Problem Solving
Activity Global Melting
The Problem-Solving Power of Units
A Brief Review: Working with Fractions
Using Technology: Currency Exchange Rates
Standardized Units: More Problem-Solving Power
A Brief Review: Powers of 10
Using Technology: Metric Conversions
Problem-Solving Guidelines and Hints
PART TWO Quantitative Information in Everyday Life
Numbers in the Real World
Activity Big Numbers
Uses and Abuses of Percentages
A Brief Review: Percentages
A Brief Review: What Is a Ratio?
Putting Numbers in Perspective
A Brief Review: Working with Scientific Notation
Using Technology: Scientific Notation
Dealing with Uncertainty
A Brief Review: Rounding
Using Technology: Rounding in Excel
Index Numbers: The CP1 and Beyond
Using Technology: The Inflation Calculator
How Numbers Deceive: Polygraphs, Mammograms, and More
Managing Money
Activity Student Loans
Taking Control of Your Finances
The Power of Compounding
A Brief Review: Powers and Roots
Using Technology: Powers
Using Technology: The Compound Interest Formula
Using Technology: The Compound Interest Formula for Interest Paid More than Once a Year
Using Technology: APY in Excel
Using Technology: Powers of e
A Brief Review: Three Basic Rules of Algebra
Savings Plans and Investments
Using Technology: The Savings Plan Formula
A Brief Review: Algebra with Powers and Roots
Using Technology: Fractional Powers (Roots)
Loan Payments, Credit Cards, and Mortgages
Using Technology: The Loan Payment Formula (installment Loans)
Using Technology: Principal and Interest Payments
Income Taxes
Understanding the Federal Budget
PART THREE Probability and Statistics
Statistical Reasoning
Activity Cell Phones and Driving
Fundamentals of Statistics
Using Technology: Random Numbers
Should You Believe a Statistical Study?
Statistical Tables and Graphs
Using Technology: Frequency Tables in Excel
Using Technology: Bar Graphs and Pie Charts in Excel
Using Technology: Fine Charts and Histograms in Excel
Graphics in the Media
Correlation and Causality
Using Technology: Scatter Diagrams in Excel
Putting Statistics to Work
Activity Bankrupting the Auto Companies
Characterizing Data
Using Technology: Mean, Median, Mode in Excel
Measures of Variation
Using Technology: Standard Deviation in Excel
The Normal Distribution
Using Technology: Standard Scores in Excel
Using Technology: Normal Distribution Percentiles in Excel
Statistical Inference
Probability: Living with the Odds
Activity Lotteries
Fundamentals of Probability
A Brief Review: The Multiplication Principle
Combining Probabilities
The Law of Large Numbers
Assessing Risk
Counting and Probability
A Brief Review: Factorials
Using Technology: Factorials
Using Technology: Permutations
Using Technology: Combinations
PART FOUR Modeling
Exponential Astonishment
Activity Towers of Hanoi
Growth: Linear versus Exponential
Doubling Time and Half-Life
A Brief Review: Logarithms
Using Technology: Logarithms
Real Population Growth
Logarithmic Scales: Earthquakes, Sounds, and Acids
Modeling Our World
Activity Bald Eagle Recovery
Functions: The Building Blocks of Mathematical Models
A Brief Review: The Coordinate Plane
Linear Modeling
Using Technology: Graphing Functions
Exponential Modeling
A Brief Review: Algebra with Logarithms
Modeling with Geometry
Activity Eyes in the Sky
Fundamentals of Geometry
Problem Solving with Geometry
Fractal Geometry
PART FIVE Further Applications
Mathematics and the Arts
Activity Digital Music Files
Mathematics and Music
Perspective and Symmetry
Proportion and the Golden Ratio
Mathematics and Politics
625
Activity Congressional District Boundaries
Voting: Does the Majority Always Rule?
Theory of Voting
Apportionment: The House of Representatives and Beyond
Dividing the Political Pie
665
Credits
Answers | 677.169 | 1 |
Quick Links
4 — The Homework Book
Homework is a vital part of studentsí learning. Our Homework Book provides
homework for every Lesson, allowing students to extend their learning beyond
the classroom. All worksheets can be detached for ease of grading.
Key features of our Homework Book:
Each assignment reinforces the CA Math standard objective
Hints and tips to extend those from the textbook
Worked example in every sheet to provide additional reinforcement of teaching
Questions increase in difficulty to provide practice for all abilities
Extensive support for parents and suggestions for parental involvement | 677.169 | 1 |
Math Homework Answers
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Math Homework Answers GetMath answers Step by Step From Framing of Formulas to Expansions, Indices, Linear Equations to Factorization and Quadratic Equations you get all Math Homework Answers online using our well structured and wel thought out Math tutoring program. Students get not just the answer but answers step by step. Below is provided a demo example of getting math answers step by step from us: Example: Find out the area of a triangle, height 8 cm, base 6 cm. Answer: 242 cm Steps to follow: 1. Since, Area of a triangle formula = 1/2 x b x h (b = base, h = height) 2. Here, base = 6 cm and height = 8 cm 3. Therefore, the area of the given triangle = 1/2 x 6 cm x 8 cm 4. Math answer to the given problem = 242 cm This is a geometry example. Likewise get free answers to al your math problems. Now make your math easy with Tutorvista. | 677.169 | 1 |
Costs
Course Cost:
$175.00
Materials Cost:
None
Total Cost:
$175
Special Notes
State Course Code
02074AlgebraA graphing calculator is recommended, but not required. A graphing program (Gcalc) available throughout the course.
Description
This is comprehensive course featuring geometric terms and processes, logic and problem solving. Includes topics such as parallel line and planes, congruent triangles, inequalities and quadrilaterals. Various forms of proof are studied. Emphasis is placed upon reasoning and problem solving skills gained through study of similarity, areas, volumes, circles, and coordinate geometry.
This course has been specifically built with the credit recovery student in mind. The course content has been appropriately chunked into smaller topics to increase retention and expand opportunities for assessment. With each topic, diagnostic quizzes are presented to the student, allowing students to pass through areas of content that they have previously studied successfully. Post-topic quizzes are presented with each topic of content. Audio readings are included with every portion of content, allowing auditory learners the opportunity to engage with the course. Test pools and randomized test questions are utilized in pre- and post-topic quizzes as well as unit exams, ensuring that students taking the course will not be presented with the same exams. | 677.169 | 1 |
Question 4379
The Codes for Math Differ depending on what school you go to, the course should have a course desciption, if not you need to ask a guidance person or a math teacher at the school, Math 111 does not "mean" anything in the world of mathematics in general | 677.169 | 1 |
Advanced Placement Program* Summer Institute
AP* Calculus AB, July 22-25, 2013
Lead Consultant: Candace Smalley
What to Bring
A graphing calculator
Experienced teachers should bring an AP* level activity to share with participants
Course Description
This session is specifically designed to help interested teachers build a successful AP* Calculus AB course. The week will include an analysis of the current curriculum, including an examination and discussion of various teaching strategies that reflect the current philosophy and goals of the course. Included will be an overview of the AP* program; suggestions for pacing and sequencing of concepts; a study of numerous AP* level problems; activities with graphing calculators (including CAS systems); a review of the AP* Exam including format, scoring standards and student responses; a discussion of the grading process from the perspective of an AP* Table Leader; and an overview of available resources and materials for AP* teachers.
About Candace Smalley
Candace Smalley currently teaches mathematics at Trinity Valley School in Fort Worth, TX after retiring from her teaching position in Oklahoma where she taught for twenty-two years. In Oklahoma, she taught the AP* Calculus AB course since 1995 and the AP* Calculus BC course since its inception in the district in 2000. At Trinity Valley School she currently teaches Calculus, AP* Calculus AB and an Advanced Calculus/AP* Calculus BC class.
Candace has served as a College Board Consultant since 1998 and is a table leader for the AP* Calculus exams. She has served on the College Board's Southwest Region Advisory Council and the Southwest Region Conference Planning Committee. She has been a presenter at many AP* Conferences including a recent workshop in Hong Kong, and lead instructor at numerous AP* summer institutes. Candace is a recipient of the College Board's Advanced Placement Special Recognition Award and also received recognition for her work with the AP* program as a Siemens Award for Advanced Placement winner.
2012 Participant Testimonials
"Wonderful workshop. Very informative. Great presenter."
"This course is excellent. The teacher did an outstanding job conducting this course. She did a great job integrating all the materials and using different resources."
"I especially loved learning how she teaches students and what she uses as her hooks!!"
* Advanced Placement Program and AP are registered trademarks of the College Board and have been used with permission. | 677.169 | 1 |
In this area we build the foundation of Algebra as we study the topic of Pre-Algebra. In this online math course, we will learn in detail about negative and positive numbers, exponents, order of operation, basic equations, and much more!
Section 1: Real Numbers and their Graphs
Section 2: The Number Line In this section, the concept of the number line is introduced and explained in detail. The concept of a negative number is illustrated by examples from everyday life and their relationship to positive numbers is shown on the number line. The student practices using the number line through numerous examples in this section, including basic addition and subtraction of integers. . . . View the lesson
Section 3: Greater Than, Less Than, Equal To In this section, the student learns how to properly use the greater than, less than, and equal to symbols in Pre-Algebra. Numerous problems illustrate how to compare positive or negative numbers with these symbols. The number line is used as a graphical reference to reinforce the concept. . . . View the lesson
Section 4: Adding Integers In this section, the student learns how to add two integers together and get the correct answer every time. Numerous examples of adding positive and negative numbers together are presented and by the end of the lesson the student will have memorized the simple rules for integer addition. The number line is also used to reinforce the concept. . . . View the lesson
Section 5: Subtracting Integers In this section, the student learns how to subtract two integers from one another and get the correct answer every time. Numerous examples of subtracting positive and negative numbers together are presented and by the end of the lesson the student will have memorized the simple rules for integer subtraction. The number line is also used to reinforce the concept. . . . View the lesson
Section 6: Multiplying Integers In this section, the student learns how to multiply two or more integers together. We begin the section by explaining the rules of integer multiplication. Next, we work numerous problems which give the student extra practice in multiplying negative and positive numbers together. . . . View the lesson
Section 7: Dividing Integers In this section, the student learns how to divide integers. We begin the section by explaining the rules of integer division. Next, we work numerous problems which give the student extra practice in dividing negative and positive numbers together. . . . View the lesson
Section 8: Powers and Exponents In this section, the student learns about the concept of an exponent and how it relates to pre-algebra. Numerous examples are provided to solidify this concept prior to moving on the the multiplication and division rule of terms that have exponents with the same base. . . . View the lesson
Section 9: Order of Operations In this section, the student learns about the concept of the order of operations in pre-algebra. This deals with understanding what order the student should perform calculations in an algebraic expression. . . . View the lesson
Section 10: Factors and Multiples In this section, the student learns how to calculate the factors of a number and the multiples of a number. These concepts will be central when we move into algebraic expressions later in this course. . . . View the lesson
Section 17: Adding Fractions In this section, the student will learn how to add fractions. We learn how to add regular fractions along with improper and mixed fractions and we learn to simplify the result. . . . View the lesson
Section 18: Subtracting Fractions In this section, the student will learn how to subtract fractions. We learn how to subtract regular fractions along with improper and mixed fractions and we learn to simplify the result. . . . View the lesson
Section 19: Multiplying Fractions In this section, the student will learn how to multiply fractions. We learn how to multiply regular fractions along with improper and mixed fractions and we learn to simplify the result. . . . View the lesson
Section 20: Dividing Fractions In this section, the student will learn how to divide fractions. We learn how to divide regular fractions along with improper and mixed fractions and we learn to simplify the result. . . . View the lesson | 677.169 | 1 |
The activities in the exponential functions unit are based upon students'
real life. If they just study the types of functions and don't relate their
knowledge in explaining things happening in their life, there is no meaning
of learning. In particular, the exponential functions can be a good model
for increasing or decreasing functions which are not linear functions. But
The activities in this exponential functions unit should follow after having
a firm knowledge of linear and quadratic functions and studying a general
idea of exponential functions. The examples which can show the forms of
the exponential functions are plentiful in life. So the activities will
be the combination of the real life based explorations and theoretical examinations
with technologies. Growth of an investment, price increases due to inflation,
interest owed while repaying loans, population growth, and radioactive decay
are some examples of them. This unit is composed of two-day activity . The
first day activity is answering some questions of a simple bank business
problem and its extensions. The second day activity is examining some exponential
functions with Algebra Xpressor. Students are supposed to be familiar with
the shapes of different exponential functions through the second day activity.
In addition, a logarithmic functions will be introduced by the concept of
reflection. This is to offer an informal concept of the logarithmic functions
for further study.
First Day Activity
Question 1 : Suppose that Christy borrows $3,000 at the begging
of every year from 1991 through 1996 at an annual interest rate of 10 %.
How much money does she have to pay back at the end of 1996?
Answer : Students will make a table. A graphic calculator or spreadsheet
can be used. A teacher is a
facilitator of this class and all activities are done by the students.
If a students use a TI-82 graphic calculator, then he obtains the following
( example 1 ).
3000*1.10 3300 1991
(Ans+3000)*1.10 6930 1992
10923 1993
15315.3 1994
20146.83 1995
25461.513 1996 ( TI-82 )
If a student use a spreadsheet, then she optains the following ( example
2 ).
In 1996, Christy owes $25,461.513. Since an algorithmic process is involved
in the process of calculation the teacher needs to check the process of
how the students can write "(Ans+3000)*1.10" in TI-82 and "
=(a2+3000)*1.1" in the spreadsheet.
(example 3) 3000+(3000*0.10)=3000*1.10 in 1992
(3000+(3000*0.10)) *0.10+3000+(3000*1.10) =3000*(1.10) in 1993 ...
That is to say, the process of example 3 should be understood by the
students.
Question 2 : Does Christy owe the same amount of money every five
years?
Answer : The students have already looked at their graphs and
the graphs showed that the money was not increased by the same amount. Therefore,
the answer would come up quickly. "No, she does not." But, the
answer could be difficult for some students without calculating the money
difference since the teacher was asked to find the money in 5 years and
the graph might look like a linear function. So the students are encouraged
to examine the money in 10 years or more. The spreadsheet work can be effective
in this case.
What are some of the characteristics of the graph? The students now can
apply their knowledge of the exponential functions to the graph when they
want to suggest things that will happen to the money in years 30, and 40?
Question 3 : Now, Christy wants to repay the loan including the
interest from 1997. Assume that she repays $3,000 at the beginning of every
year. In what year will Christy be free of debt?
In TI-82, (Ans-3000)*1.10 is used. The next data is obtained by the spreadsheet
(example 4).
Answer : As the students can show in the graph above, in 16 years
Christy is free of debt.
Question 4 : How about changing $3,000 into $1,000 or $2,000?
Examine each repayment process after loaning the money for 5 years.
Answer : The amount of money that Christy borrowed does not matter
in deciding the years that she needs to repay with the same rate. The students
have to find the answer through their activity with the spreadsheet or the
graphic calculator. But the use of spreadsheet is recommended (example 5).
Question 4 can cause another question. Then, what if the bank change
the rate from 10% into less than or greater than 10%? This question can
be raised naturally by the students. The teacher should derive the students
if they need a help.
Question 5 : Examine the cases of interest rate 9%, 12%, and 13%.
For the case of 9% interest rate, the students can make a conjecture
with it. The lower the interest rate is, the less the year is needed. But
for the case of the other two cases, they have to make each table and check
the results (example 6).
If Christy was 21 years old in 1991. She will be 60 years old when she
repays the money with 12% interest rate. For the case of 13% interest rate,
it is very interesting for the students to see the result.
Christy would not be free of debt even though she will be able to live
upto 100 years old. The graphs show the fact clearly (example 7).
The students have to understand the dynamic fact of their daily life
through the activity 1. The teacher gives a final wrap-up session for his
students. The students are given a homework set with a similar type of problem. | 677.169 | 1 |
Advanced suggestions for presenting these materials.
Over a period of time, I have developed a set of in-class assignments, homeworks, and lesson plans, that work for me and for other people who have tried them. If I give you the in-class assignments and the homeworks, but not the lesson plans, you only have ⅔ of the story; and it may not make sense without the other third. So instead, I am giving you everything: the in-class assignments and the homeworks (the Homework and Activities book), the detailed explanations of all the concepts (the Conceptual Explanations book), and the lesson plans (the Teacher's Guide). Once you read them over, you will know exactly what I have done.
This digital textbook was reviewed for its alignment with California content standards.
and the "Advanced Algebra II: Teacher's Guide" collections (coming soon) to make up the entire course.
Ahlan wa Sahlan: Functional Modern Standard Arabic for Intermediate Learners: Instructor's Handbook by Mahdi Alosh can be used by anyone who is an Arabic teacher or would like to become one, whether Ahlan wa Sahlan is used in the classroom or not. It includes tips on teaching from how to create the right kind of atmosphere in the classroom to specific drills used with Ahlan wa Sahlan. The example drills in the book can be generally applied to any language-learning textbook.
A work in progress, CK-12's Algebra I Second Edition is a clear presentation of algebra for the high school student. Topics include: Equations and Functions, Real Numbers, Equations of Lines, Solving Systems of Equations and Quadratic Equations.
Arabic complete is a website that offers Arabic Revisited, a free ebook that is a step-by-step guide complete with audio pictures available for Kindle, iPad, iPhone, iPod touch, Blackberry, and Android. The site further includes 80 podcasts, 7,000 audio recordings, and grammar lessons. Many of the lessons include a recorded dialogue that offers a transcription and translation of the dialogue. Classical Arabic, Modern Standard Arabic, and Egyptian dialect lessons are offered for students who are at an advanced and intermediate level.
This is a textbook for beginning Arabic language learning. The textbook is divided into twelve lessons. Each lesson focuses on an activity and common theme to introduce the basics of Arabic. Each lesson starts with a short video, which you'll be asked to watch. To help you understand the video, each lesson also includes a transcript (in English), a list of vocabulary (with audio clips), and language and grammar notes.
Several chapters of this beginning Arabic textbook are available for download and classroom or personal use. Arabic for Life takes an intensive, comprehensive approach to beginning Arabic instruction and is specifically tailored to the needs of talented and dedicated students. Arabic for Life is not specifically focused on either grammar or proficiency and, instead, offers a balanced methodology that combines these goals. Arabic for Life offers a dynamic and multidimensional view of the Arab world that incorporates language with Arabic culture and intellectual thought.Bassam Frangieh is professor of Arabic at Claremont-McKenna College. He previously taught at Georgetown, Yale, and the Foreign Service Institute. He is the author of Anthology of Arabic Literature, Culture, and Thought from Pre-Islamic Times to the Present, published by Yale University Press.
The site provides a common and free platform for any authors in Indonesia to publish and share their "scientific or educational textbooks" for free. It is a kind of SourceForge.net but for open textbooks | 677.169 | 1 |
The explosion of applications of linear dynamical systems over the past several decades makes the study of it both exciting and fundamental. Linear differential equations are now used in communications, economics and finance, mechanical and civil engineering, and many other fields.
This course offers an introduction to linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. The course will begin with a review of linear algebra, provide an overview of autonomous linear dynamic systems, and then explore systems with inputs and outputs as well as basic quadratic control and estimation. | 677.169 | 1 |
Lecture 26: Defining a plane in R3 with a point and normal vector
Embed
Lecture Details :
Determining the equation for a plane in R3 using a point on the plane and a normal vector
Course Description :
Matrices, vectors, vector spaces, transformations. Covers all topics in a first year college linear algebra course. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra. | 677.169 | 1 |
Last Updated:
Section:
This collection page contains all the GCSE resources from the Mathematics Enhancement Program (MEP) produced by CIMT. The resources are leveled, broken down into topic areas, and each topic area contains the following resources:
Pupil Practice Book
Activities
Lesson Plans
Mental Tests
Overhead slides
Revision Tests
Teaching Notes
Leveled Extra Exercises
Please Note: The MEP GCSE course is divided up into four ability levels: Standard, Academic, Express and Special.
Broadly speaking, Standard is equivalent to Foundation level, Academic are students who would have been entered for the old Intermediate tier and now would be borderline Foundation/Higher, Express is equivalent to Higher, and Special are Gifted and Talented mathematicians.
For a comprehensive breakdown of which particular parts of each unit need to be covered for each of these ability levels, please see the individual Teaching Notes files which have been uploaded with each unit | 677.169 | 1 |
"But why do I need math?" Now, using this series, give students a clear, definitive, and logical answer. Math is necessary to get the job done in most technical fields, including auto mechanics, electricity/electronics, and the building trades. Each video shows real-life problem situations solved by using practical math and actual computations on the screen. Use Introduction to Math in Technology as an overview and then progress to specific topics. At last...a program to help your students succeed in the world of technical math.Reading a Ruler: English and Metric Measurements In the first lesson, the different forms of English measurement are discussed and displayed as they would appear on a ruler. The viewer also learns how to understand fractions when measuring and how to find exact measurements using a ruler. The secon...(more details)
DVD
$79.95
DVD + 3-Year Streaming
$119.93
3-Year Streaming
$79.95
Area and Volume This video describes how to calculate the area of rectangles and other shapes-both geometrical and irregular-and how to determine the volume of a rectangular solid. Dramatized segments and computer animations focus on calculating lawn dimensions at a...(more details)
DVD
$69.95
DVD + 3-Year Streaming
$104.93
3-Year Streaming
$69.95
Surface Area and Volume Whether wallpapering a footlocker or filling a cylinder with corncobs, a knowledge of three-dimensional shapes is essential. This program demystifies the subjects of surface area and volume by sharing solid information backed up by the surface area f...(more details)
DVD
$99.95
DVD + 3-Year Streaming
$104.93
3-Year Streaming
$99.95
Measurement This video describes how to estimate costs of products and services, determine the circumference of an object and its effect on motion, and calculate area and volume. Dramatized segments and computer animations illustrate ways to use measurements tak...(more details)
DVD
$69.95
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Units, Perimeter, Circumference, and Area When it comes to measuring flat shapes, geometry generously provides a formula for every occasion. This program begins with an overview of how to convert English and metric units of measurement. Next, finding the perimeter of polygons is illustrated,...(more details) | 677.169 | 1 |
Guys, I am in need of aid on subtracting exponents, sum of cubes, angle-angle similarity and angle-angle similarity. Since I am a beginner to Remedial Algebra, I really want to understand the basics of Remedial Algebra fully. Can anyone suggest the best resource with which I can start reading the fundamental principles? I have a class test next week.
Hey brother. Let me tell you some thing, even mathematicians in this field sometimes are weak in a particular topic. Mathematics is such a vast subject, that it sometimes becomes impossible to excel every topic with equal ease. If you are facing problems with math slope worksheets, why don't you try Algebra Buster. This program has rescued many colleagues of mine and I have used it a couple of times as well. I was quiet happy with it.
Hello there. Algebra Buster is really amazing! It's been months since I tried this software and it worked like magic! Algebra problems that I used to spend answering for hours just take me 4-5 minutes to answer now. Just enter the problem in the program and it will take care of the solving and the best thing is that it shows the whole solution so you don't have to figure out how did the software come to that answer.
I am a regular user of Algebra Buster. It not only helps me complete my assignments faster, the detailed explanations offered makes understanding the concepts easier. I suggest using it to help improve problem solving skills.
It's right here: Buy it and try it, if you don't are not impressed with it (which is highly improbable) then they even have an unquestionable money back guarantee. Try using it and good luck with your assignment. | 677.169 | 1 |
Reading technical material does not come easily. It takes practice and dedication to get the most out of it, just as it does to get the most out of James Joyce or Toni Morrison. As time goes on, you should find it getting easier and easier. In the meanwhile, keep these suggestions in your book and re-read them frequently.
Expect reading to take time. You should spend as much time on your reading assignments as you do on your homework. Reading the text well will make class more meaningful and your homework easier. (Reading the text "well" does not mean understanding everything you've read.)
Pay attention to graphs and tables. Graphs and tables are part of the reading. Make sure that if the text refers to a table, you understand where the authors get their results from.
Read with pencil, paper, and calculator. Check all the authors' calculations.
If they ask you to do something, do it!!!! If you don't understand how they get from one sentence to the next, they probably left out some details. Try to figure them out!Don't write too much in your book, because it will become cluttered and hard to re-read or study from.
Try reading aloud. Sometimes, a sentence will make no sense to you. Often, you simply need to read it aloud.
Reflect. Periodically pause and reflect on what you've read. How does it fit together? How does it tie in with subjects we've discussed in the past? Why is it important?
Make a list of questions. As you're reading, on a separate sheet of paper, make a list of questions. Then go back and re-read, and try to figure out the answers to your questions.
Re-read each section. Math prose is not light reading, and you will need to re-read it to get the most out of it. It's also important to re-read each section after we discuss it in class, as well as before. You'll find that by doing this, you reach a much deeper understanding of the material. | 677.169 | 1 |
Technical Mathematics with Calculus, 6th Edition
This text is designed to provide a mathematically rigorous, comprehensive coverage of topics and applications, while still being accessible to students. Calter/Calter focuses on developing students' critical thinking skills as well as improving their proficiency in a broad range of technical math topics such as algebra, linear equations, functions, and integrals. Using abundant examples and graphics throughout the text, this edition provides several features to help students visualize problems and better understand the concepts. Calter/Calter has been praised for its real-life and engineering-oriented applications. The sixth edition of Technical Mathematics has added back in popular topics including statistics and line graphing in order to provide a comprehensive coverage of topics and applications—everything the technical student may need is included, with the emphasis always on clarity and practical applications. WileyPLUS, an online teaching and learning environment that integrates the entire digital text, will be available with this edition.
for Technical Mathematics with Calculus, 6th Edition. Learn more at WileyPLUS.com
Clarity of presentation: This is the feature most mentioned by reviewers, and has obvious benefits to students and instructors.
Technical Applications: The technical applications provide motivation for the student and examples for an instructor who may not have a technical background. Additionally, an Index to Applications aids in finding applications in a particular field, such as electrical technology.
Estimation: Shows a student whether an answer is reasonable or not reasonable. They show common pitfalls for both student and instructor and are flagged and boxed, wherever appropriate.
Formulas: Formulas used in the text are boxed and numbered, and listed in the Appendix as the Summary of Facts and Formulas.
Writing, Projects, Internet: Every chapter concludes with a section of optional enrichment activities. Many students are attracted to the magic and history of mathematics and welcome a guided introduction into this world. These writing questions aim to test and expand a student's knowledge of the material and perhaps explore areas outside of those covered in class while team projects foster "collaborative learning." | 677.169 | 1 |
Mrs. Valentine's Homework Page
Algebra/Math
A10 - Homework is a very important part of any math class.
The only way to learn math is to do math. When I collect papers
and correct them, I will leave comments on them to aid the students in
their learning. Encourage your child to look these notes
over. It is their job to learn from their errors and not repeat
them. I also use homework to determine if any re-teaching needs to
be done. If I find that a class is weak in a specific area, I will
re-teach that concept. On the same note, if I find no errors I
will know that we are ready to go on or be tested. I sometimes
find that students will not hand in papers that are not perfect if they
are struggling with it, trying to hide their weaknesses from me. This
is not a good idea; if I think that all is well, I will not
readdress issues that your child may need to have readdressed. In
math, much like life, we learn from our errors.
Math
12X - Homework will be assigned and opportunities
for getting help on errors will be during class time. This time is
very important and students should be sure to use the time to get their
problems straightened out. In college, professors seldom collect
homework. It is the student's responsibility to do the homework,
correct the homework and seek assistance when necessary. I am
hoping that using this format will help prepare your child for an easier
transition to the collegiate level. | 677.169 | 1 |
Pre-algebra
Topics include a review of whole numbers, fractions, and decimals, a complete development of percent, ratio/proportion, exponents, order of operations, integers, the use of variables, and simple equation solving. Course is graded on a pass/no pass basis. Prerequisites: Designated placement test score as shown on current indicator chart and RD20. A scientific calculator is required. Course does not transfer.
Fundamentals of Algebra I
Beginning algebra introduces the study and application of real numbers, operations with real numbers, exponents, order of operations with linear expressions, mathematical modeling, solving linear equations, methods of problem solving, slope, graphs of lines, equations of lines, and systems of linear equations. Working with real data, formulas, and applications will be stressed. Course is graded on a pass/no pass basis. Prerequisites: MTH20 and RD30 or designated placement test score as shown on current indicator chart. A scientific calculator is required. There is a significant online component in this class. Course does not transfer.
Applied Technical Math
Introduces the study and application of algebra topics and applications of real numbers in work-related settings for occupations requiring professional-technical training. The use of real numbers, exponents, number notation, manipulation of formulae, ratio, proportion, and percentage applications for calculating and solving various situational applications for rates of change, slope, proportional relationships and unit analysis will be emphasized. Course is graded on a pass/no pass basis. Prerequisites: MTH20 and RD30 or designated placement test score as shown on current indicator chart. A scientific calculator is required, and there is a significant online component in this class. Course does not transfer.
Fundamentals of Algebra II
Includes the study and application of exponents, polynomials, factoring rational expressions and equations, and inequalities. Course is graded A through F. Prerequisites: MTH60 and RD30 or designated placement test score as shown on current indicator chart. A scientific calculator is acceptable, but a graphing calculator is recommended. There is a significant online component in this class. Course does not transfer.
Fundamentals of Algebra II Recitation
Designed for students needing additional help with MTH65. Course is optional. Includes the study and application of exponents, polynomials, factoring, and rational equations and functions. Graded on a pass/no pass basis. Prerequisites: Concurrent enrollment in MTH65. A scientific calculator is required. Course does not transfer.
Intermediate Algebra, Part I
Designed for students who need a slower pace for MTH95. Introduces the study and application of functions and radical expressions and equations. Course is graded A through F. Satisfactory completion of both MTH93 and MTH94 is equivalent to MTH95. Prerequisite: MTH65, Part II
Designed for students who need a slower pace for MTH95. Introduces the study and application of quadratic, exponential, and logarithmic expressions and functions. Course is graded A through F. Satisfactory completion of both MTH93 and MTH94 is equivalent to MTH95. Prerequisite: MTH93
Topics include the basics of functions and the study of applications of radical, rational, exponential, and logarithmic functions and equations. Course is graded A through F. Prerequisites: MTH65 and RD30 or designated placement test score as shown on current indicator chart. A graphing calculator is required (instructor will be using the TI-83 or TI-84 graphing calculator in class) and there is a significant online component in this class.
Intermediate Algebra Recitation
Designed for students needing additional help with MTH95. Course is optional. Includes review of MTH65 material, using a graphing calculator, and focuses on topics and concepts of particular difficulty presented in MTH95. Graded on a pass/no pass basis. Prerequisite: Concurrent enrollment in MTH95. A graphing calculator is required (instructor will be using the TI-83 or TI-84 graphing calculator in class). Course does not transfer.
Introduction to Contemporary Mathematics
Designed for liberal arts students. Includes the study and application of logic and reasoning, problem solving, set theory, geometry, probability, statistics, and math of finance. May also include number theory, systems of equations and inequalities, matrices and determinants, counting theory, and numeration systems. Prerequisite: MTH95. A scientific or graphing calculator is required (instructor will be using the TI-83 or TI-84 graphing calculator in class). There is a significant online component in this class.
College Algebra
Topics include graphing polynomials, rational and inverse functions, systems of equations, zeros of polynomials, exponential and logarithmic functions, and conic sectionsCollege Algebra Recitation
This is an optional course that can be taken concurrently with MTH111. Provides additional help with MTH111 concepts. Reviews MTH95 material and using the graphing calculator, and covers the topics and concepts of particular difficulty presented in MTH111. Prerequisites: MTH95 or appropriate placement test score and concurrent enrollment in MTH111.
Elementary Functions
Covers trigonometryElementary Functions Recitation
This is an optional course that can be taken concurrently with MTH112. Provides additional help with MTH112 concepts. Reviews MTH95 material and using the graphing calculator, and covers the topics and concepts of particular difficulty presented in MTH112. Graded on a pass/no pass basis. Prerequisites: MTH95 or appropriate placement test score and concurrent enrollment in MTH112.
Special Studies in Mathematics
Fundamentals of Elementary Math I II III w/Lab
Presents various topics in mathematics designed to create an understanding andProbability and Statistics w/Lab
Descriptive statistics covering the nature and presentation of data, measures of central tendency, probability and probability distributions (normal and binomial), confidence intervals, sample sizes, and tests of hypotheses. Course is graded A through F. Prerequisites: MTH95 and RD30 or designated placement test score as shown on current indicator chart; a graphing calculator is required (instructor will be using the TI-83 or TI-84 graphing calculator in class). There is a significant online component in this class.
Inferential Statistics
Covers inferential statistics with an emphasis on applications. Topics include: review of estimation, hypothesis testing, correlation and regression, inferences using Chi-square, the F distribution, and one-way and two-way ANOVA. Course is graded A through F. Dual numbered as BA282. Prerequisites: MTH243; a graphing calculator is required (instructor will be using the TI-83 or TI-84 graphing calculator in class); and CS125ss (one-credit version) highly recommended. There is a significant online component in this class.
Calculus I (Differential) w/Lab
Topics include limits, the derivative, and applications. Course is graded A through F. Prerequisites: MTH111 and MTH112 or designated placement test score as shown on current indicator chart. A computer lab is required. A graphing calculator is also required (the TI-83, TI-84, TI-89 or TI-92 graphing calculators are recommended) There is a significant online component in this class.
Calculus II (Integral) w/Lab
Topics include techniques of integration and applications and transcendental functions. Course is graded A through F. Prerequisites: MTH251Calculus III w/Lab
Topics include infinite series, polar coordinates, conics, parametric equations, and introduction to vectors. Course is graded A through F. Prerequisites: MTH252Vector Calculus w/Lab
Topics include integration and differentiation of multivariable functions and vector calculus. Course is graded A through F. Prerequisites: MTH253Differential Equations w/Lab
First course in ordinary differential equations for science, mathematics, and engineering students. Includes first order differential equations, linear second order differential equations, and higher order linear differential equa-tions, with applications. Additional topics include Laplace transforms, series solutions of linear differential equa-tions, and systems of differential equations, with applications. A computer lab is required. Prerequisite: MTH253 or instructor approval. A graphing calculator is also required (the TI-83, TI-84, TI-89 or TI-92 graphing calculators are recommended).
Linear Algebra w/Lab
Topics include line vectors, n-tuples, algebra of matrices, vector spaces, and linear transformations. Offered on demand only. Course is graded A through F. Prerequisite: MTH252. A computer lab is required. A graphing calculator is also required (the TI-83, TI-84, TI-89 or TI-92 graphing calculators are recommended).
Cooperative Work Experience/Mathematics | 677.169 | 1 |
Originally Broadcast 8/28/09Running Time: 21 min Part 1: Introductions, Goals and Overview
First day of the statewide Algebra for All train the trainers event developed by the Michigan Mathematics and Science Centers Network in order to improve math skill among Michigan students.
This segment (1 of 9) focuses on Introductions and orientation to the course. PowerPoint review of course content and participant expectations. | 677.169 | 1 |
More About
This Textbook
Overview
The long-awaited second edition of Norman Bigg's best-selling Discrete Mathematics, includes new chapters on statements and proof, logical framework, natural numbers, and the integers, in addition to updated chapters from the previous edition. Carefully structured, coherent and comprehensive, each chapter contains tailored exercises and solutions to selected questions, and miscellaneous exercises are presented throughout. This is an invaluable text for students seeking a clear introduction to discrete mathematics, graph theory, combinatorics, number theory and abstract algebra | 677.169 | 1 |
The Algebra Buster could replace teachers, sometime in the future. It is more detailed and more patient than my current math teacher. I, personally, understand algebra better. Thank you for creating it! C.B., Iowa
My daughter is in 10th grade and son is in 7th grade. I used to spend hours teaching them arithmetic, equations and algebraic expressions. Then I bought this software. Now this algebra tutor teaches my children and they are improving at a better pace. Malcolm D McKinnon, TX Candice Murrey, OR09-06 :
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Introductory Algebra - 2nd edition
ISBN13:978-0077281120 ISBN10: 0077281128 This edition has also been released as: ISBN13: 978-0073406091 ISBN10: 0073406090
Summary: Introductory Algebraoffers a refreshing approach to the traditional content of the course. Presented in worktext format,Introductory Algebrafocuses on solving equations and inequalities, graphing, polynomials, factoring, rational expressions, and radicals. Other topics include quadratic equations and an introduction to functions and complex numbers. The text reflects the compassion and insight of its experienced author team with features developed to address the specific needs of dev...show moreelopmental level students. ...show less
2nd Edition Paperback slight water damage, still very good book, may have wear and/or considerable writing, ships fast!!!, textbook only unless specified previously
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Still wrapped, some shelf wear WN-10
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BookCellar-NH Nashua, NH
0077281128 | 677.169 | 1 |
Prealgebra - With Cd (paper) - 5th edition 5eis appropriate for a 1-sem course in Prealgebra, and was written to help students effectively make the transition from arithmetic to algebra. To reach this goal, Martin-Gay introduces algebraic concepts early and repeats them as she treats traditional arithm...show moreetic topics, thus laying the groundwork for the next algebra course your students will take. ...show less21 +$3.99 s/h
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SellBackYourBook Aurora, IL
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The course presents to students knowledge on basic numerical methods:
matrix operations, solving systems of linear algebraic equations and regression. Another part of the lecture deals with polynomial interpolation and solution of one-dimensional nonlinear equations.
After successful passing of the course the students should be able to
- list and describe basic numerical methods lectured
- successfully apply these methods for solving a specified problem.
Syllabus
1) Number representation in a computer,precision, accuracy.
Errors in numerical algorithms,
propagation of the errors.
Stability of the algorthims.
Ill-posed methods. | 677.169 | 1 |
Specification
Aims
The programme unit aims to discuss ordinary differential equations with applications to physical situations using Matlab to illustrate some of the ideas and methods.
Brief Description of the unit
The unit will be in 3, approximately 11 lecture sections. The first part on first order ordinary differential equations; the second part on motion in space; and the final part on second order ordinary differential equations.
Learning Outcomes
On completion of this unit successful students will be able to solve first order and second order linear problems and first order separable equations analytically. Use substitution methods and power series methods to find solutions. Be able to investigate solutions using direction fields and Euler's method. Have used Matlab as a mathematical tool and used differential equations to solve problems in mechanics and other applications. | 677.169 | 1 |
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