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Mathematics
The Mathematics Division is committed to offering courses that allow students to satisfy and exceed school and state graduation requirements, as well as to build a rich understanding and appreciation of mathematics. Because math is vital to the development of thinking and questioning minds, the division offers opportunities for all students to discover and appreciate mathematical ideas. There are classes available to students of all abilities and grades, as well as opportunities to advance within the math sequence. Mathematics is vital to students leaving high school to enter college, the work force, or any future aspirations. Courses range from algebra through calculus, with statistics and computer science as additional options. The Mathematics Division wants to help students to stretch to their fullest potential, so that they can become independent learners, adept at using technology, and be comfortable in future mathematical endeavors.
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Description
This text prepares students for future courses that use analytic ideas, such as real and complex analysis, partial and ordinary differential equations, numerical analysis, fluid mechanics, and differential geometry. This book is designed to challenge advanced students while encouraging and helping weaker students. Offering readability, practicality and flexibility, Wade presents fundamental theorems and ideas from a practical viewpoint, showing students the motivation behind the mathematics and enabling them to construct their own proofs. CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Table of Contents
Preface
PartI. ONE-DIMENSIONAL THEORY
1. The Real Number System
1.1 Introduction
1.2 Ordered field axioms
1.3 Completeness Axiom
1.4 Mathematical Induction
1.5 Inverse functions and images
1.6 Countable and uncountable sets
2. Sequences in R
2.1 Limits of sequences
2.2 Limit theorems
2.3 Bolzano-Weierstrass Theorem
2.4 Cauchy sequences
*2.5 Limits supremum and infimum
3. Continuity on R
3.1 Two-sided limits
3.2 One-sided limits and limits at infinity
3.3 Continuity
3.4 Uniform continuity
4. Differentiability on R
4.1 The derivative
4.2 Differentiability theorems
4.3 The Mean Value Theorem
4.4 Taylor's Theorem and l'Hôpital's Rule
4.5 Inverse function theorems
5 Integrability on R
5.1 The Riemann integral
5.2 Riemann sums
5.3 The Fundamental Theorem of Calculus
5.4 Improper Riemann integration
*5.5 Functions of bounded variation
*5.6 Convex functions
6. Infinite Series of Real Numbers
6.1 Introduction
6.2 Series with nonnegative terms
6.3 Absolute convergence
6.4 Alternating series
*6.5 Estimation of series
*6.6 Additional tests
7. Infinite Series of Functions
7.1 Uniform convergence of sequences
7.2 Uniform convergence of series
7.3 Power series
7.4 Analytic functions
*7.5 Applications
Part II. MULTIDIMENSIONAL THEORY
8. Euclidean Spaces
8.1 Algebraic structure
8.2 Planes and linear transformations
8.3 Topology of Rn
8.4 Interior, closure, boundary
9. Convergence in Rn
9.1 Limits of sequences
9.2 Heine-Borel Theorem
9.3 Limits of functions
9.4 Continuous functions
*9.5 Compact sets
*9.6 Applications
10. Metric Spaces
10.1 Introduction
10.2 Limits of functions
10.3 Interior, closure, boundary
10.4 Compact sets
10.5 Connected sets
10.6 Continuous functions
10.7 Stone-Weierstrass Theorem
11. Differentiability on Rn
11.1 Partial derivatives and partial integrals
11.2 The definition of differentiability
11.3 Derivatives, differentials, and tangent planes
11.4 The Chain Rule
11.5 The Mean Value Theorem and Taylor's Formula
11.6 The Inverse Function Theorem
*11.7 Optimization
12. Integration on Rn
12.1 Jordan regions
12.2 Riemann integration on Jordan regions
12.3 Iterated integrals
12.4 Change of variables
*12.5 Partitions of unity
*12.6 The gamma function and volume
13. Fundamental Theorems of Vector Calculus
13.1 Curves
13.2 Oriented curves
13.3 Surfaces
13.4 Oriented surfaces
13.5 Theorems of Green and Gauss
13.6 Stokes's Theorem
*14. Fourier Series
*14.1 Introduction
*14.2 Summability of Fourier series
*14.3 Growth of Fourier coefficients
*14.4 Convergence of Fourier series
*14.5 Uniqueness
Appendices
A. Algebraic laws
B. Trigonometry
C. Matrices and determinants
D. Quadric surfaces
E. Vector calculus and physics
F. Equivalence relations
References
Answers and Hints to Exercises
Subject Index
Symbol Index
*Enrichment section
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Touch it - Easy-glide Touchpad operates like a computer with a mouse.
Graph it - The new Scratchpad on the enhanced Home screen allows you to quickly perform calculations and graphs without saving your work.
See it - Split screen allows you to see a math problem in different ways - a graph, equation, table, geometric figure or text.
The student software enables your home computer to function just like the handheld graphing calculator. So you can use the larger screen to easily create, edit and transfer TI-Nspire documents between computer and handheld.
Recharge it - Even though four AAA alkaline batteries are included, you can also choose to purchase the TI-Nspire Rechargeable Battery (sold separately) for extended battery life. It easily charges with the wall adapter that is included in its package, or you can use a USB c...
Features: Mode menu
The menu is structured for easy, intuitive access to commands. Select degrees/radians, floating/fix, Classic/MathPrint or number format.
Memory variables
Store real numbers and expressions that result in real numbers as one of seven available memory variables.
Data list editor
Enter statistical data in up to three lists, with a maximum of 42 items per list. Any list formulas that are entered can accept all calculator functions. Readily perform one- and two-variable analysis, and display six different regression models.
Solvers
Choose from three solvers to use: numeric equation, polynomial and system of linear equations.
Function Table
Display a defined function in a tabular form.
Derivative & Integral
Determine the numeric derivative and integral for real functions.
Vectors & Matrices
Perform vectors...
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If you are having difficulty with algebra, these pages may be of some
help because they offer different sorts of explanations, in some sense
more "psychologically complete", than are usually found in algebra texts.
It is my belief that the way algebra is typically
presented to students leaves out some ideas and explanations that are helpful,
even sometimes necessary, for them to be able to do algebra well and to
have a "feel" for it.
There are at least three different kinds of things
taught in algebra courses: (1) language conventions, (2) logical numerical
manipulations using those conventions, and (3) deducing answers to problems
by using the conventions and the logical manipulations of them. I
will explain as I go. But it is important for students to keep in mind
whether in a given lesson they are supposed to be learning a convention,
a manipulation, or a way of solving problems by using conventions and manipulations.
It is also my belief that school "culture"
is such that, even contrary to good teachers' warnings, students will often
think they are simply supposed to memorize formulas and recipes in math,
rather than (also) understand them. Such memorization becomes a problem
in courses, such as algebra, where understanding is at least as important
as specific knowledge.
This is a two-fold problem. (1) Teachers need
to try to give useful and helpful explanations -- and they need to be aware
of as many typical student misunderstandings and confusions as they can;
and teachers need to constantly try to monitor students for confusion and
misunderstandings about what has been presented; waiting until there are
test results is often too late. But also, (2) students need to know that
THEY are the ones who will have to ultimately make the material make sense
to them, and that they need to keep trying until it does. They may have
to consult others, find a different book, or just sit down and think about
the material, if they cannot understand their teacher's explanation about
some aspect of algebra or other. There is simply no guaranty that any particular
explanation will provide automatic understanding. Understanding requires
reflective thinking of one's own. Explanations often are only a help to
such thinking; and what serves as a great explanation for one student may
not be helpful at all to another.
(My own first difficulty in "pre"-algebra was not understanding what
letters such as "x" had to do with anything, and why letters were chosen
to represent quantities at all, or how you worked with them when you had
them. I vividly remember when the light dawned on me about this
particular lack of understanding, in part because I still do not know why
or how the teacher's particular explanation "worked" on me. She was
saying that doing algebra was like unwrapping a package in the reverse
way it was wrapped to begin with. It may be that I figured out what I needed
to know while she was talking instead of because of what
she specifically said, or it may be that what she said had some sort of
meaning to me subconsciously somehow. I don't know, since "unwrapping"
is not the way I see (or even then saw) algebra. But what follows are explanations
of the sort that seem to me the most meaningful about some aspects of algebra
many students typically have trouble with. Further explanations of
other aspects of algebra can be found at A
supplemental introduction to the first chapter of an algebra book and
at Rate, Time Problems.)
The following question was asked on the Math-Help forum. It is typical
of the kinds of problems had by students who don't really understand in
general "what is going on" in algebra -- why you do certain manipulations
of formulas, or how you choose which manipulations to do. Particular algebraic
manipulations do not make sense to them because they don't have a general
sense of what algebra is about, or what the point of the manipulations
is. After I give the response to this question, a response which will include
both general and specific problem-solving ideas, I will make come comments
about how a typical algebra course is structured, and why it is structured
that way.
I have a big exam Monday in algebra and I have
no idea how to do linear equations! Can someone please help quick? Her
are examples of a few that I am having problems with. 3(3 - 4x) + 30=5x - 2(6x-7) and 5x²-[2(2x²+3)]-3=x²-9
I am also having a few problems with this:
x + 3 + 2x = 5 + x + 8 (5) I am supposed to figure out if 5 is the answer,
and tell how I got the answer.
My response: It looks to me from this last problem that you perhaps don't have an
UNDERSTANDING of what doing algebra with equations is all about, which
makes doing any problems a bit difficult. But let's see what we can do
for you here. The following may be too much for you to absorb before your
test, though I hope not; but I think it is stuff you will need to know
for future tests as well, so maybe it will help you for them even if it
is too much for tomorrow's test.
Take the last problem first. Do you understand that if "five is the
answer," that simply means that IF YOU WERE TO SUBSTITUTE 5 AS THE VALUE
EVERYWHERE THERE IS AN X, THE STATEMENT THAT THE LEFT SIDE OF THE EQUATION
EQUALS THE RIGHT SIDE WOULD BE TRUE? If 5 is NOT the solution, then when
you make the substitution, the statement will not be true that the left
side of the equation is equal to the right side.
Take a simple case first: X = 27 - 4 There is only one number X can be for this statement to be true; 23,
right? So 19 would NOT be a solution to this equation; that is, X cannot
equal 19 and the statement still be true that the left side equals the
right side.
Now make it just a bit harder: X + 3 = 27 -
4 There is still only one number this can work for but it is a different
number, because now we know that it is not X that equals 23, but some number
that, when you add 3 to it, gives you 23. So what number gives you 23 when
you add 3 to it? 20, right? That means X must be 20 in that equation.
It gets a little harder when you start putting X's on both sides of
the equations and add or subtract some multiplications and divisions, etc.,
but the idea of what is going on is the same.
So if we look at the equation you gave last: if X does equal 5 in the
equation x + 3 + 2x = 5 + x + 8, then
that would mean
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Dedicated to all things science, math, and teaching!
Getting Started Assignments
While most students quickly understand how to enter their answers in WebAssign, it nevertheless improves their confidence to provide access to a simple "Getting Started" assignment that walks them through different question types.
So, just in time for the start of a new semester, WebAssign now offers a collection of "Getting Started" questions as a way to introduce your students to our system. We currently offer questions for 3 different disciplines: Developmental Math, Calculus, and Physics. When creating your courses for the fall, be sure to select the Additional Resource called "Getting Started with WebAssign" to be able to quickly create your own "Getting Started" assignment from our bank of pre-coded questions.
Or, if you've already created your courses, we have a super easy shortcut for you! Simply search for one of the the assignment ID numbers given in parentheses below to quickly access and schedule a pre-made Getting Started assignment. To read more about scheduling, please refer to our Instructor Support.
Getting Started with WebAssign – Mathematics (2609125)
Getting Started with WebAssign – Calculus (2609188)
Getting Started with WebAssign – Physics (2609189)
The questions in these assignments are designed especially to coincide with the types of questions that are available in the textbook that you have selected for your class. These assignments are not intended to evaluate the students' knowledge of the subject matter, but we recommend they be used at the start of the term to gently introduce students to the WebAssign experience. They utilize several great assignment features, such as Answer Format Tips, Hints and Feedback, and numerous submission attempts to allow for greater student exploration.
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The textbooks are free to read online and on mobile phones or you can order a hardcopy through us.
Why use the Siyavula textbooks?
•The curriculum broken down and delivered in an easy-to-get format
•Step-by-step guides to help you make sense of formulas and concepts.
•Explaining the definitions covered in the South African curriculum in basic terms
•A wide range of worked examples that will help you practice your skill and craft your thinking
•This textbook is free to read online and on mobile
Intelligent practice
A new online practice service which allows learners to practice the types of questions they may find in their tests and exams. This practice service is well integrated with the Siyavula textbooks and work together to ensure learners excel in Maths and Science. Learners are able to practice using their mobile phones or computers.
Why use the Siyavula practice?
•A multitude of exam style questions that covers the entire curriculum for grade 10, 11 and 12 Maths and Science.
•Intelligent practice allows learners to fill out final answer, rather than choose from multiple choice options.
•After answer is submitted, the full worked solution is given with all necessary steps and tips.
•Progress is monitored. A dashboard showing the learners frequency in practice and how well they are doing in the different chapters.
•Identify and improve on problem areas. The dashboard allows you to see specifically which areas you should be working on and which you have mastered
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epub shortcomings, mathematics
epub shortcomings, mathematics
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Geometry: Teaching About Shapes and Their Measures begins February 13, 2012.
Register today to take advantage of this opportunity.
Course registration remains open for the spring offerings of math/numeracy
online professional development courses from
**********************
Geometry: Teaching About Shapes and Their Measures
Adult basic education students need foundational geometry and measurement
skills not only to succeed in GED math, but also in the workplace. In this
course, you will explore key topics in geometry, such as area, perimeter,
and volume, and their importance in everyday life. You'll look at numerous
instructional activities for teaching about angles, spatial relationships,
similarity, and figure transformations on a coordinate graph system.
Course dates: February 13 to March 26, 2012
Full course description: download PDF
<
Registration link:
Course instructor: Barbara Goodridge
Course fee: $179.00
Data: Helping Students Interpret Statistical Representations
Data, or numerical information, can be described, represented, analyzed, and
interpreted in various ways for various purposes. This course looks at some
common uses (and misuses) of data. Learn about the measures of central
tendency statistics, graphs, and probability. Through the course readings,
activities, and discussions, you'll review basic concepts and explore
strategies for introducing and teaching these concepts to your adult
students.
Course dates: March 19 to April 30, 2012
Full course description: download PDF
<
Registration link:
Course instructor: Pam Meader
Course fee: $179.00
Algebra: Introducing Algebraic Reasoning
Research suggests that math topics, including algebra, should be taught at
all levels, not just when a student is ready for GED preparation. In this
course, you'll learn how to introduce algebraic reasoning to your students,
and you'll experiment with strategies for teaching numeric patterns,
relationships, and functions based on real-life situations. You'll also
explore strategies to help students model quantitative relationships using
graphs, tables, words, and equations.
Course dates: April 23 to June 4, 2012
Full course description: download PDF
<
Registration link:
Course instructor: Barbara Goodridge
Course fee: $179.00
Introduction to College Transition Math
Through the readings and activities in this course, you will reflect on your
own and your students' math backgrounds, examine and experience the college
placement test your students take, try out math activities and exercises you
can use in your classrooms, and explore the math knowledge and skills you
will want to present to your own college transition students.
Course Dates: February 27-April 23, 2012
Full Course Description:
Required Text: Unlatching the Gate: Helping Adult Students Learn Mathematics
by Katherine Safford-Ramus (Bloomington, IN: Xlibris Corporation, 2008),
ISBN 978-1-4363-5120-1. Allow at least two weeks for delivery.Bottom of Form
Course Instructor: Pat Fina
Estimated Completion Time: 24 hours/6 weeks
Course Fee: $249.00
Registration:
**********************
Group discounts available! Call (888) 528-2224 ext. 221 or email
prodev at proliteracy.org <mailto:%20prodev at proliteracy.org> for more
information.
Questions? Please e-mail prodev at proliteracy.org
<mailto:%20prodev at proliteracy.org>
ProfessionalStudiesAE.org is a partnership of World Education, Inc., and
ProLiteracy/New Readers Press. Visit
<
professionalstudiesae.org&srcid=4593&srctid=1&erid=443971>
for a complete listing of available courses.
**********************
See you online,
Kaye
Kaye Beall
Project Director
World Education
kaye_beall at worlded.org
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Algebra: A Complete Online Course from VideoText
Covers all the essential elements in
Pre-Algebra, Algebra 1, and Algebra 2
Can be completed in one year if a
student does 1 lesson each day, 5 days a week. Two years if your
student does 1 lesson every other day.
Lessons are
Only 5-10 minutes long
Taught using computer generated
graphics and animation.
Taught conceptually and for
mastery.
Students are
Never taught tricks, shortcuts,
rules or formulas.
Never asked to memorize
anything.
Rules and Formulas
Just show up once the student(s)
learn the how, where and why of the concept
This program teaches you the language
of math!!!
How does this online program
work?
To begin a lesson, the student is
told whether a quiz on a previous lesson is necessary.
If a quiz is necessary, the
instructor will give the student access to the appropriate online
quiz or test, by clicking on the appropriate test icon. As well,
the test may be printed out for the student.
The instructor will grade the
students test by clicking on the appropriate icon.
Watch the new Video Lesson
online.
Click on the prompt to automatically
bring up the appropriate Course Notes.
Click on the prompt to automatically
bring up the appropriate WorkText pages.
While viewing the exercises on the
screen, the student works on a separate sheet of paper.
Click on the prompt to automatically
bring up the appropriate Solutions Manual pages.
Click on the prompt to end the
lesson for the day.
($299 pricing reflects licensing for two
students. Add an additional student in your family's household for
$49. A student license will last three years from the date it is
activated for each student.)
FROM
VIDEOTEXT-
The reason that we named our program "Algebra: A Complete
Course," is that we believe the best way to learn Algebra is to
start at the beginning and end at the end! In this program you will
find a complete study of the essential material covered in a
traditional Algebra 1 and Algebra 2 course.
However, we need to continue a little further
with this answer because Algebra 1 and Algebra 2 are terms that
refer mostly to the traditional way that Algebra has been taught.
Traditional Algebra 1 classes attempt to cover most of Algebra in
the first year, but the methods that are used, and the speed with
which the material is covered, hinders student understanding
of the material. Instead, the student is just exposed to memorizing
rules, formulas, tricks, and shortcuts. By the time they get to
what is called an Algebra 2 course, (sometimes after they
take a Geometry course), they have forgotten almost all of the
Algebra that they memorized. So, that Algebra 2 course
(which is by definition, a rehash of whatever has been called
Algebra 1), must repeat practically all of the Algebra 1
course. In fact, it usually repeats a lot of the Pre-Algebra
material as well. This is usually referred to as the "spiral
method" of learning, and it is not very effective in
helping students to excel, especially at this level of
mathematics.
We think that this huge overlap is generally
unproductive, and largely unnecessary if the concepts are taught
analytically. Therefore we call our program "Algebra: A Complete
Course," because we employ a mastery-learning approach, sometimes
moving at a slower pace, but without the overlap. As a result,
students often complete the course even more quickly.
When a student
completesGeometry: A Complete
Course
along withAlgebra: A Complete
Course, the
publisher states that the student will gainfour mathcredits -
Algebra 1, Algebra 2, Honors Geometry and Pre-Calculus.
Once you purchase this course you will be contacted with the online
access information.
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OCR Mathematics for GCSE Specification B: Teacher Pack Unit 2
OCR Mathematics for GCSE Specification B - Unit 2 Teacher Pack has been published to support teachers of the OCR course. The resource has been written and edited by experienced examiners and authors, combining their teaching and examining expertise to deliver relevant and meaningful coverage of the course. Each teacher pack provides support for the complete coverage of each of the seven modules that make up Specification B. Students use the the combination of units best suited to their needs and the course is designed so that it can be tailored to the requirements of each student. The content also supports delivery of the revised Assessment Objectives - including Problem Solving. - Endorsed by OCR for use with Mathematics GCSE Specification B - Full teacher support notes for the topics and assessment objectives required by the course, including the teaching of AO3 Problem Solving and Quality of Written Communication - Answers to all of the questions and activities provided in the accompanying student books - Additional photocopiable Assessments and Revision Exercises (and associated answers) to use with students
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Math Made Visual
Claudi Alsina and Roger Nelsen
Is it possible to make mathematical drawings that help to understand mathematical ideas, proofs and arguments? The authors of this book are convinced that the answer is yes and the objective of this book is to show how some visualization techniques may be employed to produce pictures that have both mathematical and pedagogical interest.
Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece and India but only in the last thirty years has there been a growing interest in so-called "proofs without words". Hundreds of these have been publised in Mathematics Magazine and The College Mathematics Journal, as well as in other journals, books, and on the Internet.
Often times, a person encountering a "proof without words" may have the feeling that the pictures involved are the result of a serendipitous discovery or the consequence of an exceptional ingenuity on the part of the picture's creator. In this book the authors show that behind most of the pictures "proving" mathematical relations are some well-understood methods. As the reader shall see, a given mathematical idea or relation may have many different images that justify it, so that depending on the teaching level or the objectives for producing the pictures, one can choose the best alternative.
Print-on-Demand (POD) books are not returnable because they are printed at your request. Damaged books will, of course, be replaced (customer support information is on your receipt). Please note that all Print-on-Demand books are paperbound.
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Firefox Internet Explorer 7 Safari (Mac and PC)
Math instructors promoting calculator usage in college classrooms may want to rethink their teaching strategies, says Samuel King, postdoctoral student in the University of Pittsburgh's Learning Research & Development Center. King has proposed the need for further research regarding calculators' role in the classroom after conducting a limited study with undergraduate engineering students published in the British Journal of Educational Technology.
"We really can't assume that calculators are helping students," said King. "The goal is to understand the core concepts during the lecture. What we found is that use of calculators isn't necessarily helping in that regard."
Together with Carol Robinson, coauthor and director of the Mathematics Education Centre at Loughborough University in England, King examined whether the inherent characteristics of the mathematics questions presented to students facilitated a deep or surface approach to learning. Using a limited sample size, they interviewed 10 second-year undergraduate students enrolled in a competitive engineering program. The students were given a number of mathematical questions related to sine waves—a mathematical function that describes a smooth repetitive oscillation—and were allowed to use calculators to answer them. More than half of the students adopted the option of using the calculators to solve the problem.
"Instead of being able to accurately represent or visualize a sine wave, these students adopted a trial-and-error method by entering values into a calculator to determine which of the four answers provided was correct," said King. "It was apparent that the students who adopted this approach had limited understanding of the concept, as none of them attempted to sketch the sine wave after they worked out one or two values."
After completing the problems, the students were interviewed about their process. A student who had used a calculator noted that she struggled with the answer because she couldn't remember the "rules" regarding sine and it was "easier" to use a calculator. In contrast, a student who did not use a calculator was asked why someone might have a problem answering this question. The student said he didn't see a reason for a problem. However, he noted that one may have trouble visualizing a sine wave if he/she is told not to use a calculator.
"The limited evidence we collected about the largely procedural use of calculators as a substitute for the mathematical thinking presented indicates that there might be a need to rethink how and when calculators may be used in classes—especially at the undergraduate level," said King. "Are these tools really helping to prepare students or are the students using the tools as a way to bypass information that is difficult to understand? Our evidence suggests the latter, and we encourage more research be done in this area."
King also suggests that relevant research should be done investigating the correlation between how and why students use calculators to evaluate the types of learning approaches that students adopt toward problem solving in mathematics
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MATHEMATICS DEPARTMENT
Course Offerings
This course is designed for the advanced math
student who is preparing to take Honors Pre-Calculus or college mathematics.
Second year algebra topics will be reviewed and extended to include
Pre-calculus concepts. Students will leave this course with a strong
analytical foundation that will allow them to be successful in a Calculus or
Statistics course in either high school or college. This course may be used
to meet the UC/CSU "C" or "G" requirement.
Algebra 1-2 is a logical and systematic extension of generalized
arithmetic. Algebra 1-2 covers the four basic operations on
the real numbers, solutions of first and second degree
equations in one variable, factoring, rational expression,
solutions of inequalities, functions and relations, graphing
linear equations and inequalities, irrational numbers, and
the quadratic formula. Fundamental operations with algebraic
representations and related applications are studied. This
course may be used to meet the UC/CSU "C" requirement.
This course is a review and extension of first year algebra.
Topics include, but are not limited to,
the study of linear, quadratic, and higher-order functions; rational
functions; exponential & logarithmic functions; inequalities; matrices;
complex numbers; and, trigonometry. This course may be used to meet the
UC/CSU "C" requirement.
Length of course/credits: 2 Terms (Semester 1
& 2); 1st and 3rd quarters earn elective credit and 2nd and
4th quarters earn math credit. This is a second year algebra
course. Topics studied will be identical to the Algebra 3-4
course with extended class time for mastery. Topics include,
but are not limited to, the study of linear, quadratic, and
higher-order functions; rational functions; exponential &
logarithmic functions; inequalities; matrices; complex
numbers; and, trigonometry. This course may be used to
meet the UC/CSU "C" requirement.
This course is a college-level class for
students who have completed the equivalent of 4 years of
college preparatory mathematics. Students will receive
little or no review. Topics include derivatives,
differentials, integrations, and applications. Many problems
are atypical and require students to synthesize new
solutions. A graphing calculator is required. The course is
designed to prepare students to take the Advanced Placement
Exam for Calculus AB. This course may be used to meet the
UC/CSU "C" or "G" requirement. UC approved for extra honors
credit (A=5, B=4, C=3).
In Trigonometry, the topics covered include special triangles,
the unit circle, using the graphing calculator, proving
trigonometric identities, solving equations, solving
triangles, angular velocity, and the laws of sines and cosines. This course may be used to meet
the UC/CSU "C" or "G" requirement. Statistics is a college preparatory
course which will introduce students to the major concepts and tools for
collecting, analyzing, and drawing conclusions from data. Probability and
counting methods are included. Students will apply descriptive statistics to
a wide range of disciplines. This course may be used to meet the UC/CSU "C"
or "G" requirement.
This course is designed to build upon the fundamentals of computer
programming. The emphasis is on object-oriented programming
methodology, problem solving and algorithm development, and
is equivalent to a first-semester college course in Computer
Science. Topics include arrays, recursion, inheritance,
sorting and searching algorithms, and a case study of a
complex program. This course may be eligible for
college credit if the student enrolls at the appropriate
college while attending the Westview class and receives a grade of A or B all four
quarters of the year-long course. Click here to learn more about the
program. This course meets the UC/CSU "G"
requirement and the District's Computer Literacy requirement. UC approved
for extra honors credit (A=5, B=4, C=3).
The
multidisciplinary aspects and applications of statistics
make it one of the most rewarding classes to take. The study
blends the rigor, calculations, and deductive thinking of
mathematics, the real-world examples and problems of social
science, the decision-making needs of business and medicine,
and the laboratory methods and experimental procedures of
the natural sciences. This course is designed to prepare
students to take the Advanced Placement Exam for Statistics.
This course may be used to meet the UC/CSU "C" or "G"
requirement. UC approved for extra honors credit (A=5, B=4,
C=3).
This course is offered in the Fall semester, outside of the
regular 4 period day for 2.5 elective credits. It is
designed to help students review Calculus AB topics in
preparation for the AP Calculus BC course which is offered
in the Spring semester only.
This course follows AP Computer Science A. It covers a more
formal and in-depth study of algorithms, data structures,
design and abstraction. The topics include Big-O analysis,
exceptions, and advanced data structures (such as linked
lists, stacks, queues, trees, heaps, sets and maps). It is
equivalent to a second semester college course in Computer
Science. Students who enroll in this course need to also
enroll in AP Computer Science A 1-2. This course may be
eligible for college credit if the student enrolls at the
appropriate college while attending the Westview class and receives a grade of A or B all four quarters of the
year-long course. This course meets the UC/CSU "G" requirement and the
District's Computer Literacy requirement.
This is a second course in high school
mathematics with a main focus on Descriptive Geometry (two-
and three- dimensional geometry) and a minor emphasis in
geometric proofs and trigonometry. It is based on the
standards set by the State of California with a major
emphasis on measurements of two- and three-dimensional
figures, geometric constructions, Pythagorean applications,
special right triangles, rigid motions on geometric figures,
and coordinate geometry. This course is an integration
of high school geometry and Project Lead the Way curriculum
for Introduction to Engineering Design. The intent is to
integrate more geometry and/or teach geometry as a basis for
the course and use the project-based learning tools of
Introduction to Engineering Design as problem solving to
create a more in-depth learning experience for geometry
students. The focus of the course is depth of knowledge,
with less breadth than a standard geometry course. This
course may be used to meet the UC/CSU "C" math requirement.
This course teaches deductive reasoning and organized
thinking. Students study postulates, definitions, theorems
for use in formal proofs and use algebraic skills to solve
problems. Students study plane geometry and solid geometry.
Students also learn straightedge and compass constructions
and transformations. This course may be used to meet the
UC/CSU "C" requirement.
This course provides the foundation for students to proceed
on to Calculus. Reviews are done of trigonometry, geometry,
and algebra. The study of polynomials including synthetic
division, graphing theory, limits, and derivatives are
introduced. This course may be used to meet the UC/CSU "C"
or "G" requirement.
This course is designed to teach students the fundamentals
of computer programming. Topics covered include
variables and data types, methods, decision structures and
loops. The emphasis is on structured and
object-oriented programming methodology. This course
is linked with AP Computer Science A 1-2. This course
may be eligible for college credit if the student enrolls at
the appropriate college while attending the Westview class
and receives a grade of A or B all four quarters of the
year-long course. This course may be used to meet the
UC/CSU "G" requirement and the District's Computer Literacy
requirement.
This class is designed for the student who needs to master
computational skills such as fractions, decimals, and
percents. The main focus of this class is to help build the
foundational skills required to be successful in Algebra and
beyond. This course meets the PUSD math requirement.
This course is for students who have completed four years of
college preparatory math including Calculus AB. New topics
covered include parametric equations, vector functions,
indeterminate forms of limits, polar curves, advanced
integration techniques, infinite series, and Taylor
polynomials. This course prepares the student to take the
Advanced Placement Exam for Calculus BC. This course may be
used to meet the UC/CSU "C" or "G" requirement. UC approved
for extra honors credit (A=5, B=4, C=3).
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Meshoppen ACTAlgebra is the gateway discipline that opens the world of higher math to students---but that gate will remain closed if students miss the fundamentals of the subject. Giving kids the best chance to learn requires a plan and the patience to help each student understand. Algebra is one of the main branches of mathematics; it concerns the study of structure, relation and quantity
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Materials will be presented as
lesson plans that can be used in elementary and middle grades. Most
lessons will have a large "hands- on" component using projects and
technology, including the TI-108 and possibly TI-34 calculators.We will not use a text book;
we will use materials from Breaking Away from the Math Book:Creative Projects for Grades K-6 (2004), Breaking Away from
the Math Book II:More
Creative Projects for Grades K-8
(2004), and Breaking Away from the
Algebra and Geometry Book: Original and Traditional Lessons for Grades
K-8, by Dr. Patricia Baggett
and Andrzej Ehrenfeucht, as well as
extensive handouts and units on their website,
A course pack of materials is
available from Prof. Baggett for just the cost of the binder and
Xeroxing, $16.There are
no tests in the class!
This course intends to provide future K-8 (and higher) teachers
with adequate algebraic and geometric knowledge in a format that can
be directly used in their classrooms. We will combine algebra
with geometry based on measurement of distance, providing hands-on
activities suited even for the youngest students in kindergarten,
first, and second grade. Many lessons that we will study are
appropriate for middle school, and some can be adapted for high
school. We will use the TI-83/84, TI-34, and TI-108 calculators.
We will not use a text book; we will use materials from Breaking
Away from the Math Book: Creative Projects for Grades K-6 (2004),
Breaking Away from the Math Book II: More Creative Projects
for Grades K-8 (2004), and Breaking Away from the Algebra
and Geometry Book: Original and Traditional Lessons for Grades K-8, by
Dr. Patricia Baggett and Andrzej Ehrenfeucht, as well as extensive
handouts and units on their website,
A coursepack of materials is available from Prof. Baggett for just the
cost of the binder and Xeroxing, $17.00. There are no tests in
the class! Many lessons have been used in workshops, and
most have been classroom tested. We hope that you will find some of
them suitable to try with students in your future classes.
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approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in the general setting of normed linear spaces and inner product spaces; best uniform polynomial approximation; orthogonal polynomials; Newton-Cotes , Gauss and Clenshaw-Curtis quadrature; the Euler-Maclaurin formula; approximation of periodic functions; the uniform convergence of Fourier series; spline approximation,with an extensive treatment of local spline interpolation,and its application in quadrature. Exercises are provided at the end of each chapter less
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Overview
Main description
Tough Test Questions? Missed Lectures? Not Enough Time?
Fortunately for you, there's Schaum's.
problems, and practice exercises to test your skills.
This Schaum's Outline gives you
1,600 fully solved problems
Complete review of all course fundamentals
Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time--and get your best test scores!
Table of contents
Schaum's Outline of College Mathematics, 4ed Elements of Algebra Functions Graphs of Functions Linear Equations Simultaneous Linear Equations Quadratic Functions and Equations Inequalities Locus of an Equation The Straight Line Families of Straight Lines The Circle Arithmetic and Geometric Progressions Infinite Geometric Series Mathematical Induction The Binomial Theorem Permutations Combinations Probability Determinants of Order Two and Three Determinants of Order Systems of Linear Equations Introduction to Transformational Geometry Angles and Arc Length Trigonometric Functions of a General Angle Trigonometric Functions of an Acute Angle Reduction to Functions of Positive Acute Angles Graphs of the Trigonometric Functions Fundamental Trigonometric Relations and Identities Trigonometric Functions of Two Angles Sum, Difference, and Product Trigonometric Formulas Oblique Triangles Inverse Trigonometric Functions Trigonometric Equations Complex Numbers The Conic Sections Transformations of Coordinate Points in Space Simultaneous Quadratic Equations Logarithms Power, Exponential, and Logarithmic Curves Polynomial Equations, Rational Roots Irrational Roots of Polynomial Equations Graphs of Polynomials Parametric Equations The Derivative Differentiation of Algebraic Expressions Applications of Derivatives Integration Infinite Sequences Infinite Series Power Series Polar Coordinates Introduction to the Graphing Calculator The Number System of Algebra Mathematical Modeling
Author comments
The late Frank Ayres, Jr., Ph.D., was formerly a professor in and head of the Department of Mathematics at Dickinson College, Carlisle, Pennsylvania. He is the author or coauthor of eight Schaum's Outlines, including Calculus, Trigonometry, Differential Equations, and Modern Abstract Algebra.
Philip A. Schmidt, Ph.D., has a B.S. from Brooklyn College (with a major in mathematics), an M.A. in mathematics, and a Ph.D. in mathematics education from Syracuse University. He is currently the program coordinator in mathematics and science education at The Teachers College at Western Governors University in Salt Lake City, Utah.
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Number puzzles, spatial/visual puzzles, cryptograms, Sudoku, Kokuro, logic puzzles, and word games like Frame Games are all a great way to teach math and problem-solving skills to elementary and middle school studentsIn Meaningful Games, Robin Clark explains in an accessible manner the usefulness of game theory in thinking about a wide range of issues in linguistics. Clark argues that we use grammar strategically to signal our intended meanings: our choices as speaker are conditioned by what choices the hearer will make interpreting what we say. Game theory--according to which the outcome of a decision depends on the choices of others--provides a formal system that allows us to develop theories about the kind of decision making that is crucial to understanding linguistic behavior.
Well known for accuracy, Soo Tans APPLIED CALCULUS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES, Eighth Edition balances applications, pedagogy, and technology to provide students the context they need to stay motivated in the course and interested in the material. Accessible for majors and nonmajors alike, the text uses an intuitive approach that introduces abstract concepts through examples drawn from common, reallife experiences to which students can relate.
This course is primarily devoted to the fundamental principles of valuation. We will learn and apply the concepts of time value of money and risk to understand the major determinants of value creation. We will use both theory and real world examples to demonstrate how to value any asset.Mind Power Math - High School and College Math | 1.46 GB Genre: eLearningPseudo-random sequences are essential ingredients of every modern digital communication system including cellular telephones, GPS, secure internet transactions and satellite imagery. Each application requires pseudo-random sequences with specific statistical properties. This book describes the design, mathematical analysis and implementation of pseudo-random sequences, particularly those generated by shift registers and related architectures such as feedback-with-carry shift registers. The earlier chapters may be used as a textbook in an advanced undergraduate mathematics course or a graduate electrical engineering course; the more advanced chapters provide a reference work for researchers in the field. Background material from algebra, beginning with elementary group theory, is provided in an appendix.
The Oxford User's Guide to Mathematics in Science and Engineering represents a comprehensive handbook on mathematics. It covers a broad spectrum of mathematics including analysis, algebra, geometry, foundations of mathematics, calculus of variations and optimization, theory of probability and mathematical statistics, numerical mathematics and scientific computing, and history of mathematics
For Dummies is an extensive series of instructional/reference books which are intended to present non-intimidating guides for readers new to the various topics covered. Despite the title, their publisher has taken great pains to emphasize that the For Dummies books are not literally for dummies. The subtitle for every book is, "A Reference for the Rest of Us!". To date, over 1,600 For Dummies titles have been published. The series has been a worldwide success with editions in numerous other languages.The books are an example of a media franchise, consistently sporting a distinctive cover-usually yellow and black with a triangular-headed cartoon figure known as the "Dummies Man," and an informal, blackboard-style logo. Prose is simple and direct; bold icons, such as a piece of string tied around an index finger, are placed in the margin to indicate particularly important passages. review. Annotated printouts from SPSS and SAS indicate what the numbers mean and encourage interpretation of the results. In addition to demonstrating how to use these packages, the author stresses the importance of checking the data, assessing the assumptions, and ensuring adequate sample size by providing guidelines so that the results can be generalized. The book is noted for its extensive applied coverage of MANOVA, its emphasis on statistical power, and numerous exercises including answers to half.
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Studying
The Mathematics Degree Programme provides a general picture on mathematics and its applications as well as a detailed picture on some of the branches of mathematics.
Mathematics is characterized by its conceptuality and exactness. It is considered a hard subject and needs hard work. On the other hand, talented students will find the studies both interesting and challenging. The most important aspect is not to learn things by heart but, rather, to understand and absorb the way of thinking, solving and proving in mathematics.
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Perfect Circle 83+ After you input both the center and radius, this program displays the equation of a circle and puts it into Y1/Y2. It resets the window and scale so that the circle actually looks like a circle, but it you want to set your own window, you can always use the equations put into "Y=". Uses some letter variables.
Mandelbrot Set This program draws the Mandelbrot Set on your calculator. Note: this program takes hours upon hours to draw because the algrithm is slow, but very accurate. Please use, study, and modify the program for your own needs. See the README for more information.
Change of Base For Logs This program will compute the change of base for logs, the user inputs the old base and the value to evaluate. After the output is displayed the calculator will pause so that the graph of log_a (x) can be displayed. Enjoy!
Parabola and Conics Calculator Enter a parabola with x^2 or y^2 term, and receive all of the information, such as focus, etc. As well, enter an equation in the forms ax^2+bx+cy^2+dy=e and the completing the square is done to simplify the equation.
Curve Fitting Calculates the polynomial of least degree that passes exactly through any number of data points (Lagrange interpolation). Coefficients are stored in list and matrix form for your mathematical convenience and pleasure.
curves * Area between curves This is a nifty little program to enhance the computational ability of your TI83 family calculator. I'm not sure about you, but my calculus teacher told me there was no way for my calculator to calculate the area between curves at the touch of a button. Well, these TI89's are off the chain but I've come up a with a nice little patch that lets our little beaut's perform just the same. ** Entering equations If both Y1 and Y2 are populated, curves will choose those two equations and find the area between them. If one or more are blank, you will be prompted for both. *** Change your mind? Press `Y=' during calculations to change the equations, or `TRACE' (window) to change the domain in which intersections are calculated. ** Caveats I wasn't in class long enough to make this program sophisticated enough to comprehend vertical bounds, or know how to react if only one equation was within range of the window. This program will function just fine if you can see everything of interest on the graph, so just use those settings and let this do its magic. ** Output After calculation, the totaled area will be shaded, the final answer stored to Ans, and a message will be printed on the screen.
Grapher v1.0 for Doors CS This handy program lets you graph an equation or expression without leaving Doors CS. You can graph in the form Y=, view the resulting equation, and use it for math purposes. Check it out!
Dragon Curve Fractal Generator This is the first file I upload. I don't know if it is, but it sounds easier then the other program here what is doing the same. The program is also drawing the Dragon Curve Fractal (a.k.a. Jurassic Park Fractal). Read the README file for more information. (The screenshots are not the nicest you can make)
Dragon Curve Fractal Drawer If you've ever read "Jurassic Park", then you'll know what the Dragon Curve fractal is. This is a program that prompts the user for the number of iterations to draw and then it generates a code and draws it on the graph screen. It can draw up to a maximum of 8 iterations. Great for exploring fractal iterations. Please read important documentation.
Dynamic Recursive Fractal Generator v1.2 Dynamic Recursive Fractal Generator v1.2 (DRFG v1.2) is an advanced program for z80 calculators meant to produce arbitrarily-recursive fractals. The program lets you choose the coefficient of fractalization, hence the dynamic nature of the program. The efficient built-in recursive fuction allows for infinite recursion, limited by the memory on most calcs to about 300 recursive steps. Doors CS v5.0 optimized.
Dynometer 3.0 This program is a dynometer calculator. It's purpose is to change the torque or horsepower inputed, and output the other, then to graph it! It can (with minor tweaking) calculate 125, 250, and 500 RPM intervals. After you exit the program, I left the inputs and outputs for you to do as you please, as (list)FIR and (list)SEC.
EQGraph Table-based equation grapher. Very simple. it reads from table one, if there is a third column, that is Z (this may only work if you select the third option to run it) otherwise, all the same. X,Y,Z vars can be accessed, with the normal run option, Y-col [A](*,2) is overwritten. This program uses nearly every available variable in the calc. after it finishes, it will clean up. these vars include [A] letter vars A~Z L1, L2 Str0~Str9 and theta. All written by me. If you wish to redistribute, credit me. re-code distribs also need to credit me. I spent around a month on this. by hand.
EZ Graph - Gives nice plottable points EZGraph is a program that will take your equation and look for points on the graph that have integer X and Y values. It is great for graphing rational functions and for any other types of graphs as well. This is a must have for any student whos math teacher makes them plot graphs by hand!
Graph3D 2 Graph3D:The sequel! Still graphs a line in 3D-space and shws you one point at a time, but with a new look and more features! Download and send to calc. Any suggestions I will gladly accept-by email. Please note that the buttons are slightly different, thus GRFHELP2 is needed too.
Graph3D Basically, graphs a line in 3D space based upon the two equations you give it, both with Z as the independant varable, and shows you one Z-value at a time. All included programs must be included for it to work. The program to run once installed is "GRAPH3D." Press F1 (Y=) for help.
Graph 3D FIRST OF A KIND! I created this as a response to my TI 92 being stupid. Although, no competition with Kirk Meyer's Graph3, This one is in basic and is just a test. E-mail me if you have any questions, comments, or suggestions. This Program has plenty of potential, but still needs a lot of imoprovement.
Graphs v3.0 Have you ever needed touse the statistical plots on your TI-83 or TI-83 Plus,well I have and I wrote this program tomake it much much easier to do so.Instead of typing in a string like "{2,3,4,5,6}->L1:{3,2,4,5,6}->L2:Plot1(Histogram,L1,L2,•):DispGraph" on the home screen just to make one plot,all you do with this is run the program, pick the type of plot you want to make,enter in your list data in the prompts,and press enter.Then after viewing the graph you can choose wether you want to save the data or clear it.Its menu driven and user friendly.No known bugs.
Graphix This program alows you to easily manipulate graphs without needing to go through the menus on the calc. By placing comonly used functions like zoom in and out zoom standard and graph scale on the keys, the program is able to speed up the veiwing of graphs. Enter your graph as you normaly would then open the program to manipulate it.
X-Grapher v2.1 Have you ever wanted to graph an equation in the form X=, when the built-in graph tools ony allow you to enter an equation in the form Y=? Now you can! With this tool, you can enter any equation with any variables, tools, and symbols allowed by the built-in Y= grapher, view the graph using your current window settings, or view the table using your current table settings! Check out the screenshots; Doors CS v4.0 optimized.
Graph Setings Utility Graph Settings Utliy is a unique program that allows you to choose a grphing format. This makes it so that you don't have to go throught the MODE, ZOOM, and FORMAT menus yourselft to adjust the graph proporties. The pogram lets you choose from Normal, Trig, Stats, polar and a optimize function. The optimize function will nealy double the speed of multi function graphing. MirageOS compatable.
Conic graphing program With a size 1/33 of Conic graphing app, it "nearly" the shadow of it.However , i improved some of the aspects that Conic graphing APP lack of like multiple conic objects graph, trace , table, calculate. THIS PROGRAM IS A MUST HAVE FOR THOSE OF YOU WHO ARE STRUGGLING TO DRAW A CIRCLE! This program is completely free, and can be modify (unprotected) for best use (modify the output graphs from Y1 to Y0). Like i said , this program graph circles , parabolas, hyperbolas, ellipses. It contains many other functions like clear all graphs,display focis,directrix,asymptotes... you can actually draw a circle and THEN draw a line cross it AND find the intersections. I used formulas that are available in textbook. You dont need to look anywhere further than Conic chapter. This program REALLY free up some space which can be used for good purposes (including gaming, yay!) (This is the updated version, the last version have an ugly bug in it. DO NOT WORRY, THE BUG IS SQUASHED . PLEASE DOWNLOAD THIS PROGRAM AGAIN. ) i included TI-CODER for those of you wanted to know how i program this.
IFS Fractal Generator This program uses the Iterated Function System to draw 5 fractals in the same way as the Sierpinski Triangle in the TI-83 Plus Manual is drawn: The Sierpinski Triangle, Sierpinski Carpet, a 5-sided crystal, what I call the x-fractal, and a fern, which is very cool. Check out the screen shots.
Implicit Graph Very simple BASIC program to graph implicitly-defined functions. See README for more information. Needs a lot of improvements (functionality and especially speed), but it gets the job done for now.
Inequality Plot This is just a simple program I wrote to plot any inequality of X and Y. Just enter an inequality into Y1 (pretend the Y= isn't there) and run the program. It will start plotting points and the graph will slowly become more and more visible. I'm sorry it doesn't go faster but that's a limitation of TI-BASIC, and I don't know ASM well enough yet to make it faster. Press any key when the graph is clear enough to stop the program. Simple documentation is also included in the program's source code.
Inequality Grapher 2 this is the best inequality grapher out there! It can graph 1,2, or even 3 lines! It can also graph vertical! Used it at my school and it helped a ton of people with there homework.
Inequality Graphing In the first menu you chose the equation, you then are prompted for the numbers associated with that equation. The next menu you chose the inequality. It then spits the graph out and according to the inequality shades the correct side. It is better than doing the math!!!
Julia Set Grapher This program graphs a Julia set, which is produced by iterating the comlex polynomial function f(z)=z^2+a+bi where a and b are the inputed values. The rest is explained in the read-me file.
Mandelbrot Set Generator Amaze your teachers and friends with the Mandelbrot Set on calculator! Features: User-friendly interface Automatically sets graph parameters; no need to mess around Extremely accurate calcualation time estimates Ability to change the number of iterations Extremely memory efficient; uses For loops rather than While loops. Only 500 bytes! If you can program in assembly and can convert this program to a much faster assembly version, PLEASE email me at jkgg2001@hotmail.com.
Param3D A simple 3D parametric graphing program meant to supplement Derive 6 and best used on a TI-Emulator or the TI-Flash Debugger due to the slower speed of TI-BASIC. Supports scaling, rotation, and loading of autosaved graphs.
Piecewise Funtion grapher this program does basically what most people can do in their Y= screen, but takes up more space. Allthough, it may make graphing a piecewise function easier for some. It will only graph a Piecewise with 2-4 functions. Instructions in read-me. Not sure if the 83's can graph piecewise, but it should work, it's just basic.
Point Power "Point Power", the revolutionary point program, does everything its name infers. It finds MIDPOINT, SLOPE, and DISTANCE! If you feel it's missing something don't hesitate. Email me right away and I'll add it.
Graphing Lines This is Final Version if there are any bugs email doboy0@gmail.com with program and problem This program comes with no warranty whatsoever For instructions how to use visit youtube.com/doboy What does it do? find useful properties of points such as slope, xy intercepts, and distance How to use 1)Run program (press PRGM then press POINTS) 2)Program will prompt user if they have 1 point + slope or 2 points 3)Program will then display the slope,xy intercepts, and so on.. 3)DO NOT EXIT BY TURNING OFF OR PRESSING ON if you do so then your functions will be turned off and your axes will be off How to fix problems that might occur #Axes are turned off Press 2nd Format then switch Axes On #Functions are turned off Press Y= and hover over the plus signs, press enter while on a plus sign to turn functions off and on
Polar graphing screensaver This program was designed by me and my friend in math class. It can make 3 types of screensaver graphs. Polar, parametric, and function. It is pretty cool because it graphs until you stop it. It makes a different one each time
QUADRATe The Program GRAPHS Y = AX^2 + BX + C and SOLVES AX^2 + BX + C = 0. 1. The solutions display in the best PRETTY PRINT form of any program available, and also in decimal form, 2. The graph shows the intercepts and vertex allowing you to move from point to point using TRACE and the arrow keys, 3. The vertex (H, K) is given allowing you to create the form Y = A(X – H)^2 + K, and 4. The discriminant D and the focus are also given.
Rotate Shape Reasonably fast program that continuously rotates a shape defined by points in a list in the format {x1, y1, x2, y2,...} around the origin of the graph screen by a given increment. Sample list included. Great for boredom! :)
Rotate A program that allows for you to enter a point on a graph and the number of degrees to rotate by and it will tell you the rotated point. Can run from the prgm menu or from MirageOS. With MirageOS can be launched from both ROM and RAM.
Schwarzian Derivative This program will graph the Schwarzian derivative. The user inputs the first derivative to a function and the output is a graph of the Schwarzian Derivative over a standard window. This derivative is used in chaotic one-dimensional maps
Scatter Plots v1.2 This is a basic Linear/Parabolic regression program. It inputs data into L1 and L2 automatically after typing it in, and you can choose between several methods to get a line of best fit. It auto-formats the graph window to display the scatter plot. Any comments and suggestions you have would be helpful. *Allows you to either enter fresh data into your lists or use data already in your lists. *Linear, Parabolic (quadratic), and Manual fit regression choices. *Rounds all calculations to 3 decimal places. This will run out of Archive with Doors, but I recommend running it from RAM due to a quirk with the Graph Screen.
Slope Field This program calculates a slope field for a given derivative. The slopes can be defined in terms of both y and x. There are also many menus that allow you to customize your slope field. You can set the window and the amount of resolution. It eats up a ton of memory while you're running it, so you may need to either archive things, or set the resolution to "low". This update cleans up a couple of minor issues and also includes some screenshots.
Stat Graph v2.0 This program graphs data as a scatter plot graph. It does everything for you; it finds the best equation and puts into Y=, it sets the ideal window, and it graphs it! All you have to do is enter the x values and the y values! Enjoy.
TABLEX 0.4.1 An intuitive table that has more unique features than TI-Table. It has the ability to scroll up, scroll down, page up, page down, choose a y= equation, and can enter an x value within the table. DoorsCS7 is needed to run the program.
Transformations 2 This program is different from my first transformations program in that instead of asking for A, B, C and D in the form: Af(Bx-C) + D, it asks for this information in a listing style format. So if a problem is something like: Given x^2, perform the following transformations... this program will may be helpful. IMPORTANT NOTE: This program assumes the order of applying transformations to be: 1) horizontal shifts, 2) horizontal rescaling, 3) vertical rescaling, 4) reflections, 5) vertical shifts. So if the problem does not ask for the transformations to be applied in this order, then the program will not produce the correct graph in general. This ordering is usually the ordering used when transformations are not specified in a given order. Great for teaching transformations. Enjoy!
Transformations This program demonstrates how transformations work. The user enters in a base function and then the values A, B, C and D for the form: A*f(Bx-C) + D. It is designed to demonstrate what each value does to the graph. The program will graph each transformation and compare to the original base function's graph. Great for teaching transformations of graphs. Enjoy!
Ultimate Graph Utility This program contains an X= editor, Y= Editor, a special function that increases the precision and decreases time of graphing by about 2 times. Then we still have the graph on and off function and the reset default function. This program is a must have for all students.
Variation Chart of ANY function This program take the function stored in y1 and displays the variation chart (according to the derived function). User-friendly and precise. It is possible to change precision settings to make the program run faster!
Wave Grapher v1.02 Wave Grapher is a cool program usful for Math and Physics. It allows you to graph the two equations of two waves using very simple queries. So instead of having to know the complex trigonmoetirc eqution, you only need to know what the amplitude and period is; making it much easier to graph! Also, once the two graphs have been graphed, they you can solve various things with them and you can see what happens after the waves have interfered with each other - so for those who know physics - what the resulting wave or graph will look like after the original 2 have undergone constructive or destructive interference. Also, you can twiddle around with the resolution, screen size and graph quality!
Weirstrass Function This program generates the graph of a Weirstrass function to show that a continuous function need not be differentiable. The user enters the number of iterations to use and then waits for a graph to be generated. See the accompanying pic to get an idea. Enjoy!
X Equals Function Grapher v1.0 This powerful tool allows you to graph equations using X= instead of Y=. The program is completely BASIC and draws the lines relatively quickly. Works for linear and nonlinear functions. Check for later versions including tables and trace tools.
X= equation grapher yay! another x equation grapher! this one is pretty good, though. after graphing, it allows you to graph again, calculate specific values, change the graphing resolution (higher number = faster, but less accurate, graphing), clear the screen of graphs, or quit. PLEASE REVIEW AND/OR RATE THIS AND MY OTHER PROGRAMS. THANK YOU!
X Y intercept This program finds the X and Y intercepts of a line, when you input the slope and Y intercept. It then graphs it and shows you all the work it did. First program I thought was worthy, hope you like it
Zeroes * Zeroes Zeroes is a program to display all the zeroes of a function (Y1) across the current visible window. ** Invoking Zeroes Feeding information into zeroes is simple. If Y1 currently has a value, zeroes will use that value as its input. If Y1 is empty the user will be prompted for an equation. ** Examining the zeroes To examine the zeroes, scroll the list left and right with the arrow keys. ** Changing the domain or function At any point during the examination of data, press the `TRACE' key (or windows) to adjust the window, or `Y=' to adjust the current function. ** Quitting Press enter to quit zeroes.
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Geometrical Vectometrical Vectors Book Description
Physics/Mathematics
Every advanced undergraduate and graduate student of physics must master the concepts of vectors and vector analysis. Yet most textbooks cover this topic by merely repeating the introductory-level treatment based on a limited algebraic or analytic view of the subject.
By contrast, Geometrical Vectors
Written in an informal and personal style, Geometrical Vectors provides a handy guide for any student of vector analysis. Clear, carefully constructed line drawings illustrate key points in the text, and a set of problems is provided at the end of each chapter (except the Epilogue) to deepen understanding of the material presented. Pertinent physical examples are cited to show how geometrically informed methods of vector analysis may be applied to situations of special interest to physicists. Every advanced undergraduate and graduate student of physics must master the concepts of vectors and vector analysis. Yet most books cover this topic by merely repeating the introductory-level treatment based on a limited algebraic or analytic view of the subject. "Geometrical Vectors" Written in an informal and personal style, "Geometrical Vectors" provides a handy guide for any student of vector analysis. Clear, carefully constructed line drawings illustrate key points in the text, and problem sets as well as physical examples are provided.
About the Author :
Gabriel Weinreich has contributed to Geometrical Vectors as an author.
Weinreich is emeritus professor at the U of Michigan.
Popular Searches
The book Geometrical Vectors by Gabriel Weinreich
(author) is published or distributed by University of Chicago Press [0226890481, 9780226890487].
This particular edition was published on or around 1998-7-6 date.
Geometrical Vectors has Paperback binding and this format has 126 number of pages of content for use.
This book by Gabriel Weinreich
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Geometry: A Fresh Approach (called Geometry from
here on) is a complete high-school geometry course. The student
book includes solutions to odd-numbered problems. Geometry is
intended to be a consumable worktext, but you could write your
answers on lined or graph paper to use the book for future students.
An even-numbered problem solution guide is also available. With
these two books, paper, and a pencil, your student will be ready
to tackle geometry. Algebra 1 is a prerequisite.
Geometry consists of 13 chapters and two appendices.
Lessons are written directly to the student; consequently, a parent
does not need to teach the lessons. Every chapter is made up of
several parts, and beginning in chapter 2 each chapter ends with
a mixed review. The mixed review could be used as a chapter test. Geometry does
not contain tests or final exams.
Appendix A reviews algebraic concepts and is a good starting point
for most students. Appendix B includes answers to the odd-numbered
problems.
Ms. Walters wrote Geometry, as well as Algebra 1 and Algebra
2, after years of providing one-on-one tutoring to students.
She used her knowledge of what students struggled with to write
an easy-to-use curriculum that will instruct students in what
they need to know. You won't find flashy colors, comics, or off-topic
word problems in Geometry - Ms. Walters does not ask
your student how he feels about the hypotenuse of triangle B
or any other unrelated questions. She sticks to the subject at
hand -- geometry.
I found the author's explanations to be thorough and complete,
making Geometry an excellent text for students who learn
well on their own. However, students who need more instruction
(i.e., video or direct teacher involvement) or who are easily frustrated
may not find this text is for them.
I like how Ms. Walters presents each lesson and how she starts
students using proofs in Chapter 1. Her "Direct and Indirect Proofs" lesson
contained enough explanation so that even I could understand it
(math is NOT my strong subject).
For future revisions, I hope that Ms. Walters will put all answers
into one solutions guide. I don't mind the odd problem solutions
remaining in the student book, but I really dislike having to go
back and forth to correct a lesson. This edition lacks a glossary
and an index, which are also things I'd like to see added into
future revision.
I wish I could say that my children loved this course. I don't
think that any geometry course would get that recommendation from
them. I think Geometry is a worthy addition to the selection
of curricula available to homeschoolers, and I think that it will
benefit many families.
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1
Chapter 1
Introduction
Nature of the problem
There is a tremendous amount of pressure placed upon students and teachers to
achieve proficient scores on end of level math testing. High expectations dealing with
math have created many different10
CHAPTER 2: MATERIALS & METHODS
DNA Extraction and Regions Sampled
Ancient maize specimens were previously collected from the Corngrowers Site and identified based on their depth of occurrence from the trench surface. These specimens were ground...
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The first edition of this book (1965; Zbl 0193.34701) consisted of three parts: basic concepts, field theory and linear algebra, and as a modern down-to-earth approach with a personal touch it attained great popularity. The second edition (1984; Zbl 0712.00001) added some topics, mainly on commutative algebra and homological algebra.\par The current third edition has grown again, the additions dealing with topics close to the author's heart from number theory, function theory and algebraic geometry. For the math graduate who wants to broaden his education this is an excellent account; apart from standard topics it picks out many items from other fields: Bernoulli numbers, Fermat's last theorem for polynomials, the Gelfond-Schneider theorem and (as an exercise, with a hint) the Iss'sa-Hironaka theorem. This makes it a fascinating book to read, but despite its length it leaves large parts of algebra untouched. Semisimple algebras get a very cursory treatment (no mention of crossed products or the Brauer group) and there is only the merest trace of Morita theory; there are no Ore domains, Goldie theory or PI-theory. Graphs, linear programming and codes, constructions like ultraproducts and Boolean algebras are also absent, and lattices are only of the number-theoretic sort (reseaux, not treillis).\par Bearing these limitations in mind, the reader will nevertheless find a very readable treatment of many modern mainline topics as well as some interesting out-of-the-way items.\par Editorial comment: Note that there is also a 3rd ed. published by Addison-Wesley 1993 reviewed in Zbl 0848.13001. [Paul M.Cohn (London)]
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Linear Algebra
Every student of mathematics needs a sound grounding in the techniques of linear algebra. It forms the basis of the study of linear equations, matrices, linear mappings, and differential equations, and comprises a central part of any course in mathematics. This textbook provides a rigorous introduction to the main concepts of linear algebra which will be suitable for all students coming to the subject for the first time.
The book is in two parts: Part One develops the basic theory of vector spaces and linear maps, including dimension, determinants, and eigenvalues and eigenvectors. Part Two goes on to develop more advanced topics and in particular the study of canonical forms for matrices. Professor Berberian is at pains to explain all the ideas underlying the proofs of results as well as to give numerous examples and applications. There is an abundant supply of exercises to reinforce the reader's grasp of the material and to elaborate on ideas from the text. As a result, this book presents a well-rounded and mathematically sound first course in linear algebra.
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Vector Spaces
Linear Mappings
Structure of Vector Spaces
Matrices
Inner Product Spaces
Determinants (2 x 2. and 3. x 3)
Determinants (n x n)
Similarity (Act I)
Euclidean Spaces (Spectral Theorem)
Equivalence of Matrices Over a Principal Ideal Ring
Similarity (Act II)
Unitary Spaces
Tensor Products
Table of Contents provided by Publisher. All Rights Reserved.
List price:
$39.95
Edition:
1992
Publisher:
Oxford University Press, Incorporated
Binding:
Trade Cloth
Pages:
376
Size:
7.69" wide x 9.56" long x 1.04
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Students in Years 7 and 8 follow a comprehensive mathematics course, which is in line with the statutory National Curriculum.
Key Stage 4
The department also offers the possibility of studying for a linear GCSE examination. If students complete the GCSE course in Year 10 there is the possibility of studying for a GCSE in statistics in Year 11.
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300-level Algebra
classes at Stony Brook
The Mathematics Department has reorganised its 300 level algebra
classes in order to clarify their different purposes and emphasize their
different teaching styles.
There are three ``entry level"
algebra classes with 200 level prerequisites
MAT 318 (Classical Algebra),
MAT 312 (Applied Algebra) and
MAT 310
(Linear algebra)
that are offered each
semester, and two more advanced classes
MAT 313 (Abstract Algebra) and
MAT 311 (Number Theory)
with 300 level prerequisites, offered in the
Fall and Spring, respectively.
MAT 318 involves writing a project, while MAT 312 involves work with
computers. The other three classes are more theoretical with a considerable
emphasis on proofs.
A list of
the classes in approximate order of difficulty follows.
MAT 318: Classical Algebra. An examination of
algebra from a
historical perspective. Topics include Euclid's algorithm, congruences and
the unsolvability of the three ``great problems" (trisecting the
angle, squaring the circle and solving quintics). All students write an
extended project, on topics ranging from the quaternions to Pascal's triangle.
Fall and Spring
Mandatory Prerequisite: MAT 211 or AMS 210.
MAT 312: Applied Algebra. Applications of
conguence arithmetic to cryptography and applications of group theory
to the theory of error-correcting codes. Students
participate in computer
workshops that illustrate these applications. Crosslisted with AMS 351.
Fall and Spring
Mandatory Prerequisites: MAT 203 or 205 or AMS 261, and MAT 211 or AMS 210.
MAT 310: Linear Algebra. Develops the basic theory of
vector spaces and linear transformations. Together with MAT
320, it is a core course for the mathematics
major in which students are taught how to
write proofs. Fall and Spring
Mandatory Prerequisites: MAT 203 or 205 or AMS 261, and MAT 211 or AMS 210.
MAT 313: Abstract Algebra. Describes the basic
properties of groups, rings and fields. Students are expected to have taken
either MAT 312 and 318, which provide
relevant examples of the general theory, or MAT 310 which gives
experience with the theoretical development of algebraic structure.
Fall only
Mandatory Prerequisites: MAT 318 or 312 or 310 or
permission of the instructor.
MAT 311: Number Theory. The fascinating properties of numbers
are one of the main driving forces of mathematics. This course discusses
some accessible parts of number theory such as continued fractions,
quadratic residues, and properties of prime numbers. In order for
this course to be to cover some interesting material,
students are expected to
know congruence arithmetic before they start. Spring only
Mandatory Prerequisites: MAT 318 or 312 or 313 or
permission of the instructor.
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Geometry, Perspective Drawing, and Mechanisms
The aim of this book is to examine the geometry of our world and, by blending theory with a variety of every-day examples, to stimulate the imagination of the readers and develop their geometric intuition. It tries to recapture the excitement that surrounded geometry during the Renaissance as the development of perspective drawing gathered pace, or more recently as engineers sought to show that all the world was a machine.
The same excitement is here still, as enquiring minds today puzzle over a random-dot stereogram or the interpretation of an image painstakingly transmitted from Jupiter.The book will give a solid foundation for a variety of undergraduate courses, to provide a basis for a geometric component of graduate teacher training, and to provide background for those who work in computer graphics and scene analysis. It begins with a self-contained development of the geometry of extended Euclidean space. This framework is then used to systematically clarify and develop the art of perspective drawing and its converse discipline of scene analysis and to analyze the behavior of bar-and-joint mechanisms and hinged-panel mechanisms. Spherical polyhedra are introduced and scene analysis is applied to drawings of these and associated objects. The book concludes by showing how a natural relaxation of the axioms developed in the early chapters leads to the concept of a matroid and briefly examines some of the attractive properties of these natural structures.
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Preface
Combinatorial Figures
Drawing figures
Modeling figures
The circuits of a figure
Combinatorial Geometries
The definition of a combinatorial geometry
Lines and planes of a combinatorial geometry
Two families of combinatorial geometries
Sketches of planar geometries and figures
Models of some combinatorial cubes
Subgeometries of a combinatorial geometry
Isomorphic combinatorial geometries
Planar Geometries and Projective Planes
The intersection of coplanar lines
Projective planes
Subgeometries of a projective plane
An extended Euclidean plane
Pencil and roller constructions
Coordinatizing an extended Euclidean plane
Sylvester's Theorem and the Fano plane
Non-Planar Geometries and Projective Spaces
Projective spaces
Subgeometries of a projective space
Desargues' Theorem and projective spaces
Extended Euclidean space
Coordinatizing extended Euclidean space
Perpendicular lines and planes
Pythagoras' Theorem, length and angle
The existence of a tetrahedron
Perspective Drawings
The definition and basic properties of a perspective drawing
Perspective drawings in a combinatorial geometry
Practical perspective drawing methods
Vanishing points
Perspective drawings of a box
Perspective rendition from an ideal viewpoint
Binocular Vision and Single Image Stereograms
Binocular vision
Binocular vision and random-dot stereograms
Single-image stereograms
Scene Analysis
Perspective drawings of intersections of planes
Scenes and other planar figures
The existence of boxes
Completing a partial scene
Two problems
Distortion and Anamorphic Art
Viewing perspective drawings
Anamorphic art
Distortion in 3-point perspective drawings
Distortion in 2-point perspective drawings
Distortion in 1-point perspective drawings
Distortion in affine projections
Planar Bar-And-Joint Mechanisms
Bar-and-joint models
Four-bar linkages
Rocking and rotation in 4-bar linkages
Coupler curves
Parallelogram and kite linkages
Plagiographs
Cognate linkages
Approximate and exact linear motion
Non-Planar Hinged-Panel-Mechanisms
Hinged-panel models
Four-panel cycles
Panel cycles of at least five panels
Polyhedral models
Graphs, Models and Geometries
The definition of a graph
Connected graphs and acyclic graphs
The rigidity of a one-story building
Hinge graphs and developments
Graphs that are also geometries
Spherical Polyhedra
The definition of a polyhedron
Planar graphs and three-connected graphs
The definition of a spherical polyhedron
Vertices, edges, and faces of a spherical polyhedron
The existence of spherical polyhedra
D�rer's melancholy octahedron
Scene Analysis and Spherical Polyhedra
Perspective drawings of a spherical polyhedron
Some applications of the theorem
Perspective drawings of a wider class of unions of polygonal regions
. Matroids
The definition of a matroid
Geometries, graphs, and matroids
Bases of a matroid
The rank function of a matroid
Isomorphism and representable matroids
Projective and affine geometry
Dual matroids
Restrictions and contractions of a matroid
Minors of a matroid
Paving matroids
Bibliography
Index
List price:
$82.00
Edition:
2011
Publisher:
World Scientific Publishing Company, Incorporated
Binding:
Trade Cloth
Pages:
340
Size:
6.25
|
High School Mathematics
Bogged down by rote-memorization drills and predictable homework exercises, EDC's Al Cuoco was frustrated teaching math in the 1970's. "Like many math teachers, I was always dissatisfied with most of the commercially available curricula I had." Over the past five years, he has been working on behalf of today's teachers "to create the texts I always yearned for." As principal designer of a major mathematics textbook initiative, the CME Project, he says he is nearing his goal.
"While these texts have been in development for over five years," states Cuoco, "in a real sense I've been working on the ideas in this program for close to four decades."
Many high school mathematics teachers still face the dilemma that Cuoco did years ago. They must choose between traditional texts, on the one hand, that follow an accepted structure and progression—algebra, geometry, advanced algebra, and precalculus—but do not integrate lessons and themes across topics and chapters, and, on the other hand, more progressive texts that challenge students yet organize the material in a manner that is unfamiliar to teachers and parents.
"In far too many classrooms, mathematics is taught as a disconnected set of facts and procedures, a body of knowledge to be learned in much the same way as one learns a list of terms for a vocabulary test," says Cuoco, who works in EDC's Center for Mathematics Education.
The CME Project, funded by the National Science Foundation (NSF), features a series of textbooks focusing more on comprehension of core math concepts and less on rote memorization of facts and formulas. These new texts present mathematics in progressive and innovative ways, challenging students to develop robust mathematical proficiency. The new texts will be available in fall 2007.
Rater than forcing students to churn through chapter after chapter of disjointed topics—from graphing equations to triangle trigonometry to complex numbers—without connecting themes and ideas, CME texts present ideas thoroughly for students to get a firm handle on the material. Topics are revisited in later chapters to deepen students' understanding of them and their connection with other ideas, while the clutter of extraneous topics is omitted.
Drawing on lessons learned from high-performing countries in the Pacific Rim and Northern Europe, the program also employs the best American models that call for "experience before formality." This practice encourages students to grapple on their own with ideas and problems before the teacher presents the lesson in class.
The texts go beyond "real life" examples to make math interesting. Many of the tasks posed by CME are purely mathematical, such as "find the sum of integers between one and 100" and "find a simple rule that would generate the following input/output table of numbers."
"We were surprised to discover when asking our student advisory board that they found these purely mathematical problems to be very realistic," says Cuoco. "They didn't need a 'real-life' situation or context to grasp the meaning behind the problems and apply their problem-solving skills."
The program has drawn on the expertise of teachers, mathematicians, researchers, and students and has been extensively field tested in sites across the country—urban, suburban, and rural. The geometry and precalculus courses were field tested for their initial release, and the newer course materials have been field tested nationally for the last 2-3 years. While CME sets high expectations for students, field tests have demonstrated that these expectations can be met by students of all abilities and backgrounds.
The new texts will be published in two stages by Prentice Hall which is promoting them at the National Council of Teachers of Mathematics conference. The first collection of bound books will be released in November 2007 for adoption in 2008, starting with Algebra 1. The next two books will be published six months after that.
Mathematical "Habits"
Developers hope that students will develop ways of thinking—the habits of mind—used by mathematicians, scientists and engineers and in other professions.
"One of the most useful things students can take away from a mathematics course is the style of work, the way mathematicians think about things," states Cuoco. "It turns out when you ask students about high school math, that's what they find most useful later on in life. This relates to their ability to be able to visualize things that don't exist, or their ability to think about a collection of isolated steps into one coherent process."
For example, in designing a house, a person must be able to picture something in their mind that doesn't exist and then reason about that, including how many sheets of plywood they might use to cover all sides or how many windows they will need for the house to look the way they want it to.
"It's a way of visualizing things that don't yet exist in order to predict what they will be like when they come to life," states Cuoco.
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Book Description: Preempt your anxiety about PRE-ALGEBRA! Ready to learn math fundamentals but can't seem to get your brain to function? No problem! Add Pre-Algebra Demystified, Second Edition, to the equation and you'll solve your dilemma in no time. Written in a step-by-step format, this practical guide begins by covering whole numbers, integers, fractions, decimals, and percents. You'll move on to expressions, equations, measurement, and graphing. Operations with monomials and polynomials are also discussed. Detailed examples, concise explanations, and worked problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning. It's a no-brainer! You'll learn: Addition, subtraction, multiplication, and division of whole numbers, integers, fractions, decimals, and algebraic expressions Techniques for solving equations and problems Measures of length, weight, capacity, and time Methods for plotting points and graphing lines Simple enough for a beginner, but challenging enough for an advanced student, Pre-Algebra Demystified, Second Edition, helps you master this essential mathematics subject. It's also the perfect way to review the topic if all you need is a quick refresh
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Mathematics for Elementary Teachers
9780321447173
ISBN:
0321447174
Edition: 2 Pub Date: 2007 Publisher: Addison-Wesley
Summary ...just on the mechanics of how it works. Fully integrated activities are found in the book and in an accompanying Activities Manual. As a result, students engage, explore, discuss, and ultimately reach true understanding of the approach and of mathematics.[read more]
Ships From:Mishawaka, INShipping:Standard, Expedited, Second Day, Next Day
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by Patricia W. Hammer, Department
of Mathematics and Statistics
and Jessica A. King, Department of Computer Science
Hollins University
and
Steve Hammer, Department of Mathematics
Virginia Western Community College
In this project, students will complete a series
of modules that require the use of polynomial and trigonometric functions to
model the paths of straight stretch roller coasters. These modules
involve the mathematical definition of thrill and calculation of thrill for
several real coasters (Module A), design and thrill analysis of single drop
coaster hills (Modules B and C) and design and thrill analysis of several drop
coasters (Modules D and E). The ultimate goal of this interactive project is
successful completion of an optimization problem (Module F) in which students must design a straight stretch roller
coaster that satisfies the following coaster restrictions regarding height,
length, slope and differentiability of coaster path and that has the maximum
thrill (as defined below.)
Roller Coaster Restrictions
The total horizontal length of the straight
stretch must be less than 200 feet.
The track must start 75 feet above the
ground and end at ground level.
At no time can the track be more than 75
feet above the ground or go below ground level.
No ascent or descent can be steeper than 80
degrees from the horizontal.
The roller coaster must start and end with
a zero degree incline.
The thrill of a drop is defined to be the
angle of steepest descent in the drop (in radians) multiplied by the total
vertical distance in the drop. The thrill of the coaster is defined
as the sum of the thrills of each drop.
The path of the coaster must be modeled
using differentiable functions.
Students must use Maple8 (or any later version) to complete the project.
Students must already be familiar with derivatives and their
use in determining maximum and minimum function values. These ideas play a crucial role in the design and analysis
of the coasters.
To complete this project, student should work
through each of the modules given below.
A.Introduction to Roller Coaster Design - In this
module, students use an
interactive coaster window to mark peaks and valleys of real-life coasters and
then calculate the thrill of each drop using the above definition. Be
sure to record the x and y coordinates of the peak and valley points and the
slope at the steepest point. You will need this information to complete
parts B - E below.
B. Design
and Thrill of One Coaster Drop Using a Trig Function- In this module,
students model one drop of a coaster by marking the peak and valley of the drop
and then by fitting (in height and slope) a trig function of the form f(x) =
Acos(Bx+C)+D to the marked points. Once the function has been determined,
students then calculate the thrill of the single drop. A downloadable
Maple worksheet with commands and explanation is provided.
C.
Design and Thrill
of One Coaster Drop Using a Polynomial Function - In this module, students
model one drop of a coaster by marking the peak and valley of the drop and then
by fitting (in height and slope) a cubic polynomial to the marked points.
Once the function has been determined, students then calculate the thrill of the
single drop. A downloadable Maple worksheet with commands and explanation
is provided.
D. Design and Thrill
of a Straight Stretch Coaster Using Trig Functions - In this module,
students model a straight stretch coaster (several hills) by marking peak and
valley points and then by fitting (in height and slope) a trig function to each
consecutive pair of marked points. Once the functions have been
determined, students then calculate the thrill of the coaster. A
downloadable Maple worksheet with commands and explanation is provided.
E. Design and Thrill
of a Straight Stretch Coaster Using Polynomial Functions - In this
module, students model a straight stretch coaster (several hills) by marking
peak and valley points and then by fitting (in height and slope) a cubic
polynomial function to each consecutive pair of marked points. Once the
functions have been determined, students then calculate the thrill of the
coaster. A downloadable Maple worksheet with commands and explanation is
provided.
F. Project Assignment
- Design the Most Thrilling Straight Stretch Coaster - Students use
the ideas from modules A- E above to design a coaster (that satisfies all
restrictions) with the maximum possible thrill. Completion of this project
requires ingenuity, creativity and extension/modification of many of the ideas
and Maple commands presented in modules A-E.
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This is a classic introductory text for students interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions.
This will be the main text for the course, and will be supplemented with additional materials posted or handed out.
This is an excellent reference work for students in search of a quick explanation of the mathematics found in the first one to two years of the college science curriculum. If you feel that you are rusty in background mathematics of this course, this text is highly recomended.
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Does anybody here know anything concerning prentice hall worksheets? I'm a little puzzled and I don't know how to finish my math homework regarding this topic. I tried reading all materials about it that could help me figure things out but I still don't get. I'm having a hard time answering it especially the topics algebra formulas, mixed numbers and interval notation. It will take me days to answer my algebra homework if I can't get any help. It would really help me if someone can recommend anything that can help me with my math homework.
Well of course there is. If you are determined about learning prentice hall worksheets, then Algebra Buster can be of great help to you. It is designed in such a manner that almost anyone can use it. You don't need to be a computer professional in order to operate the program.
Yeah! That's a great substitute to the costly private coaching and expensive online coaching. The single page formula list provided there has helped me in every Algebra 1 internal that I have had in the past. Even if you are an intermediate in Intermediate algebra, the Algebra Buster is very useful since it offers both simple and challenging exercises and drills for practice.
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John Orr (our TA) is in office RLM 11.146, and his office hours are:
Monday, 12:30 to 2:00 and Tuesday, 3:30 to 5:00.
If you have any questions, you should definitely come talk to one of us! You can get much more personalized answers in office hours than you can in class. If these office hours don't work and you want to make an appointment (or you have any other questions), send me an e-mail at olenab(at)math.utexas.edu.
The first midterm is on Thursday, September 22nd in class. It will be 75 minutes, and will not contain multiple choice.
There is currently a review assignment on Quest.
Here is a sheet with all the concepts to review.
Disclaimer: these grades are just to give you an idea. What will actually be curved is your final grade, and I will be using the combined homework and exam scores to calculate that. Furthermore, the final grades will use the +/- option (that is, we will have the grades A+, A, A-, B+, etc.) while here I'm just going to give an idea of the ranges without that. With that in mind:
A: at least 80/95, which is about 84%. There were 32 of these.
B: between 70/95 and 79/95, which is about 74% to 83%. There were 29 of these.
C: between 61/95 and 69/95, which is about 64% to 73%. There were 21 of these.
D: between 51/95 and 60/95, which is about 54% to 63%. There were 21 of these.
F: anything below (and including) 50/95. There were 19 of these.
The average for the test was about 68/95, or approximately 72%. (The above curve corresponds to adding about 6% to your grade.) The standard deviation was about 18 points out of 95.
Same disclaimer as for Midterm 1: these grades are just to give you an idea for how you did on this test. I will not be providing estimates of the +/- option, and these are certainly not exact. That being said:
A: at least 76/85. There were 43 of these.
B: between 68/85 and 75/85. There were 24 of these.
C: between 59/85 and 67/85. There were 19 of these.
D: between 51/85 and 58/85. There were 13 of these.
F: 50/85 and below. There were 17 of these.
The guidelines above are fairly close to the standard A/B/C/D percentage cut-offs: that is, an A is 90 and above, a B is between 80 and 89, etc.
The average on the test was about 66/85, or 79%. The median was about 71/85, or 84%. The test was fairly well done!
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4600/7602 Signal and Image Processing II Tutorial 3(Due date: Friday 1/5/09)1. Automatically locate the number plate in the following image. (Available as You may try a 2D cross-correl
Integration by substitutionThere are occasions when it is possible to perform an apparently dicult piece of integration by rst making a substitution. This has the eect of changing the variable and the integrand. When dealing with denite integrals, t
ELEC4600/ELEC7602 Signal and Image Processing IITutorial 1 (Due date: Friday 27/03/09)1. We wish to extract tones at 50 and 100 Hz from tones at 1000 and 1100 Hz and then downsample the output by the largest possible factor. Assume the signal cont
ELEC4600/7602 Signal and Image Processing IITutorial 5 (Extended due date: 30/5/2008) 1. Stereo reconstruction is only useful for reconstructing a simple scene from two nearby views1. It can be difficult to extend to complicated scenes with occlusio
Image AnalysisExtracting Information From Images9/04/2003ELEC4600/7602 Signal and Image Processing IIBrian Lovell1Image Analysis The first step in image analysis is generally to segment the image. The level of segmentation depends on th
MATH1050 Semester 1, 2008Week 6 Tutorial ProblemsWork through the following problems, show your tutor then record your name before the end of your Week 6 tutorial. You are encouraged to discuss these questions and your solutions with your peers a
MATH1050 Semester 1, 2008 Week 12 Tutorial Problems Work through the following problems, show your tutor then record your name before the end of your Week 12 tutorial. You are encouraged to discuss these questions and your solutions with your peers a
MATH1050 Semester 1, 2008Week 3 Tutorial ProblemsWork through the following problems and have your tutor sign your solutions and record your name before the end of your Week 3 tutorial. You are encouraged to discuss these questions and your solut
Lesson 5 Sec 8.3 Maxima and Minima of Functions of several variables (Continued) We have learned the second derivative test to determine whether a function of two variables has a relative maximum or a relative minimum in previous lecture. In this lec
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COSC 235BDavid A. SykesQuiz 6April 18, 20081. Show the output of the program on the second sheet given the following user inputs [bold]:Welcome to the frog simulation. Enter the depth of the well: 10 Enter the height of the frog above the bott
Dao127-+Talk-+Spectral Analysis of 2-Colour 3-Pulse Photon Echoes on a Femtosecond Time Scale-+AbstractThe spectral analysis of photon echo signals is used to study a semiconductor-doped glass and a laser dye (RhB) in methanol solution. The d
Eco 301 Problem Set 12Name_ 10 December 20081. The demand curve for a monopolist is given by P = 350 - 7Q, and the short-run total cost curve is given by TC = 500 + 70Q. What is the profit-maximizing price and quantity? Find the monopolist's econ
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CS 235 Preliminary Student SurveyThis survey is not meant to invade your privacy. I created it to help me get to know you better. If there is a question that you feel uncomfortable answering, please ignore that question. However, returning the surve
GABAergic Influences Increase Ingestion across All Taste Categories Liz Miller Molly McGinnis Lindsey RichardsonA research thesis submitted in partial completion of PSY451 senior research thesis, at Wofford College2 Abstract Each year six million
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Math 110 – College Algebra
Office Hours: W 9:00-11:00. Other times can be arranged by appointment.
Additional help: Individual help is also available in the Learning Center located in MC 312. Youcan sign up for individual tutoring at any time or drop in for homework help.
Text:
College Algebra: Concepts and Models, Third Edition by Larson, Hostetler, Hodgkins
Course Catalog Description:
Review of basic algebra, second-degree equations and inequalities, roots of polynomials, exponential and logarithmic functions, and systems of equations. Not applicable toward mathematics major or minor sequence. Prerequisite: acceptable score on placement exam, grade of B-minus or better in one year of high school algebra, or grade of C or higher in Math 001.
Core Skill Objectives:
Communication Skills
Writes competently within the major and for a variety of purposes and audiences.
Reads with comprehension and the ability to analyze and evaluate.
Speaks effectively, both formally and informally.
Listens with an open mind and responds with respect.
Accesses information and communicates using current technology.
Thinking Skills
Uses reasoned standards in solving problems and presenting arguments.
Life Values
Analyzes, evaluates and responds to ethical issues from an informed personal value system.
Aesthetic Skills
Develops an aesthetic sensitivity.
Cultural Skills
Participates in activities that broaden the student's customary way of thinking.
Course Objectives:
Communication Skills
Produces both written and oral communication throughout course; particular attention is paid to the accurate and appropriate use of the language of algebra.
Uses technology to solve problems and to be able to communicate solutions and explore options.
Thinking Skills
Study briefly the basic ideas of a first algebra course.
Learn to solve quadratic equations by factoring, completing the square, and by use of the quadratic formula
Explore exponential and logarithmic functions, including application problem and the efficient and appropriate use of logarithms and their properties.
Learn the techniques of solving systems of equations and appropria`tely applying these processes to work problems.
Life Values
Adheres to the Academic Honesty Policy.
Aesthetic Skills
Develops an appreciation for symmetry.
Cultural Skills
Understand how knowledge is developed and verified in mathematics.
Course Outline:
Ch 1: Equations and Inequalities
Ch 2: The Cartesian Plane and Graphs
Ch 3: Functions and Graphs
Ch 4: Polynomial and Rational Functions
Ch 5: Exponential and Logarithmic Functions
Ch 6: Systems of Equations and Inequalities
Attendance and Academic Honesty:
Attendance is essential. You are adults and mature enough to realize that in order to succeed in this class it is vital that you be here. If you cannot make it to class and have any questions, contact someone in the class or myself for information on what was covered. You are responsible for all information given during class. Missed quizzes and exams may be made up if and only if you contact mebefore the quiz or exam and have a legitimate excuse.
Cheating will not be tolerated. First offense will be a zero for the particular work; a second offense will result in an F for the course.
Responsibility:
My responsibility is to help you learn the material in this class through presenting new concepts, modeling the process of solving problems, and challenging you do your best. I will do this to the best of my ability.
Your responsibility is to be actively engaged in the process of learning through attending class, reading the text, listening attentively, taking notes, practicing the concepts through doing daily assigned homework, asking questions when you need clarification, and seeking outside help when you need it. You will not succeed in this class if you are unwilling to put time into practicing the concepts outside of class. I encourage you to study with others and to seek a tutor if you find the material very difficult.
You are responsible for all information and assignments given during class, even if absent.
Americans with Disabilities Act:
If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see Wayne Wojciechowski in Murphy Center, Room 320 (796 - 3085) within ten days to discuss your accommodation needs.
Individual and group assignments, for grade, will be given throughout the semester. Group assignments are to be completed as a group. Every member of the group will receive the same grade. If a member of your group is not pulling his/her weight contact me. Any student who does not actively participate in completing group assignments may be asked to complete them alone. Writing Assignments: I will assign a number of related writing projects during the semester. I will collect and read them twice - at mid-semester and at the end of the semester. Writing Assignments will be graded on accuracy, completeness, thought put into your responses, and writing skills.
Quizzes: (10%)
Quizzes will be given at least once a week, with the possible exception of exam weeks. You will have a quiz the last day of every week (usually Thursday). A pop quiz can occur at any time.
Final Exam: (30%)
Your final exam grade will consist of a take home group, open book, exam and a comprehensive individual, closed book, exam given on Tuesday Dec 10 from 5:45 to 7:45 PM. The two will be combined to form one exam grade as follows: group exam (1/3), individual exam (2/3).
Late Assignments and Writing Assignmentss will be accepted up to three days late. For each day late your grade will be deducted 10 percentage points (one grade level). After three days a zero will be given for that assignment. Any extra credit assignments will not be accepted late.
Extra Credit assignments may be offered during the semester. Extra credit assignments are not accepted late. Extra Credit is graded on a point for each problem correctly done and the points are added to your quiz scores. Extra Credit will not raise your grade more than one half grade level. I.e. it can raise your grade from a BC to a B but not from a C to a B.
Missed Quizzes and Exams: Missed quizzes and exams may be made up if and only if you contact me before the quiz or exam and have a legitimate excuse.
Schedule:
This schedule may change as we progress through the course. You will be notified of any changes. You are responsible for knowing these dates. Graded assignment due dates will be announced as they are assigned.
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Secondary Mathematics WWW Resources
This
is a selective, annotated list of recommended Web sites about secondary
mathematics.
TIP:
Press Ctrl/f
and enter a part of a word or phrase in the Find what: box and
click on Find Next to search for a topic on this page. For example,
type math to search for
math, mathematics, mathematical.
Awesome
Library: Middle-High School Math
This site provides links
about teaching Algebra, By Subject and Standard, Calculus, Data Analysis,
Geometry, Graphing, Pre-Algebra, Pre-Calculus, Probability and Statistics,
& Trigonometry. The site also includes links to Assessment Information,
Math Lessons, Problem Solving, & Standards and Discussions. The Awesome
Library uses specific selection
criteria and methods for including links on the web site.
Cornell
Theory Center Math and Science Gateway: Mathematics
At this site, sponsored by Cornell University's Department of Education, you
can locate links to resources in mathematics for educators and students in
grades 9-12; topics covered include: fractals, geometry, history of mathematics,
mathematics software, commercial software, and tables/constants/definitions.
Frank
Potter's Science Gems - Mathematics
A professor of physics at the University of California at Irvine produces
an annotated list of math sites arranged by topic and grade level; subjects
include: algebra, calculus, geometry, history of mathematics, number theory,
probability and statistics, and trigonometry.
Infinite
Secrets
This PBS/NOVA Web site
about the concept of infinity explores the life of Archimedes and the recently
discovered manuscript which shows he came quite close to discovering calculus.
The site includes a number of interviews, short articles, a teacher's guide
and interactive features, including an "Approximating Pi" demonstration
that illustrates how Archimedes calculated pi around the year 250 BCE.
Interactive
Mathematics
An extensive,
award winning mathematics site which includes games, puzzles, analog gadgets,
polls, and more! Additionally a Chronology of Updates for "an insight
of this site's evolution, chronology updates may be used for word searches."
Math
in Everyday Life
Funded by Annenberg/CPB, this site
explores using math to help us in everyday life situations, such as playing
games or cooking, buying or leasing a new car, and predicting retirement savings.
Math
Forum@ Drexel
The Math Forum, a center for math education on the Internet, is funded by
the National Science Foundation. Check out the following resources from theForum:
PBS
TeacherSource PBS provides links to excellent math resources on the Web and to
recommended books for grades 9-12.
Teaching
Mathematics Teaching Mathematics provides a number of
teaching articles on topics that include: Teaching Secondary Mathematics,
Theories of Mathematical Learning, Enhancing Thinking Skills in the Sciences
and Mathematics, and Symbolizing and Communicating in Mathematics Classrooms:
Perspectives on Discourse, Tools, and Instructional Design. A person can also
search by books, journals, magazines, newspapers, or encyclopedias. Advanced
search options are also available on this site.
Webmath
Webmath offers help in Math for Everyone, General Math, K-8 Math, Algebra,
Plots & Geometry, Trig. & Calculus, and Other Stuff. "This site
has over 100 instant-answer, self-help, math solvers, ready to help you get
your math problem solved." Webmath also offers an ask the expert area
and math software for your computer.
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Paul C Emekwulu
Title:
Mathematical Encounters for the Inquisitive Mind
Genre:
Teaching / Educational
ISBN:
9784535510
Synopsis :
Some school books are not written strictly in line with any traditional curriculum. They
fall into the category of supplemental materials. The right supplemental materials in
mathematics are analogous to novels and other reading materials. Novels, the language
of expression notwithstanding, build language skills in the areas of vocabulary, reading
and comprehension, spelling, grammar etc. Similarly, the right supplemental materials
in mathematics build vocabulary, computational, language, reasoning and logical
thinking skills. Mathematical Encounters for the Inquisitive Mind is a unique collection
of articles written by the author over the years under different circumstances and each
has some dose of mathematical insights for the inquisitive mind. The book can help
students and the general reader to be logical in their approach to mathematics and life
situations.
Full Table of Contents is available @:
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97815595306Each Mathercise book is a set of 50 blackline-master activities designed by Discovering Geometry author Michael Serra as warm-up activities for the start of class. Each activity takes 10 minutes and includes one reasoning exercise, one solving exercise, one sketching or graphing exercise, and space for a review exercise of your own design.
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Topic: this is a mathematics education question (but applies to other sciences too).
Assumtions
Assumptions
Specializing early
Topic: this is a mathematics education question (but applies to other sciences too).
Assumtions
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PROFESSOR: Hi, I'm Gilbert Strang, and I'm a math professor at MIT. And I hope these highlights of calculus will be helpful. I started the project this year, because the linear algebra lectures which were in class have been watched by a lot of people on OpenCourseWare. And so I looked at what there was for calculus.
And I saw two or three types of things. One was lectures, sort of very serious, too mathy. And another was supported by foundations, an effort to make math look so terrifically exciting and wonderful and connect with everything. And yet, I feel a lot of people are taking math courses, calculus, in high school, in college, and simply want a little help to see what's the main point.
And maybe that's the idea of these lectures, is to try to tell you the main point without all the heavy things that a giant textbook would do, and without all the practice that you'll get in class, and doing exercises and so on. So these are kind of short, but I hope alive. And if they help, I'm very happy.
So I guess I'm hoping everybody might watch this who'd like a little help or a second look at calculus, both high school and college students. I wanted to capture key ideas that you could use for review and see new examples and see just coming from a second person. That seems to be what succeeds with linear algebra. The videos are sort of just to add, to supplement what you're actually seeing in class and in the textbook.
I think of the textbooks as often so large and so many exercises that it's totally easy to lose the key point, what's essential about calculus and what is just kind of routine and practice. So in short videos, it has to be the essential points, the three groups of functions, like powers of x, sine and cosine of x, and e to the x. If you understand those, you've got the main ideas.
We're starting out with a first group of five videos. Maybe big picture is the words that we think of for those. And then that'll be the first group that'll be on OpenCourseWare. And then I've done 12 after that, that do sort of the rest of differential calculus, big words just meaning how to find the derivative, the slope, the speed. You'll see in the videos. And then after that could come integral calculus, if you think I should.
I don't think of a lot of prerequisites for these videos. I guess I'm always hopeful that you could watch them even if you haven't started calculus, to see what's coming, what it's about. I've taught math for a long time, and it's so easy to get into the course and jump over the opening, the introduction that tells what's important here. And that's maybe what these videos are aimed at.
FEMALE SPEAK
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The Algebra Tutor DVD series introduces the fundamentals of Algebra through fully worked, step-by-step example problems.
The "Addition & Multiplication" episode covers fractions, combining whole numbers & decimals, word problems using these qualities & more, teaching viewers through example problems that progress in difficulty. Emphasis is placed on giving students confidence by gradually building skills that are committed to long term memory. Grades 5-9.
This DVD is part of the "Algebra Math Tutor Series" series, which comprises 5 sold-separately volumes. 31 minutes on DVD.
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Next: Radical Transformations
Previous: Manual Fit
Chapter Outline
Loading Content
Chapter Summary
Description
This chapter explores the graphing of square root functions through the Transfrm program, defines the distance and midpoint formulas, and goes over utilizing a box and whisker plot on a graphing calculator.
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Free Graphing Calculator
Free Graphing Calculator has a clear-cut layout, which is ideal for this type of an app. It only has five tabs, all listed at the very bottom of the screen: calculator, equations, graph, reference and more. The first three are self-explanatory. The last two have more details. The reference-tab offers many references not only applicable to algebra, but also to calculus, mechanics, fractions, geometry, language, logic, trigonometry, vectors and many more! The more-tab is where you'll find your settings, information about the full version, a place to make an in-app purchase of $0.99 to eliminate ads, as well as table, polynomial and triangle solvers!
Because Free Graphing Calculator is all about numbers and being precise, itsads do bother me. However, they only cost a buck to remove permanently, and this app is worth way more than a buck! If you need a little help with your algebra, this graphing calculator could make your grade! It's that good! It offers more than features than the paid calculator apps, and it's FREE!
Graphing Capabilities:
• Graph up to four equations at once.
• Graphs are labeled.
• You can drag the graph or pinch to zoom in or out.
• Calculator can find roots and intersections.
A unit converter: With a tap, you can enter the result of your conversion into the calculator. Currently converts different units of the following: acceleration, angle, area, density, distance, energy, force, mass, power, pressure, speed, temperature, time, and volume. Great for doing physics homework!
Constants for scientific calculations — speed of light, strength of gravity at Earth's surface, etc. etc. etc. Tapping on a constant will insert it into your calculation — i.e, you don't have to key in the value. Again, great for doing physics homework!
It can make a table of the values of any function you care to enter. You can choose the starting x value of the table, as well as how much x increases for each successive row.
Help screens linked directly to many of the available functions and constants. Tap the disclosure arrow to see the definition.
Forgot the quadratic formula? Or the double-angle formulas for sine and cosine? The math/science reference hits the high points of various subjects. Currently includes algebra, differential and integral calculus, geometry, trigonometry, vectors, vector calculus, and classical mechanics.
App Review Details
Free Graphing Calculator
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Useful Links
The Khan Academy contains over 2,000 video lessons. Subjects taught range from basic arthemitic and algebra up through multivariable calculus and linear algebra. There are also computer generated practice problems where you can master everything from adding numbers to using the chain rule.
If you prefer to read through examples and explinations then this is the site for you. There are extensive notes and examples for Algebra, Calc I through Calc III, Linear Algebra, and Differential Equations.
MathTV features videos on high school math subjects including Algebra, Geometry, Trigonometry and Calculus. This site should be especially useful for secondary education majors with a math concentration.
PatrickJMT is a website full of instructional math videos. There are videos on Algebra, Calculus, Differential Equations, Linear Algebra and more. The site isn't organized very well, but there are plenty of great videos if you're patient enough to search through them.
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Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
their education.
Math 442Homework # 1SolutionsTexas A & M UniversitySpring 20111. You are a professional modeler at Texas Department of State Health Services. You havebeen assigned to study an inuenza epidemic which occurred in a boarding school in the northof Dall
Math 442Homework # 4Due April 4Texas A & M UniversitySpring 20111. The simple pendulum consist of a particle P of mass m suspended from a xed point O bya light string of length a, which is allowed swinging in a vertical plane. If there is no frictio
Math 442Lab 1 - WorksheetTexas A & M UniversitySpring 2011In this course we will be using Matlab for numerical analysis of mathematical models. A lot ofuseful information about Matlab is available at http:/ begin we mus
Math 442Lab 2 - WorksheetTexas A & M UniversitySpring 20111. Consider a city with population of 3 106 . Suppose that one third of the people livingin that city have been infected with inuenza. In the absence of antibiotics, health ocialsestimate an
Math 442, Quiz # 5Name & ID number:(Solutions)Texas A & M UniversitySpring 2011[15 points] 1. What is the process of validating a model? When can we accept a model?First we propose a test (e.g. whether the model predictions match with the recorded d
Math 442, Quiz # 1 (solutions)Name & ID number:Texas A & M UniversitySpring 2011[30 points] 1. What are the main assumptions of the lake purication model discussed in section1.1 of the textbook?1.2.3.4.The lake has a constant volume.The lake is Research individual
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0471923850
9780471923855 and practice of the numerical computation of internal and external flows. In this volume, the author explains the use of basic computational methods to solve problems in fluid dynamics, comparing these methods so that the reader can see which would be the most appropriate to use for a particular problem. The book is divided into four parts. In the first part, mathematical models are introduced. In the second part, the various numerical methods are described, while in the third and fourth parts the workings of these methods are investigated in some detail. Volume 2 will be concerned with the applications of numerical methods to flow problems, and together the two volumes will provide an excellent reference for practitioners and researchers working in computational fluid mechanics and dynamics. Contents Preface Nomenclature Part 1 The Mathematical Models for Fluid Flow Simulations at Various Levels of Approximation Introduction Chapter 1 The Basic Equations of Fluid Dynamics Chapter 2 The Dynamic Levels of Approximation Chapter 3 The Mathematical Nature of the Flow Equations and their Boundary Conditions Part II Basic Discretization Techniques Chapter 4 The Finite Difference Method Chapter 5 The Finite Element Method Chapter 6 Finite Volume Method and Conservative Discretizations Part III The Analysis of Numerical Schemes Chapter 7 The Concepts of Consistency, Stability and Convergence Chapter 8 The Von Neumann Method for Stability Analysis Chapter 9 The Method of the Equivalent Differential Equation for the Analysis of Stability Chapter 10 The Matrix Method for Stability Analysis Part IV The Resolution of Discretized Equations Chapter 11 Integration Methods for Systems of Ordinary Differential Equations Chapter 12 Iterative Methods for the Resolution of Algebraic Systems Appendix Thomas Algorithm for Tridiagonal Systems Index «Show less... Show more»
Rent Numerical Computation of Internal and External Flows, Fundamentals of Numerical Discretization 1st Edition today, or search our site for other Hirsch
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-Still in Development-: Algebra for K-2 (MTH2551: Algebra for K-2)
The focus of this course is to provide strategies for K-2 teachers to explore the algebraic character of elementary mathematics that are present throughout the existing curriculum. Research shows us that given the proper conditions and activities elementary school children can reason algebraically and meaningfully use the representational tools of algebra. This course will focus on identifying previously overlooked opportunities to explore the algebraic character of early mathematics as well as investigating new and innovative methods of algebraic inclusion in the early childhood classroom. As a final product in this course participants will be participating in the creation of a collaborative unit of study.
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These experienced authors have been praised for their in-depth explanations and their commitment to avoiding a cookbook approach. Their text addresses three critical issues in teaching college algebra: poor student preparation, the need for thoughtful integration of the graphing calculator, and poor student study skills. Their texts have a strong reputation built on mathematically sound presentation, excellent applications, and on challenging students to develop algebraic, graphical, and verbal mathematical skills. Goodman and Hirsch help students go beyond the mechanics of mathematics to developing a coherent strategy to solving problems.
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Calculus A, the first of a two-semester course, centers on limits, differentiation, and applications of differentiation. Topics in this course apply to many problems studied in physics and engineering. Students review algebra concepts and learn fundamental calculus concepts, along with working problems for limits and derivatives. Students apply rules for finding different derivatives as well as learn the applications of the derivative. After finding the area under a curve using several different methods, students will complete an essay assignment that applies this to a real-world problem. Students conclude the course by applying theorems and demonstrating knowledge of basic rules for anti-derivatives. After successful completion of this course, students will have a fundamental understanding of the principles of calculus.
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Libros de: ECONOMIA CUANTITATIVA
Learn the science of collecting information to make effective decisions Everyday decisions are made without the benefit of accurate information. Optimal Learning develops the needed principles for gathering information to make decisions, especially when collecting ...
Hirsch, Devaney, and Smale's classic "Differential Equations, Dynamical Systems, and an Introduction to Chaos" has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a ...
Volume II is devoted to generalized linear mixed models for binary, categorical, count, and survival outcomes. The second volume has seven chapters also organized in four parts. The first three parts in volume II cover ...
Although there are currently a wide variety of software packages suitable for the modern statistician, R has the triple advantage of being comprehensive, widespread, and free. Published in 2008, the second edition of Statistiques avec ...
Packed with more than a hundred color illustrations and a wide variety of puzzles and brainteasers, Taking Sudoku Seriously uses this popular craze as the starting point for a fun-filled introduction to higher mathematics. How ...
Making good decisions under conditions of uncertainty - which is the norm - requires a sound appreciation of the way random chance works. As analysis and modelling of most aspects of the world, and all ...
Designed specifically for business, economics, or life/social sciences majors, "Calculus: An Applied Approach, 9E, International Edition" motivates students while fostering understanding and mastery. The book emphasizes integrated and engaging applications that show students the real-world ...
This book introduces in a systematic manner a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important and varied applications in medical diagnostics, image analysis, and machine ...
Graphical models in their modern form have been around since the late 1970s and appear today in many areas of the sciences. Along with the ongoing developments of graphical models, a number of different graphical ...
This book provides analysis of stochastic processes from a Bayesian perspective with coverage of the main classes of stochastic processing, including modeling, computational, inference, prediction, decision-making and important applied models based on stochastic processes. In ...
Business Statistics: First European Edition provides readers with in-depth information on business, management and economics. It includes robust and algorithmic testbanks, high quality PowerPoint slides and electronic versions of statistical tables. Furthermore, the text features ...
The aim of this book is to facilitate the use of Stokes' Theorem in applications. The text takes a differential geometric point of view and provides for the student a bridge between pure and applied ...
This book provides a comprehensive description of the state-of-the-art in modelling global and national economies. It introduces the long-run structural approach to modelling that can be readily adopted for use in understanding how economies work,
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Using Logarithms to Determine Relationships
This unit from the Continuing Mathematics Project goes into detail on how logarithms can be used to determine the laws which connect two variables on which experimental data has been collected. The unit follows naturally from the unit entitled The Theory of Logarithms.
The objectives of the unit are that students:
(i) understand the meanings of the terms exponential growth and decay, as they are used in relation to natural phenomena;
(ii) perceive that money invested at 'compound interest' also grows exponentially in denominational terms (even if it decays exponentially in purchasing power);
(iii) be able, when the relationship between two variables x and y is of the form y = C.ax, to plot values of log y against values of x on ordinary graph paper, or to plot values of y against values of x on log-linear graph paper, and so determine the constants C and a;
(iv) be able, when the relationship between two variables x and y is of the form y = C.xa , to plot values of log y against values of log x on ordinary graph paper, or to plot the values of y against the values of x on log-log graph paper, and so determine C and a
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Attend the 3rd Annual USACAS Conference
Computer Algebra Systems (CAS) have the potential to revolutionize mathematics education at the secondary level. They do for Algebra & Calculus what calculators do for arithmetic: simplify expressions, solving equations, factoring, taking derivatives, and much more.
With CAS, students have the power to solve many problems earlier – some which would otherwise remain inaccessible. CAS enable one to delay the teaching of some manipulative skills and completely eliminate others.
In short, CAS grant teachers new freedom.
Come explore the future of mathematics education!
Discover how secondary and middle school teachers are using CAS in their own classrooms.
Get classroom-tested lesson ideas developed for CAS-enhanced classroom environments.
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In most institutions of higher learning, number theory is not a required subject for math majors. As a consequence, the total market for number theory textbooks is only about 5000 copies per year in the entire United States and Canada. Nevertheless, the proliferation of number theory textbooks continues unabated. \par The most striking feature of this particular text is the authors' lavish use of abstract algebra. Indeed, the book contains a mini-course in algebra: Sections 2.3, 3.3, and 3.4 are devoted to groups, rings, fields respectively. A well-known theorem in number theory states that if $a$ and $b$ are natural numbers, then there are integers $x$, $y$ such that $(a,b)= ax+by$. On page 62, the authors present a slightly weaker version of this theorem, with a proof based on group theory. In the opinion of this reviewer, an experienced teacher of elementary number theory, this algebra-laden approach to number theory is more likely to bring confusion than enlightenment to the mind of the student, unless the instructor is blessed with students of exceptional ability. \par The authors seem to be fond of off-beat proofs. In Chapter 1, they present an interesting proof of the divergence of the sum of the reciprocals of the primes. In Chapter 2, they offer a complicated proof of the fundamental theorem of arithmetic that is based on well-ordering rather than on Euclid's Lemma. In Chapter 7, the authors' proof of Euler's theorem regarding the form of even perfect numbers is excessively long. \par Chapter 6, which is entitled ``Residues'', deals not only with quadratic, but with cubic and quartic residues. The latter topics require the introduction of some algebraic number theory. Like most other number theory texts, this one fails to present an algorithm for solving quadratic congruences. The chapter on congruences contains the now customary homage to cryptography. \par The first seven chapters of this lengthy book (518 pages) are called ``Fundamentals''. The final four chapters are devoted to ``Special Topics'', namely sums of squares and other representational problems, number fields, partitions, and recurrences. The authors deserve applause for their inclusion of a chapter on partitions, an undeservedly neglected topic in number theory. This text contains numerous exercises, but some of them are trivial, e.g. (1) Show that the function $x/\ln x$ is increasing for $x>c$; (2) Corroborate the stated number of digits for $M_{2976221}$; (3) Show that a Mersenne prime is a $(4k+3)$ prime. \par In summary, learning from this book might be a worthwhile experience for students of above-average skill and ambition. It is most likely overly sophisticated for students with more modest goals and backgrounds. [N.Robbins (San Francisco)]
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0878915648
9780878915644 or given on an exam is covered. Starting with topics under algebraic laws, the book includes linear and quadratic equations, inequalities, logs and exponentials, and extensively illustrated applications to area/perimeters, motion, mixtures/fluid flow, numbers/digits/coins, age, work, proportions, variations, and costs. Fully indexed for locating specific problems rapidly. «Show less... Show more»
Rent The High School Algebra Tutor® 2nd Edition today, or search our site for other Ogden
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Calc III Labs
These labs were created in the Spring of 1995 by high school students
participating in the University of Minnesota Talented Youth
Mathematics Program (UMTYMP).
The course used hypertext labs and technology-based
explorations on a weekly basis, in order to better communicate the
geometry of multivariate mathematics. The course was designed and
taught by Geometry Center postdocs
Davide P. Cervone and
Frederick J. Wicklin.
As a final project for the class, students worked in groups to explore
theoretical topics in mathematicas or the application of mathematics
to modeling real-world phenomenon. Several groups of students created
labs as part of their project; we have linked in a few of them here.
When you view these documents, please bear in mind:
In order to preserve the students' style, we have not corrected typos,
nor have we altered the students' jokes or sarcasm.
There are references to packages written in Maple.
We have linked this code into the documents as plain text.
The buttons that "Launch Software" will not work outside of the
Geometry Center.
Student-Created Labs
Charles McGarraugh,
Samir Murty, and Andrew Youn
A hypertext lab to explore the tangent planes and gradient
vectors of 2-dimensional and 3-dimensional curves. It examines
explicit, parametric, and implicit surfaces. The lab takes advantage
of the graphics capabilities of Maple, and even extends them.
Carolyn Jones, Jenwa Hsung, and Brian Larson
A lab that explores the geometry and algebraic techniques
involved in the method of Lagrange multipliers for finding
extrema of a multivariable function on a bounded region. The
lab includes several applications, and gives explicit
instructions for using Maple to compute the extrema.
Erik Streed,
Tim McMurry, and
Chris Wyman
A lab that leads students through the background and
definitions needed to understand evolutes and involutes of
curves, and provides Maple code for generating these curves.
The lab includes many example, and ends with some interesting
relationships between the involutes and evolutes of cycloids.
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Scotch College
VCE: Mathematics
Rationale
Mathematics is the study of structure and pattern in number, logic and space. It provides both a framework for thinking and a means of symbolic communication that is powerful, logical, concise and unambiguous and a means by which people can understand and manage their environment. Essential mathematical activities include abstracting, investigating, modeling and problem solving. Each Mathematics study is designed to provide access to worthwhile and challenging mathematical learning in a way which takes into account the needs and aspirations of a wide range of students. It is also designed to promote students' awareness of the importance of Mathematics in everyday life in an increasingly technological society and their confidence in making effective use of mathematical ideas, techniques and processes. All students in all the mathematical units offered will apply knowledge and skills, model, investigate and solve problems. They will use technology to support learning Mathematics and its application in different contexts. Note that all VCE Mathematics students are expected to be familiar with the TI-nspire (CAS) calculator.
See Appendix 1 for an outline of the most common pathways in Mathematics from Year 10 to Year 12.
Structure
Units 1 and 2: General Mathematics (SM)
General Mathematics (SM) is an advanced mathematics course designed both to supplement students' mathematical learning in Mathematical Methods (CAS) and to provide an appropriate foundation for students who wish to undertake Specialist Mathematics in Year 12.
Topics to be covered may vary from year to year, and will include Algebra, Functions and Graphs, Trigonometry, Vectors, Analytical Geometry and Calculus. Any student undertaking this course must also be taking Mathematical Methods (CAS) and should have achieved high grades in Mathematics in Year 10.
Assessment
Examination
Common Tests
Application Task
Units 1 and 2: General Mathematics (FM)
General Mathematics (FM) is a course designed both to extend students' mathematical knowledge and skills beyond Year 10 level and to provide an appropriate foundation for students who wish to undertake Further Mathematics in Year 12.
Topics covered are almost entirely areas of Mathematics with significant applications in a wide range of careers, and will include Algebra, Functions, Graphs, Financial Arithmetic, Trigonometry, Geometry and Statistics.
Assessment
Examination
Common Tests
Application Task
Units 1 and 2: Mathematical Methods (CAS)
Mathematical Mathematics (CAS) is a demanding mathematics course which significantly extends students' knowledge in key areas of Algebra, Functions, Graphs, Combinatorics and Probability and also introduces them to the fundamental ideas of Transformational Geometry (including Matrix Methods) and Calculus. Extensive use will be made of the TI-89 Titanium or TI-nspire CAS calculator. Note that when taken alone, this course is allocated six periods per cycle, but when taken with General Mathematics (SM) it is allocated five periods per cycle. Any student undertaking Mathematical Methods (CAS) should have a strong background, particularly in Algebra, and should ideally have achieved at least a grade of B for his Semester 2 Mathematics examinations in Year 10.
Assessment
Examination
Common Tests
Application Task
Units 3 and 4: Further Mathematics
Further Mathematics covers a range of mathematical topics and techniques which are used in many day-to-day applications in a wide variety of careers. The course consists of a compulsory (core) area of study, (Data Analysis), and a selection of three from six Modules:
Number Patterns and Applications
Geometry and Trigonometry
Graphs and Relations
Business-related Mathematics
Networks and Decision Mathematics
MatricesFurther Mathematics: Examination 1 33 per cent
Examination 2 33 per cent
Units 3 and 4: Mathematical Methods (CAS)
This course both consolidates and extends the material covered in Mathematics Methods (CAS) Units 1 and 2. The main areas of study are Algebra, Functions and Graphs, Calculus and Probability. Any student attempting this course must be familiar with the content of Mathematical Methods (CAS) Units 1 and 2. Extensive use will be made of the TI89 Titanium or TI-nspire (CAS) calculator.
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Create professional-quality mathematics worksheets to provide students in grades you will .... Free download of Math Resource Studio 4.4.2
Mathematics program intended for Middle School pupils (age 12-14) ... which reconciles the struggle against failure in school and the valorisation of the most talented students. Among ... Introduction of negative integers on an axis, addition and multiplication of whole numbers, proof of the sign rules, operations on fractions, prime numbers LCM' and GCD', setting and solving linear equations .... Free download of ALGEBRA 1 : Basic Operations on whole and rational numbers 4.00.005Mathematics program intended for High School pupils (age 14-16) ... which reconciles the struggle against failure in school and the valorisation of the most talented students. Among the subjects covered: Elementary identities, properties and operations on equalities, roots of a polynomial, factorization, absolute values, square roots, properties and graphs of linear and quadratic functions, equations of .... Free download of ALGEBRA 2 : Developments & applications 4.00.005
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9:00 Plenary Talk, As Geometry is lost - What connections are lost? What reasoning is lost? What students are lost? Does it matter?, Walter Whiteley, York University, Room 1900, Fletcher Challenge Theatre
Abstract:In a North American curriculum preoccupied with getting to calculus, we witness an erosion of geometric content and practice in high school. What remains is often detached from "making sense of the world", and from reasoning (beyond axiomatic work in University). We see the essential role of geometry in science, engineering, computer graphics and in solving core problems in applications put aside when revising math curriculum. A second feature is that most graduates with mathematics degrees are not aware of these rich connections for geometry.
We will present some samples of: what we know about early childhood geometry.; and then of the critical role of geometry and geometric reasoning in work in multiple fields outside of mathematics. With a perspective from "modern geometry", we note the critical role of transformations, symmetries and invariance in many fields, including mathematics beyond geometry.
With these bookends of school mathematics in mind, we consider some key issues in schools, such as which students are lost when the bridge of geometry is not there to carry them through (caught in endless algebra) and possible connections other subjects. We also consider the loss within these other disciplines. We will present some sample investigations and reasoning which can be supported by a broader more inclusive set of practices and which pays attention to geometric features and reasoning in various contexts. In particular, we illustrate the use of dynamic geometry investigations, hands on investigations and reflections, and making connections to deeper parts of the rest of mathematics and science. Download the presentation file here. Links to sources discussed in the presentation can be found in this document.
Abstract: Who do your students think their homework is for? Does attaching credit to homework promote student understanding, or encourage students to find answers by whatever means necessary? Are they focused on calculating the answer, or seeing the big picture? Is their homework grade a true reflection of their own understanding of the material, or does it better reflect the understanding of their "support network"?
In this workshop we will describe our efforts to improve student feedback and to promote good study skills in first and second year mathematics classes.
Workshop B: What is Mathematics-for-Teaching and Why Does it Matter?, Susan Oesterle, Douglas College, Room 1530
Abstract: In this interactive workshop we will review some of the latest research on the nature of specialised mathematics content knowledge for teachers. We will examine particular examples and consider how being aware of MfT can affect not only our approach to the preparation of teachers, but our own mathematics teaching.
Abstract: Cognitive load theory (Paas 1993) provides an approach for writing appropriate level questions so that novices will be more likely to answer the intended question. Cognitive load theory focuses on excluding extraneous information and providing only essential information for the learner. Although this approach is generally used to engender the selection of fundamental component parts and ordering them to scaffold learning new material, we have also found that better test questions can be constructed using these same principles; or so we think. Come and experience the difference, learn the principles for writing questions using cognitive load theory, and find out what we have learned about the process.
Workshop D: Efficient and Effective Teaching of Learning of Mathematics for Students of Science and Engineering with Software for Symbolic Computation, J. F. Ogilvie, CECM, SFU and Universidad de Costa Rica, Room 1530
Abstract: Although computers have enabled a revolution in many academic and other activities, their impact on the teaching and learning of mathematics has been much less potent than is warranted by the pressing demands of users of mathematics in scientific and technical areas. The present and continuing development of pertinent software facilitates a reappraisal of methods of teaching mathematics, with an emphasis on both improving the understanding of concepts and principles and the implementation of mathematical applications. We discuss how software for symbolic computation can play, and has already played, a significant role in the teaching and learning of mathematics not merely in particular topics but according to an holistic appreciation of all the mathematical knowledge and capabilities that a student of science and engineering might require for a prospective technical career during the twenty-first century.
Abstract: "Math. The bane of my existence for as many years as I can count. I cannot relate it to my life or become interested in what I'm learning. I find it boring and cannot find any way to apply myself toit since I rarely understand it." (high school student)Today, mathematics education faces two major challenges: raising the floor by expanding achievement for all, and lifting the ceiling of achievement to better prepare future leaders in mathematics, as well as in science, engineering, and technology. At first glance, these appear to be mutually exclusive: But are they? Is it possible to design learning that engages the vast majority of students in higher mathematics learning? In this presentation, I will present the findings and discuss the implications from a research study that explored the ways to teach mathematics that both raised the floor and lifted the ceiling.
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I think linear transformations are abstract by nature. Of course you can construct geometrical analogies in many cases, like for projection operators, rotations etc, and you might be able to use such examples to guide students towards the general definition.
Linear Transformations in Linear algebra
I'd introduce them by showing what they actually do, take you from one space to another.
The way Gilbert Strang does it on the MIT opencourseware linear algebra course is pretty good if you want to get introduced to what they do imo
Since a primary application is to differential equations, with students who have had calculus it seems important to point out that differentiation is linear. When acting on polynomials of fixed degree it also gives the basic example of a nilpotent linear operator, not an intuitive idea without that example. And when acting on spaces of exponential functions it gives the fundamental example of eigenvectors and eigenvalues, another absolutely crucial concept to acquire.
I learned linear algebra best when I thought in terms of geometry. Unfortunately, linear algebra starts in Rn from the start which is pretty annoying from someone like me. I made everything into a simpler case in R2 or R3. Without writing my own thoughts I found a good link for how I would best learn this.
The price is slowly going up because the editions are getting farther along. I have the 2nd edition and it's wonderful for showing the intuitive and visual representation of linear algebra. This is how math should be taught.. at least for learners like me.
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Accelerated Integrated Geometry (Accelerated Math 2) 27.0920040.Accelerated Math 2 is a Honors-level course. Self-motivated students are best suited for the rigor of this class. The course builds on itself and on material from previous courses, so students who are willing to seek out additional practice or help on difficult topics will be better able to stay on top of the material and not fall behind. Because this is an accelerated course, there is little time for review or re-teaching built into the schedule. Students are expected to retain information for significant periods of time to ensure that they can apply their knowledge in new situations encountered later in the semester. Students should be self-motivated to find extra practice or to seek extra help with topics they find difficult. The work-load is moderate with homework 3 to 4 nights per week. Good attendance is essential, as in all math courses. Students in the class are freshmen and sophomores.
Students may enroll in Accelerated Math 2 upon successful completion of Accelerated Math 1 OR on-level Math 1 with the summer bridge course. Even for students who were successful in Math 1 and the bridge course sometimes have an "adjustment period" at the beginning of Accelerated Math 2 to acclimate themselves to the rigor of the new class. Students transferring from other states should be placed in Accelerated Math 2 if they have demonstrated astrong understanding of the topics covered in Accelerated Math 1 (most of Geometry, large portions of what used to be called Algebra II, some probability / statistics). After Accelerated Math 2, students will take Accelerated Math 3 (Accelerated Integrated Precalculus), followed the next year by either AP Calculus (AB or BC) or AP Statistics. Topics include exploration of the characteristics of exponential, logarithmic, and higher degree polynomial functions using tables, graphs, and algebraic techniques; explore inverses of functions; use algebraic models to represent and explore real phenomena; solve a variety of equations and inequalities using numerical, graphical, and algebraic techniques with appropriate technology; use matrices to formulate and solve problems; use linear programming to solve problems; use matrices to represent and solve problems involving vertex-edge; use right triangle trigonometry to formulate and solve problems; investigate the relationships between lines and circles; recognize, analyze, and graph the equations of conic sections; investigate planes and spheres; use sample data to make informal inferences about population means and standard deviations; solve problems by interpreting a normal distribution as a probability distribution; and design and conduct experimental and observational studies.Prerequisite: Accelerated Integrated Advanced Algebra H
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APPLIED MATH
FROM ASSORTED PUBLISHERS
57 Great
Math Stories and the Problems They
Presentby Dr. Debbie Haver, Alice Koziol, Elaine Haven, and Dan
Mulligan. Instructional Fair, 1998. This book has some of the most interesting
story problems I've ever seen for use in a middle school math class. The
attention-grabbing stories and illustrations are presented on one page, and on
the following page you have six problems that relate to the story that range
from fairly easy to more challenging. The stories themselves introduce the
background for the realistic, humorous, and sometimes whimsical problems that
follow. Subjects include sports, pets, new jobs, advice columns, new babies,
neighbors, cattle drives, gardening, and other everyday topics of interest to
those in grades 5-8. Problems are carefully created to develop critical thinking
skills and problem solving strategies. Students need to use mathematical ideas
and concepts to find solutions and employ a wide variety of computational skills
with whole numbers, fractions, decimals, and percents. The stories can be used
for individual work or cooperative learning groups. Highly recommended.
Reproducible for classroom use, and answers are provided at the back. 120 pages.
BTH-2965. $11.69-D`
Agnesi to Zeno:
Over 100 Vignettes from the History of Mathby Sanderson Smith. This
265-page survey of mathematical thought and achievement for the secondary level contains
Blackline Activity Masters and links mathematics to the whole of human development. It
traces the history of mathematics from the earliest counting systems to modern
developments in chaos theory -- in an easily presentable format. The vignettes feature
both brief biographies of influential mathematicians and introductions to mathematical
concepts, while activities encourage in-depth research, critical thinking, and class
discussion. Included are over 100 exercises from almost every branch of mathematics that
give students the opportunity to apply the concepts developed by Euclid, Maria Agnesi,
Benjamin Banneker, and many others. Answers are provided for selected exercises for which
answers do not vary, and there is an extensive bibliography to aid in research. Index is
provided. Punched for 3-hole notebook. A Key Curriculum Press Book. Cat.BTH-729. $26.06-D.
Applied Math Series
(from Garlic Press): These show students in the upper grades how various mathematics
disciplines can be used to solve everyday problems. Titles are listed below.
$8.06-D
each.
Applying Algebra: Helps students
apply algebra to daily activities. Answers included.BTH-77. $8.96-D Basic Equations:49 pages of instruction and problems to help
students understand linear equations. Emphasis is placed on translating simple algebra and
geometry concepts into the mathematical statements needed to solve everyday problems.
Covers equations and number relationship, solving basic linear equations, word problems,
and formulas. Each topic has step-by-step explanations, examples, and applications.
Answers are provided.BTH-79. $8.96-D Metrics at Work:Provides 81 pages of instruction and problems
to help learn and apply the metric system to daily activities and commerce. Covers
conversions between the SI Metrics and the English System of measurement, square and
volume measurements, temperature measurements, SI Metrics and percents. Answers to
problems provided. BTH-80. $8.96-D Solving Word Problems: Provides a consistent and logical
strategy for solving any word problem. It is meant to be used by teacher and students at
all levels from beginning algebra on through differential calculus. Covers defining
qualities, reducing the number of variables, and setting and solving equations, There are
applications to algebra, trigonometry, and calculus. 125 pages, including answers.
BTH-78. $8.96-D
Barron's Essential Math: Basic Math for
Everyday Use, by Edward Williams and Robert Atkins. This book
teaches (or reviews) the math skills needed on the job, at the supermarket, at
the bank, and at the other places you live your life. Learn to figure sales tax,
discounts, tips, overtime pay, commissions, averages and probability.
Calculator-active exercises are included. Covers whole numbers, fractions,
decimals, and percents. Excellent preparation for minimum competency exams in
mathematics. Includes lots of illustrations, practice exercises, and answers.
BTH-2889. $13.46-D
Baseball Math: Grandslam Activities and Projects for Grades 4-8 by
Christopher Jennison. Good Year Books, 2009, 3rd Edition. Both boys and girls
will enjoy the thrill of their favorite sport as they practice and apply
important math skills. Grandslam activities and projects based on historical and
real-life situations involve students in every aspect of baseball: scorekeeping,
records, statistics, schedules, salaries, travel budgets, ticket prices,
refreshments, baseball card profits and losses, and fantasy leagues. Answers are
provided. Student activity pages are reproducible for classroom use. 112 pages.
BTH-5582. $11.66-D
Binary
Power: Insights, Activities, and Problem Solving Based on the Power of 2, by
John Veltman. This book explores binary numbers and the powers of 2 and their
applications, including binary patterns and codes in calculators, photocopiers, and
spell-checkers. Using intriguing problems, activities, and games, students will
investigate computer design and memory; study population and growth patterns; decipher the
postal zip code system; examine number patterns and probability; and explore family trees
and the ancestral paradox. Answer key included. 76 pages. For grades 5 and up. This book
is designed for independent student use, and is not reproducible, but neither does
it require students to write in it. OP, but I have some available. BTH-68. $9.95*.
Exploring
Math Through Puzzles: Blackline Masters for Making of 50 Puzzles by Wei
Zhang. A Key Curriculum publication. This book includes blackline masters with
step-by-step instructions for making over 50 puzzles that can be made from common and
easily obtained materials such as string, beads, wire, wooden cubes, colored stickers,
keys, pencils, etc. Geometry teachers will appreciate the puzzles' links to
three-dimensional visualization, while algebra teachers will like the problem solving
experience they will give students. There are extensive teacher's notes that discuss the
history and background of each puzzle described, along with practical tips for making the
puzzles, a list of materials, hints for solutions, and a list of additional
resources. For grades 5-12. Soft cover, punched for 3-hole notebook. BTH-4757. $15.26-D
Extreme Math: Real
Math, Real People, Real Sports, by Kip Tyler and Marya Washington Tyler.
Prufrock Press, 2004. The authors compare math to extreme sports because both
challenge people to seek the outer limits of their potential. They face the
unknown and grow in courage as they overcome their fears. Math is also a pursuit
of the unknown. In this book, students will meet several figures who participate
in a variety of extreme sports-- freestyle kayaking, skydiving, bronco riding,
adventure racing, hang gliding, scuba diving, mountain climbing, and polar bear
swimming. As each figure is introduced in the context of his or her sport with
black and white action photos, related math concepts and problems are presented
for students to learn and solve. Answers are included. 75 pages. For grades
5-10. BTH-3804. $13.46-D
Graphic Algebra,
A
Key Curriculum book for grades 8-11. Provides activities to use with graphing calculators
and software.
Hands-On Math: Manipulative Activities for the Classroom, Grades K-1
by Virginia Johnson. Creative Teaching Press, Second Edition, 2006. This
standards-based resource book contains over 200 hands-on activities that use
commonly available materials to help reinforce math skills. The main section
headings are Numbers and Operations (which include activities on sets and
quantities, numbers and symbols, operations, fractions and place value,
estimation and money); Algebra; Geometry; Measurement; and Data Analysis
and Probability. Included are bulletin board and learning center ideas, At the
end of the book are reproducible forms and a list of related literature.144
pages. BTH-1712. Follow title link for current price.
Hands-On Math: Manipulative
Activities in the Classroom, Grades 2-3by Glenda Nugent.
This resource book contains over 200 hands-on activities that use commonly
available materials. The author believes that a teacher who is enthusiastic
about hands-on learning holds the key to success in an activities-based math
program. The core of the book consists of 14 chapters, each of which has
bulletin board ideas, a skills list, suggestions for a learning center, math
journal ideas, and about 10-15 chapter activities for children to do. Chapter
topics are Number Sense, Classifying and Sorting , Patterns, Addition and
Subtraction, Fractions, Multiplication and Division, Geometry, Graphing,
Estimation, Time, Measurement, Money, Logical Reasoning, and Probability. At the
end of the book are Parent Letters, reproducibles, and a list of related
literature. 240 pages. BTH-1713. Follow title link for current price.
The Knots Puzzle Book:
Looking at Knots in a Different Way...A Collection of Interesting Mathematical Ideas by
Heather McLeay. This delightful book of 36 ingenious puzzles appeals to anyone who
likes puzzles and is curious about concepts of a mathematical nature. It's an
easy-to-understand introduction to the theory of knots that opens up a rich and
interesting set of ideas, investigations, and surprises. The puzzles move from basic to
complex. Most can be solved by looking and thinking, but for some puzzles it's
helpful to have a length of real string or rope at hand. Spend just a few minutes with
this book and you'll find yourself drawn quickly into the fascinating geometry of
knots! Puzzle solutions and a bibliography of related readings are included. Cat.
BTH-480. $11.66-D
Math
Graphic Organizers Grades1-2: Simple and Effective Strategies for Solving Math
Word Problems by Davilla Harding. Creative Teaching Press, 2003. 112
pages. This book teaches students in grades 1-2 a 4-step process for solving any
kind of primary math word problem: (1) Find the key words in the problem.
(2) Draw or use a graphic organizer to show the activity the word problem
describes. (3) Translate that activity into a number sentence. (4) Describe the
solution in writing. This will help students who have trouble discerning what
the problem is really asking them to do be able to visualize the problems.
Math
Graphic Organizers Grades3-4: Simple and Effective Strategies for Solving Math
Word Problems by Davilla Harding. Creative Teaching Press, 2003. 112
pages. This book teaches students in grades 3-4 a simple 4-step process for
solving any kind of primary math word problem: (1) Find the key words in
the problem. (2) Draw or use a graphic organizer to show the activity the word
problem describes. (3) Translate that activity into a number sentence. (4)
Describe the solution in writing. This will help students who have trouble
discerning what the problem is really asking them to do be able to visualize the
problems.
Exposing the Mole: a logic problem presented in the form of a card
game.
The Last Second Shot: uses probability to determine strategies in the last
seconds of a basketball game.
Look to the Cookie: an investigation in geometry presented in the context
of sharing a cookie
Only the Weak Survive: a probability situation presented in the
context of a popular reality show-type scenario
Pickin' Chicken: an investigation into the purchase of combinations of
"nuggets"
Popcorn Economics: an investigation in number sense presented in the
context of buying popcorn in a movie theater
Red Rover: students use logic to determine the most efficient method of
winning a game.
Also included are reproducible pages for students to use as reflection journals
so they can write about their experiences in solving the problems. There is also
a standards correlation page for the investigations. BTH-1466. $11.66-D
Step-by-Step
problems for remediation or for introducing a specific type of problem. In this
type of problem, each step of the solution is outlined, and space is provided
for students to do the calculations and explain their work.
Prompted Practice
problems, which provide less guidance, but still offer space for student work
and explanations.
Independent Practice problems offer no help in solving the problem -- just space.
Challenge problems
likewise do not offer guidance, but they are more difficult and are appropriate
for challenging gifted students or reinforce work students have accomplished
doing the other types of problems.
Problems deal with such subjects as raising a pet, owning a
business, going on vacation, buying furniture for a house, designing a new car,
etc. 79 pages, including answers. BTH-659. $11.66-D
Math Skills for the Workforce,
by Steck-Vaughn. Teaches math necessary for job success at a secondary math level but
written at a grade 4-6 reading level. Consumable worktexts. For details and titles
in series, click here.
Money Matters: How to
Be a Smart Consumerby Katherine Howe and Judith Edelstein. A reproducible
consumer math course for grades 4-6. This unit focuses on helping students build awareness
of market forces and develop skills that enable them to ask the right questions, analyze
their motivations, and recognize their options. Students will learn to spend their money
wisely, learn to distinguish between wants and needs, budget, understand credit and
interest, use a checking account, comparison shop, and shop by mail and the
internet. They will also learn the differences between capitalism, socialism, and
communism. 47 pages. Includes group lesson plans and reproducible worksheets.
BTH-4758.
$8.96-D
The Only Math Book You'll Ever Need:
Hundreds of Easy Solutions and Shortcuts for Mastering Everyday Numbers, by
Stanley Kogelman. This book is geared to adults who have forgotten or never learned the
practical kind of math needed to solve everyday problems: estimating the amount of paint
needed to cover a wall; balancing a checkbook; handling personal and business finances;
converting recipes; and much more. Digest size paperback book, 268 indexed pages.
BTH-7890, $11.70-D
Mathematical Quilts--No Sewing Required
by Diana
Venters and E.K. Ellison. Published by Key Curriculum Press. For grades 6-12. This book
was born because two mathematics teachers who worked together also took quilting classes
together and began to see the quilt possibilities in many of the mathematical concepts in
texts and journals. They became convinced of the value of designing quilts as a learning
tool. The activities in this book help student improve their visualization skills, as well
as their skills in analysis, informal deduction, and formal deduction - levels one -four
of the van Hiele model of the five levels of learning geometry. This book should be
especially helpful to those students who have trouble with formal geometry but are
otherwise capable students because its activities take these students through the first
three levels of learning successfully so that they are able to also be successful in the
fourth level.
The book is divided into three sections, each
featuring quilts with similar designs: "Golden Ratio Quilts," "Spiral
Quilts," "Right Triangle Quilts", and the "Tiling Quilts." After
students are introduced to the theme, they encounter a series of activities that guide
them through the mathematical concepts related to that particular kind of quilt
design. Each section includes research activities, technology activities for graphing
calculators and computers, and Internet activities. In conclusion students recreate the
quilt pattern with an emphasis on the art of the design. Students can actually learn how
to sew the quilt if they are interested in doing it. 168 pages. Blackline activity masters
included. Punched to fit standard three-hole notebook. Cat BTH-482. $18.86-D
On-the-Job Math Mysteries: Real-Life Math from Exciting Careers by Marya
Washington Tyler. Prufrock Press, 2009. If your students need convincing that
math skills are important in the real work of work, this book should do the
trick. It's just like a field trip, but more practical. It takes students to a
number of workplaces where they solve occupation-related problems. Here are some
of the interesting jobs they will explore: Circus Performers, Organic Farmer,
Dogsled Musher, Beekeepers, Kayak Guide, Shellfish Farmer, County Judge,
Railroad Engineer, Videographer, Heavy Equipment Operator, Wildlife Veterinary
Technician, Software Engineer, Environmental Health Specialist, Waste Manager,
Soup Kitchen Operator, Logging Manager, Sawmill Operator, Commercial Fisherman,
Air Traffic Controller, Master Carver, Diver, and Bush Pilot. The math problems
are tied to NCTM standards, and students will use skills such as selecting an
operation, determining place value, using fractions and decimals, working with
geometry, applying measurement skills, estimating, and recording and analyzing
data. Problems are on reproducible worksheets and answer key is included. 76
pages. For grades 4-8. BTH-5335. $16.16-D
Patty
Paper Geometry by Michael Serra. A Key Curriculum Press book. Shows how
to use the paper restaurants use to separate hamburger patties as cheap manipulatives in
your geometry classes.
Racing Math: Checkered Flag Activities and Projects for Grades 4-8
by Barbara Gregorich and Christopher Jennison. Good Year Books, 2005, second
edition. Students can race with NASCAR, Indy, and Formula One greats while they
learn important math skills. The activities and projects have many exciting
twists and turns, all based on famous races, speeds, records, pit crew
performance, speedways and race courses, engines and car models. Reluctant math
students who love racing will be drawn into this book as they see how math
relates to their favorite sport. 106 pages. BTH-5583. $11.66-D
Success with Math: Prealgebra,
Prufrock Press, 2007. This book is a combination prealgebra word problem and
project books and is intended as a supplement to the regular prealgebra
curriculum. Each page focuses on one or two concepts of prealgebra and can
easily be assigned along with other homework. There is plenty of room on each
worksheet for students to show. their work. In addition to the exercises, there
are several extended projects in the second half of the book, most of which are
designed to be completed in one to two class periods. In this book, students
will review conversions, geometric properties, statistics, problem solving, and
algebraic formulas. A teacher's guide and conversion tables are also included.
For grades 5-8. 71 pages. BTH-3771. $10.76-D
Success
with Math: Decimals, Prufrock Press, 2005. For grades 5-7. The exercises
in this supplementary book allow students to work sequentially through each
concept in decimals and practice their skills before moving on to the next
concept. Each type of problem is explained in an introductory page and followed
by two practice pages. Periodic cumulative review pages may be used for
additional practice or assessment. This step-by-step approach is also good for
independent study. The books units include comparing and ordering decimals;
adding, subtracting, multiplying, and dividing decimals; rounding decimals; and
converting decimals to percents, fractions, and scientific notation. This book
meets NCTM standards. 64 pages. BTH-3772. $10.76-D
Tall Tale Math Series from Educational
Impressions : Humorous Story Problems for the Middle Grades Designed to
help instructors implement the current Curriculum and Evaluation Standards, these
books help students understand and utilize the fundamentals of mathematics. Each book is
divided into three sections:
Thought
Provokers, by Doug Rohrer. Drawings by Joe Spooner.
These 47
puzzles, both originals and embellishments of classics, are designed not to test students,
but to instruct and entertain them. Creative and well-paced hints intrigue students while
developing their problem-solving and critical-thinking skills. Designed as blackline
masters, Thought Provokers presents one humorously illustrated
problem per page. Make individual student problem sheets, or assign problems to students
working in a cooperative learning setting. Post problems on the wall as attractive and
interesting decorations for your classroom. An excellent resource for warm-up activities
in the secondary classroom. 64 pages including hints and answers. For grades 9-12.
Cat. BTH-4690. $11.66-D
More Thought Provokers:
This second volume of brain teasers intrigues readers with 50 more provocative problems.
Author Doug Rohrer entertains students with creative, instructive puzzles that foster
cooperative learning and develop critical thinking skills. Designed as blackline masters
and illustrated in the same humorous style as the original Thought Provokers,
each page contains a single problem that will spark student discussion while developing
problem-solving skills. 64 pages including hints and answers. BTH-4691. $11.66-D
Nim:Serious Math with a Simple Game, by Christopher M. Freeman. Produced
by Dandy Lion Publications.
Nim is a simple game, but winning consistently requires logic and mathematical analysis.
Exploring the many variations of the game and the strategies for winning presents
opportunities to explore several fields of math from an inductive approach. Over twenty
variations are presented with simple, attractive game rules for students and detailed
explanations for teachers. All you need is this text and a pile of paper clips for a
year's worth of educational fun.61 pages.
Reproducible for classroom use. For grades 5-8. Cat BTH-663. $10.76 Out of
print. Click title link to check availability.
-D
Piece
of Pi: Wit-Sharpening, Brain-Bruising, Number Crunching Activities with Pi by
Naila Bokhari. Discover the number that has intrigued mathematicians for centuries. Learn
all the different ways pi has been calculated through the ages, use pi to figure your hat
size, perform experiments, relate pi to the alphabet. These fascinating activities offer a
complete overview of this important number. Includes detailed lesson plans and
reproducible student worksheets. For grades 6-8. 48 pages. Features time line and
eye-catching graphics. Cat. BTH-662. $9.86-D
Unfolding Mathematics with
Unit Origamiby Betty France. Key Curriculum Press. Black Line Activity
Masters, punched to fit standard three-hole notebook. This book, with its elegant
illustrations and detailed folding and assembly directions, will show you and your
students how to create intriguing three-dimensional models. the sixteen activities, in
blackline master form, first present simple folding techniques that transform square
pieces of paper into a variety of geometric shapes. As students repeat the folding
sequences, they create identical units that combine to form tetrahedra, cubes, octahedra,
and much more. After they learn the basics, students can go on to invent their own unique
polyhedra. These activities can to used in middle and high school algebra and geometry
classes. Most can be finished in one class period. 115 pages. Cat # BTH-1420. $17.06 warehouse
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From the Publisher: Learn to think mathematically and develop genuine problem-solving skills with Stewart, Redlin, and Watson's COLLEGE ALGEBRA, Sixth reinforce what you've learned. In addition, the book includes many real-world examples that show you how mathematics is used to model in fields like engineering, business, physics, chemistry, and biology.
Description:
Over the years, the text has been shaped and adapted
to meet the changing needs of both students and educators. As always, special care was taken to respond to the specific suggestions of users and reviewers through enhanced discussions, ...
Description:
This text bridges the gap between traditional and reform approaches
to algebra encouraging students to see mathematics in context. It presents fewer topics in greater depth, prioritizing data analysis as a foundation for mathematical modeling, and emphasizing the verbal, ...
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For up-to-the-minute information about MathFest, check out the MathFest
wiki.
2009
Joint Mathematics Meetings
In January 2009, faculty and students met in Washington, DC
for
the Joint Mathematics Meetings. This national meeting of the MAA and
the American Mathematical Society (AMS) brought together many
opportunities for students to present their research, network with
faculty and meet other students. Faculty also had
opportunities
to gather information about organizing activities for math clubs and
MAA Student Chapters. See the articles below for more
information.
Other
Information
April is
Math Awareness Month.
This year's theme is "Mathematics and Climate."
Calculus, differential equations, numerical analysis, probability, and
statistics are just some of the areas of mathematics used to understand
the oceans, atmosphere, and polar ice caps, and the complex
interactions among these vast systems.
NSF Special Report - Math:
What is the problem? Highlighting the importance
of mathematics, this report features MAA President David Bressoud in
the "Learning the Language of Math" video segment,
and also has links to a variety of on-line resources.
Look to
the MAA for Career Information and Job Searching
No matter what stage of their education your students are in, the MAA
has the career resources they need. The MAA website has several places
dealing with vocational possibilities. The MAA Career Page
contains descriptions of many of the myriad of professions for people
with mathematics degrees along with links to follow for more
information. An electronic version of Andrew Sterrett's 101
Careers in Math is available. Here one can get
first-hand accounts of what mathematicians with all types of degrees
are doing in their profession. To help students find jobs, there is the
immensely successful MathClassifieds,
hosted by the MAA. Here employers post advertisements and job-seekers
can upload resumes and cover letters. After signing up for a free account,
people can search for jobs by keyword, location, or job type and can
create a Job Alert, which will notify the seeker when an advertisement
matching chosen criteria is posted. This service is for
employment-seekers at all levels (Bachelor's,
Master's, and PhD). Examine these sites and you will find
that the MAA is the place for you and your students to go for the scoop
on careers.
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Search Course Communities:
Course Communities
Lesson 9: Gaussian Reduction
Course Topic(s):
Developmental Math | Systems of Equations
An introduction to solving a 3x3 linear system of equations. Back substitution and triangular form are first introduced, and then a general procedure for solving systems is presented. Application and non application problems.
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I may start working my way through Brown myself when I finish RUSSIAN MATH by Nurk & Telgmaa.
Algebra Through Problem Solving by Hillman & Alexanderson - This book has been placed on the Web by the Science Education Team at Los Alamos National Laboratory to help students better prepare for careers in mathematics and science. The topics are essential for success in college level mathematics but tend to be taught inadequately, if at all, due to discontinuities between high school and college courses. The treatment here also provides experience with pattern recognition and other problem solving techniques. (authors also have a book on complex numbers and trigonometry posted online)
state of CA frameworks for algebra - best in the country:
Mary Dolciani
"Mary Dolciani [full citation t/k] is good, but there are others as good also. Foerster has been recommended, so should be checked out. The problem with Dolciani is she tends to be a bit TOO formal at times. But still she gives a good rigorous treatment of algebra with lots of problems."
In Don't teach in a montone, part 1, Carolyn writes that, "Early texts in a math field, written when the topic is new and hot, generally have a lot of life; they start out talking about what motivates the creation of an idea -- they do examples -- they talk about what's known and what isn't. When the theory is better understood, the presentations get terser and cleaner, less emotional, and in a very real sense less useful. This is the higher life form to which mathematics texts seem to evolve, and I think it's a mistake."
Bernie, who is Carolyn's husband, write NUMBERS AND SYMMETRY as an early text, with the life and emotion of authors discovered a new field of mathematics.
algebra online
Action Math (fantastic website teaching individual problems - aimed to middle school students I think & not limited to algebra)
Hot Math looks excellent: "We show step-by-step explanations for the actual homework problems in your math textbook." pre-algebra through calculus and college algebra; subscription website also inclues what look to be free online workbooks in each subjected created by Hotmath
Catherine speaking: I assume the Virginia tests are useful, partly because I liked the looks of the 5th grade test, and partly because Cheri Pierson Yecke was, as Virginia's Secretary of Education, involved in creating Virginia's state standards. On the other hand, the Fordham Report on The State of State Math Standards gives Virginia's math standards a grade of C. Still, it was Ralph Raimi, I believe, who told me in an email that one shouldn't obsess over finding the perfect test; he said just to pull questions from the Singapore curriculum and use those if you want to know how your child is doing in math. I'm sure he's right. The important thing is to 'test the tests.' Give your child a not-overly-involved assessment at home just to make sure that your state tests aren't way off-track. Trust, but verify!
Daily Grammar wonderful, thorough set of lessons on every aspect of grammar, including sentence variety; includes quizzes; not sure how many worksheet-type assignments there are - writeup: Mr. Bill Johanson is the author of the lessons. He has taught high school and junior high school English classes for thirty years, doing a great job of preparing his students for college.
summer reading lists
Dobbs Ferry, the town next door to me (Catherine) has an International Baccalaureate program, and most of the school reading lists I've looked at are are terrific. They include recommendations from the kids, which is great. You can also compared reading lists for the IB & AP courses to reading lists for the non-IB, non-AP courses. Grade 6 list Grade 7 list
You can access all of the lists from both of these pages.
The Paideia School's extensive lists for junior high and high school readers are probably excellent. Fiction, nonfiction, and poetry. Type "reading list" in the search field.
For ktm readers' lists of books their children liked see Comments threads here and here.
fraction manipulatives to print by Doug Sundseth (pdf files)
G
geogaphy
geometry
Geometry by Edwin E. Moise and Flloyd L. Downs
A mathematically rigorous geometry textbook from the era of New Math.
see: SmsgGeometry
Geometry by Moise Downs is good but not the only good text around. Adkins/Weeks has a good geometry text as does Jacobs. M-D is my favorite but that shouldn't be taken as the last word by any means! (Barry Garelick)
homeschooling curricula and books
homeschool law
I
J
Jaime Escalante
K
L
M
middle school math
Mathcounts web site devoted to middle school math; excellent; Mathcounts contests are major events
For late middle school and high school I am impressed by the Dolciani series, Structure and Method (McDougal-Littell). Unfortunately the most advanced Dolciani, the pre-calculus Modern Introductory Analysis, has been allowed to go out of print. Saxon also seems a decent option for the late middle school and early high school years, as does Singapore's New Elementary Mathematics. There may be plenty of other good traditional choices, but I am not familiar with U.S. high school textbook series other than Dolciani. I don't know if the Japanese mathematics textbooks (Translated by UCSMP) could be an option; they are a very strong series for the highest grades. I don't know of U.S. studies that compare outcomes of various high school curricula. Internationally, of course, TIMSS especially has shown the superiority of typical curricula used in Korea, Japan, and Singapore.
O
online algebra
online math
multipliers][Donna Young's online lesson in unit multipliers (she has many terrific printable manipulatives as well]] edHelper.com I'll probably join this site (Catherine speaking) - Susan likes it, and it has a phenomenal ability to construct whatever kind of worksheet you need, on the fly $19.99 a year - I've just subscribed, and it's very helpful. The one drawback is that you can't specify value range to the extent I would like. I needed a sheet of integer problems with integers between -20 and 20 (which I could have Christopher solve using Doug Sundseth's number lines), but wasn't able to ask the program to do this. Math for Morons horrible title, but this is probably a good & useful site - includes calculus Webmath.com looks terrific - 1,300 completely solved problems K-12 plus math experts to answer questions Grade Level Math Links K-12 (looks good) printable number lines, 8 to a page all positive numbers, unfortunately long & semi-annotated list of online resources line jumper at FunBrain add & subtract integers on a number line (kids love this site, in my experience--tons of math games)
Here's MathBrain (part of FunBrain) Math baseball at FunBrain The boys in my Singapore Math class loved this game. Lesson Tutor this looks terrific, though I haven't used it yet; seems to be associated with Teachnology, which is associated with FunBrain... interactive math links (haven't use this site as yet)
online tutorial in real analysis by Dr. Bert Wachsmuth of Seton Hall University. Some sections are incomplete, but Barry Garelick says that what is there is impressive.
online geometry
GeometryEuclid have you stumped? Archimedes run rings around your head? Well you've come to the right place. This is where you'll find almost everything you'll ever need to know about Geometry. We have a special page on constructions and plenty of sample problems to help you understand the concepts. Have a blast and don't forget to check out our Glossary - it's huge! (no idea whether this site is useful - let me know)
online story problems
Challenge Index (looks like it may be fun - sample question: How fast can an Arctic tern fly around the world?)
P
possibilities
I haven't had time to look around this web page, but on first sight, it appeals to me. It appears to have a mix of problems surrounded by lots of white space (good) and illustrated with clip art that, so far, I find stimulating as opposed to bewildering. (I love Carolyn's line about how the Prentice Hall pre-algebra book is going to make hers & Ben's eyes spin like cartoon characters. No joke.)
If you have reactions, let us know. Catherine
pre-algebra
Pre-Algebra: An Accelerated Course by Mary Dolciani ISBN: 0395591236 (almost certainly an excellent book - I haven't read it closely, but I consult it often & my neighbor's son relied on it to get through the Phase 4 class last year)
3-23-2006: I've now worked my way through all but the last 10 lessons of Saxon Homeschool 8/7, and I love it. Can't possibly praise it highly enough. This is Christopher's 6th grade year, and if he had been using Saxon 8/7 instead of Prentice-Hall Applications, he'd a) know and understand math through pre-algebra, and b) like math through pre-algebra.
pre-algebra workbooks
I've used two, and found both helpful:
Instructional Fair Pre-Algebra by Frank Schaffer is my favorite of the two. (IF workbooks can be hard to track down on the web; no idea where to get the best price.)
pre-algebra worksheets
Glencoe Pre-Algebra Parent and Student Study Guidefree online "The Glencoe Parent and Student Study Guide is designed to help you support, monitor, and improve your child's math performance. These worksheets are written so that you do not have to be a mathematician to help your child." excellent, fantastically helpful
Iím modeling this on Saxon Mathís constant repetition of 4 fact families to teach inverse operations & the commutative property (see next page). Christopher and I both found the 4-fact families terrifically effective.
We'll see how it goes.
Q
R
references
Russian Math
No idea what this book is like, but the folks at Mathematically Correct have a link to it, so I finally ordered a copy yesterday. [update: I just got my copy--it's incredible. I'm working my way through it now. 6/05 -- Catherine]
A press release from the translator has this to say:
First published in 1987, Mathematics 6 took the Soviet education establishment by storm, winning the national competition for best new math book that year.
2nd update: I love, love, love this book. I've now worked 100 of the 1100 problems in the book, have learned much, and am going to write numerous posts about it. If we were awarding stars, this MATHEMATICS 6 would have 5. more on this, and on who might want to use it, t/k. 6-12-05
3rd update: I still love this book; am now up to problem number 219. I'll probably have Christopher use this book next summer, between the 6th and 7th grades.
final update: I've studied every lesson in the book, worked every problem. It's brilliant. Makes the Singapore Math books look like overachieving strivers (and those books are terrific). Russian Math category thread here
S
Saxon Math
Saxon answer sheets, complete set These are not the answers, but the sheets on which children do their work and write their answers. You can see what they look like here. Terrifically helpful, because Saxon Homeschool Edition does not include a workbook. You may want to write each problem out by hand on these sheets; I did that for Christopher throughout Saxon 6/5, and it was a big help.
Singapore Math placement tests & guidelines
Parker & Baldridge
note: For what it's worth, I would probably skip the instructor's & teacher's guides (see below) and spend my money on Parker & Baldridge & possibly one or both of the Singapore books for parents (links below). However, I've taught only a couple of units—on fractions, ratios, & proportions—using PRIMARY MATHEMATICS, so I'm not the best person to listen to on this. (Catherine)
[update: now that I've gone to the trouble of posting all of the links for Jennifer Hoerst's Home Instructor's Guides at Sonlight.com, I find that these are the same guides sold on SingaporeMath.com, and that Ms. Hoerst runs a Singapore Math forum at Yahoo groups. I'm wondering whether she's the owner of SingaporeMath.com.]
Singapore Math's Teacher's Guides & Home Instructor's Guides
note: The Singapore Math web site offers two guides for each book, the Home Instructor's Guides by Jennifer Hoerst & the Teacher's Guides, written in Singapore. I ordered the Home Instructor's Guide for 3B and found it fairly confusing. That was back when I was first trying to teach Christopher what he'd missed at school and I was feeling pretty confused myself, so I'd probably do better with it today. Nevertheless, the graphic design is poor; every page is crammed with symbols, text, and rules. It's not Page Splatter in the manner of U.S. textbooks, but, for me, it takes a conscious act of will to read even one page. As a matter of fact, it was the 3B Home Instructor's Guide that convinced me to go with Saxon instead of Singapore!
Singapore Math middle school
Singapore Math high school
spelling
Perfect, and reasonably priced ($7 for the teacher's guide, $9.85 for the workbook). Eight books altogether, starting with Book 1 in 4th grade. Even if your child is older, it's probably a good idea to start with Book 1, since the books are sequential, and subsequent books build on the syllabication rules learned in earlier books.
Glencoe Pre-Algebra There are various editions of Glencoe Pre-Algebra available online; I have no idea which is which, or whether any substantial revisions have been made from one book to the next. There's a very funny & very negative Amazon reader review of this edition ....
touch typing
U
V
vocabulary
The Vocabulary Workshop series is excellent, IMO. Almost more importantly, Christopher is enjoying the first book he's used, Level A, for grade 6. The books begin in second grade and go through grade 12, one book per year. Grades 2 - 5 are Levels Purple, Green, Orange, & Blue. Sixth grade starts with Level A, and the books go through Level H. The cost is around $10 per book, and you don't need the teacher's edition.
Saxon worksheets are here This is a link to a page with Saxon worksheets, in Word documents, that should download to your desktop. You can print them out for every lesson (every book in the series through 8/7) and write or type the problems in the correct spaces). If you type in the problems, I'd love to get copies to upload to Kitchen Table Math. We'd have a set of Saxon workbooks people could download.
DonnaYoung.org lots of terrific printable worksheets, number lines, graph paper, pie-chart fractions, play money, paper for scale drawing & worksheets with number lines on the top (click on math)
Handwriting for Kids lovely web site maintained by homeschooling mom. The focus is on handwriting, but she has terrific visual math worksheets for kids like Andrew (autistic, nonverbal, bright). Penny Math; visual addition; she also has lots of online worksheets (child types in answer & the worksheet is graded online).
from Carolyn
Sometimes, the kid just isn't up to doing a whole math lesson (or more likely, I'm not up to giving him one, since it's something of a battle).
On those nights, something like these math worksheet generators can come in very handy. There are a lot of these generators around, but this one is very configurable; you can set the number of columns and rows of problems, and the difficulty of the problem, and the numbers of significant digits in the solution, and so forth.
Give the kid a worksheet with a few problems on it, and let him get in a little practice. Resist the urge to give him more than 4 or 5 problems on a sheet; make them easy. The most important thing is to make every learning experience a success -- especially true if this is material he is already supposed to know how to do, and will be doing independently.
But Saxon's problem generator is clean, simple, and compelling. I liked using it myself, and Christopher seemed to like it OK, too.
You decide which facts problems you want to do, how difficult the problems should be, and how many you want to do. You can also do timed or untimed problem sets. Kids love seeing their timing get faster, I find.
So if you need something for your child or student(s) to do while you're getting organized, this is probably a good choice. (I still wouldn't trust computer learning to firm up my child's math facts unless it's clear that he or she really is learning math facts online or using a software program. In our case, even after Christopher had used a little software program I bought, it was clear he wasn't gaining speed or accuracy. He didn't really get his math facts down cold until we started doing the Saxon fast fact worksheets. Interestingly, flash cards didn't work well for us, either. And we spent quite a bit of time with them...)
Saxon online math activities* Now that I've warned everyone against teaching math on a computer, I have to admit I'm kind of addicted to these animated Saxon activities, too.
Here are the 5th grade activities. Apparently the site now tells you which activities to do after which lessons in the book; plus you can download them for use when you are not online.
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Combinations of Operations with Fractions
Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses combinations of operations with fractions. By the end of the module students should gain a further understanding of the order of operations
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Statistics Bridging Courses
Early in 2013 the Mathematics Learning Centre will offer short bridging courses for students planning to undertake programmes which require the study of statistics, such as Statistics and Research Methods for Psychology, and degrees/diplomas in Public Health or other postgraduate degrees.
These courses are designed for people who lack confidence when faced with mathematical tasks or as a refresher for people who want to brush up on basic mathematical skills. They may also be useful for students who have not studied Mathematics (2 Unit) at school. They are not appropriate for students who have at any time completed the higher levels of mathematics for the Higher School Certificate.
The courses aim to review the basic mathematics needs of students in a statistics course and to develop an intuitive understanding of some fundamental statistical concepts.
The program includes:
use of a scientific calculator, including the use of statistical functions
algebra, including the use of formulae and the solution of simple linear equations
introduction to concepts in probability by means of practical activities
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Sticky FAQs
My textbook comes with a set of PowerPoint lessons. What is the difference with these ones?
The textbook lessons are by the most part written by people that knows the subject but it is not in front of a class, or does have limited teaching experience; therefore most of the textbook lessons tend to skip intermediate steps, which are a major issue for the average students, and even more for struggling students. They break the solution in several slides, so that the students loose track of the problems, and finally they favor long paragraphs as explanation instead of highlighting in the figures and graphics the steps using colors and animations. This poses a serious difficulty when trying to use them to teach a lesson. The lessons you purchase in MrPerezOnlineMathTutor.com have been written by a teacher working in the classroom for more than 10 years, and holding a teacher credential, and CLAD and BCLAD credentials. The lessons have been fully tested in the classroom.
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Shepherd, TX Calculusucius-Kung Fu-tzu or Kung the Master, born c. 551 BCE influenced Chinese culture until the early twentieth century. Temples and other monuments were built for the religion of Confucius who emphasized family and community and respect for elders. Lao Tzu born c. 604 BCE founded Taoism, more o...I can almost guarantee that you will have ?Aha! So that?s how it works!? moments as algebra becomes more familiar and understandable. Algebra 2 builds on the foundation of algebra 1, especially in the ongoing application of the basic concepts of variables, solving equations, and manipulations such as factoring.
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'Class Companion' series is designed in accordance with the CBSE syllabus. It provides supplementary content and learning resources for the school-students of higher grades seeking to solve additional problems and thereby succeeding in their academic and competitive pursuits. The interactive learning design makes learning enjoyable. Inclusion of diverse range of practice exercises— from questions that reinforce learning to questions that tickle the analytical mind to improve students' problem-solving skills. The aim of this series is not only to improve performance in regular examinations but also to aid the development of skills needed to crack the competitive examinations. An invaluable resource for teachers and students, the Class Companion will simplify both teaching and learning. Now, learning will not be complete without the 'Companion'!
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Cut The Knot!
Students' Social Choice
It's our choices, Harry, that show what we truly are, far more than our
abilities.
Albus Dumbledore, Headmaster
Hogwarts School of Witchcraft and Wizardry
Harry Potter, Year 2,
J. K. Rowling
Scholastic, 1999
The usual math sequence taken by a liberal arts major is two courses
long: some sort of intermediate algebra and one more course that is
expected to fulfill the aims of liberal arts education with regard to
mathematics. This last — the final math course — what should it
be? Years ago, this course would most certainly be of the pre-calculus
variety. It might have also been an attempt to endear mathematics on
students who gave up on the subject long, long ago by presenting its more
enticing, often recreational facets (see, for example,
a review of
[Beck], where the latter was referred to as a
magnificent fossil of a book. Sherman Stein's eminently readable
book might be in the same category. It was republished
in 1999 by Dover Publications, Inc., which places it squarely among the
venerable classics. The book can be now had at
amazon.com at a throwaway price of
$13.96, far below the expected textbook price range.)
A new trend seems to be growing roots in math departments and among
textbook publishers. I am aware of two fine representatives of this trend:
Excursions in Modern Mathematics by
P. Tannenbaum and R. Arnold and For All Practical
Purposes by COMAP. In less than a decade one underwent 4, the
other 5 editions. The books are similar in contents, execution and price
($90+).
In the Preface, the authors of
Excursions explain that the
"excursions" in this book represent a collection of topics chosen to meet a
few simple criteria:
Applicability
The connection between the mathematics presented here and
down-to-earth, concrete real-time problems is direct and
immediate.
Accessibility
Interesting mathematics need not always be highly technical and
built on layers upon layers of concepts.
Age
Modern mathematical discoveries do not have to be only within the
grasp of experts.
Aesthetics
There is an important aesthetic component in mathematics and, just
as in art and music (which mathematics very much resembles), it often
surfaces in the simplest ideas.
The following is a small sample of the topics common to the two books (I
am more familiar with the Excursions than
with the COMAP book, whose contents could be
ascertained from
the
online description.)
The Borda Method
The Borda method, named after Jean-Charles de Borda (1733-1799), is used
to select the winner of the Heismann trophy, the American and National
Baseball Leagues MVP's, Country Music Vocalist of the Year, school
principals, university presidents, and in a host of other real world
situations.
The Borda and the Plurality with Elimination (described below) methods
use preference ballots, wherein a voter lists the alternatives in
order of preference. The Borda method is about counting points. The last
alternative on a ballot receives 1 point, the next one receives 2 points
and so on. The Borda method selects the alternative with the largest point
count.
It may surprise a student to learn that the winner picked up by the
Borda method may not be the one preferred by the majority of the
voters.
(Numbers in the upper row indicate the number of votes cast for ballots
below. Letters A, B, C, D and so on denote the competing alternatives.)
Plurality with Elimination
The Plurality with Elimination is a natural extension of the majority
vote to the case of more than 2 alternatives. Alternatives with the fewest
number of (1st place) votes are dropped one after another until
only two left, of which the winner is selected by the majority rule.
The Plurality with Elimination method violates the so-called
Monotonicity Criteria. It's possible for a winner to lose the
elections after someone switched votes in its favor. To see how that may
happen, swap the first and the second alternatives on the 4th
ballot.
There are many more methods used to combine individual preferences of
the voting population into the Social Choice of the population as
a whole. Kenneth Arrow's Impossibility theorem (1951), which in its
currently common formulation asserts that no absolutely satisfactory
democratic method exists, was called by Arrow himself the General
Possibility Theorem: it pointed to a method that satisfied all the
reasonable requirements Arrow thought to impose on a Social Choice
procedure. Unfortunately, the method came out to be a dictatorship: one
fellow's social preferences become the choice of the whole population (with
or without an election).
Power Indices
The United Nations Security Council consists of five permanent members
(the US, Russia, England, France and China) and 10 nonpermanent members
elected for two year periods on a rotating basis from several country
blocks. For a motion to pass in the Security Council, it must be approved
by all five permanent members and at least 4 nonpermanent ones. The
situation is best described as a
weighted
voting system [39: 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
which indicates that
each of the five permanent members has a weight of 7 (votes),
while
each of the ten nonpermanent member has a weight of 1, and
that
for a resolution to pass in the Security Council, it must muster at
least 39 — the quota — votes.
All five permanent members have in effect veto power and thus
wield more power than is suggested by the ratio 7:1. The Banzhaf power
index has been invented to evaluated power distribution in weighted voting
systems.
A coalition of voters is called losing if the total weight of its
members does not reach the quota. Otherwise, a coalition is called
winning. A member is critical to a winning coalition if its
removal renders the coalition losing. Let there be N vote holders (players,
as they are usually called). Let Bi, I = 1, 2, ..., N, denote
the number of times the Ith player is critical. Introduce B =
B1 + ... + BN. Then the Banzhaf power index of the
Ith player is defined as BPIi =
Bi/B.
It could be shown that the Banzhaf power index of a permanent member of
the Security Council is more than 10 times greater than that of a
nonpermanent member. (The ratio goes up to about 100 for another —
Shapley-Shubik's — power index.)
Intuitively, power comes with the number of votes. More votes wield more
power. So that the following situation may come as a surprise. It is
straightforward to verify that, for the weighted system [8: 5, 3, 1,
1, 1],BPI1 = 9/19. The curious fact is
that, if the first player cedes 1 vote to the second player, such that the
weighted system becomes [8: 4, 4, 1, 1, 1], the voting power
of the first player grows. Indeed, the index BPI1 becomes
1/2 > 9/19. On the other hand, when the second player cedes a
vote to the third player, the real loser is the first player. The system
becomes [8: 5, 2, 2, 1, 1], and BPI1 drops to
10/22 <9/19.
Fair Division
Each of the players that participate in the division of goods has a
value system that tags any piece or part of the goods. A division is fair
if each of the players thinks his portion constitutes at least
1/Nth (where N is the number of players) of the total.
The problem may seem difficult, but there are several working algorithms
that apply in different situations. Not only it is possible to satisfy
everyone's idea of fairness, in many cases a tangible part of the goods
will be left over.
The method of markers applies in situations where the goods to
be divided comprise a large number of small indivisible items that could be
arranged in a line or the case where the goods naturally form a linear like
entity, e. g., a sea front strip of land.
Each of the players, unbeknownst to the others, places (N-1) markers
that divide the goods into N parts of equal (in his private estimation)
value. The markers are then combined on a single diagram. The algorithm
scans the goods left to right till it meets the leftmost of the first
markers. The owner of that marker receives the stretch from the beginning
to the marker. By construction, this is of course, in his view, a fair
part. The algorithm than scans for the leftmost of the second markers. The
owner of that marker receives the stretch between his first and second
markers, i.e. the second of the parts he designated as fair. And so on. The
last fellow receives the stretch from his last marker to the end of the
goods. In the applet below, each player is assigned a color, whereas the
black pieces belong to no one.
Kruskal's Algorithm
A number of universities and federal agencies must be connected via the
internet. Throughput and reliability of the fiber optic connections are
such that there is no need in redundant lines: it's sufficient that for any
two of the organizations involved, there exists just one (perhaps indirect,
i. e., through other organizations) communication channel. On the other
hand, the costs of connections that depend on the distance between
organizations and the terrain to dig through, may differ from one
connection to another. A very practical question is what would be the least
expensive way to build up the connection network?
After the locations of all organizations have been set up on a map, it
became obvious that not all possible connections ought to be
considered. Some organizations are too distant from each other, others are
separated by naturally impassable territory. Still, among the feasible
connections there is significant redundancy. Which combination is least
expensive?
There is a surprisingly simple algorithm to answer that
question. Kruskal's algorithm (Joseph Kruskal, 1956) proceeds in steps:
On every step mark the cheapest unmarked edge.
See that the marked edges do not form circuits (to avoid redundancy.)
Repeat 1 and 2 while possible.
(Click on connections.)
Kruskal's algorithm exemplifies one approach to problem solving. When
there are too many conditions to be satisfied, it may make sense to
temporarily drop some conditions and first try to satisfy the remaining
ones. (See, for example, a classical
geometric
construction problem.) At the outset, the requirement of having a
connected network is dropped, and the algorithm only concerns with using
the cheapest connections. But eventually a combination of the latter turns
out to be connected.
As we see, the applicability of the selected topics does not imply their
direct usability to the student. (Although the
online
summary of the COMAP book makes an astonishing
claim: "Their text, For All Practical Purposes, tackles the
question: If there were a course designed to present concepts of math that
apply to today's consumers, what should it include?" As far as I can judge,
except for the last, 20th, chapter — Models in Economics
— and chapters on statistics, there is nothing in the book of
interest to the consumer of either today or tomorrow.)
Other topics covered include additional graph algorithms, the problem of
apportionment, scheduling, growth, symmetry
and statistics. Each of the topics contributes to the notion that
mathematics is an integral part of our society and culture. Most could be
introduced with no mathematics at all. Very few require familiarity with
algebraic concepts. Most of them could be dug deeper and reveal more of
interesting mathematics and its methods. (For example, A. Taylor's book, still very popular, concentrates on
only five topics, more or less equivalent to just one of the four parts of
the Excursions, but covered in much
greater depth and by far more rigorously.)
On the whole, both books offer a nice selection of (currently)
unconventional topics. And there is a good chance that every student may
like at least one of them. (We learn about one of the courses based on the
COMAP book from the
MAA's JOMA:
The goal of the course is to get every student excited about and
involved in at least one aspect of the mathematics that we do.)
But assume that the student did love one of the topics. What then? On
reading the Excursions, I got curious
about the Social Choice theory, which led to purchasing A. Taylor'sMathematics and Politics, and the
problem of apportionment, which directly led to Balinsiki and Young'sFair
Representation. (Both are gems in their genres. One as a textbook, the
other as a comprehensive exposition.) A student, however, concerned over
fulfillment of the graduation requirements, would not have time to even
contemplate deviating from the course material. But what if there were
time? What if the student could also get credit for following his heart?
Would not then it be nice to make available to the student some material on
the level, of, say, Taylor's book. On the other hand,
I can imagine a student in one of Taylor's classes who would rather prefer
the less sophisticated chapters from the Excursions or the COMAP
book. After all, not all students are the same.
In the introduction to chapter 19, Logic and Modeling, one of the two
chapters added in the 5th edition, the authors write:
In the preface to the first edition of For All Practical
Purposes, we find the following sentence:
[This book] represents our efforts to bring the excitement of contemporary
mathematical thinking to the nonspecialist, as well as help him or her
develop the capacity to engage in logical thinking and to read
critically the technical information with which our contemporary
society abounds.
In part, For All Practical Purposes has met this challenge of
developing the capacity to think logically by illustrating how mathematical
models can be used to analyze real-world problems. But isn't this challenge
itself a real-world problem? If we want to understand what "critical
thinking" is, perhaps we can do so by constructing a mathematical model
that we can analyze.
Let's apply a similar reasoning to that final course of a liberal arts
student. We see students are being taught to make choices, fairly divide
the load and schedule jobs. Their developing capacity to think logically
can be used to analyze real-world problems. But is not selection of topics
into a course, their depth and rigor of exposition a real-world problem?
Thompson Learning provides
instructors with tools for tailoring courses to their tastes by mixing
chapters from multiple titles and by adding new material. By extension,
could not the students be permitted to create their own course they would
have a better chance of enjoying? I mean just this once, in this final
semester of their last stand vis-à-vis mathematics. You know, the
technology is out there.
The idea may not be as frivolous as it sounds. I see the topics set up
on a virtual network where connections represent a varying degree of rigor
or depth, historical background or commonality of method, relevance of
subjects, alternative approach, theory and applications. Topics are framed
into study units with practice problems and online selftests, passing which
students gain access to further topic selections. From time to time
students are required to write reports that reflect on their progress. In
class, students seek the instructor's guidance and share their ideas and
recommendations about the topics. An important graduation requirement is
the number of topics mastered. Credit is given for the student's
demonstrated ability to follow the connections and for the number of topics
mastered in depth. It's all very doable. And the opportunity is of the
once-in-a-life-time significance.
To sum up, books like Excursions in Modern
Mathematics and For All Practical
Purposes offer an excellent selection of topics. But selection of
topics and their depth is dictatorial. In that final math course of the
liberal arts graduation requirement, I think, students may be entrusted
with making a few choices of their own. Some of the students, for example,
may have a taste for recreational mathematics.
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A complete and comprehensive course in calculus. Applications in the physical and natural sciences are emphasized as well as the underlying theory and the logical development of the material. Topics include limits, continuity, derivative rules, maximum- minimum concavity, separable differential equations, area, and the fundamental theorem. Skills prerequisite: ENG 020. Prerequisite: MAT 122C or MAT 122.
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This 8-day course continues the sequence from the Making Math Real Overview, 4 Operations & The 400 Math Facts, and Fractions, Decimals & Advanced Place Value courses, and provides the essential development for meeting the challenges of transitioning students from elementary math to algebra.
The cognitive demands of algebra require a strong and comprehensive developmental foundation including recognizing and extending patterns, generalizing, sequential processing, and especially, detail analysis. The specific outcome of a successful pre-algebra experience is the establishment and full integration of algebraic law that defines and supports all algebraic processes of simplifying and solving. The most crucial component of successful instruction and learning is to include all of the incremental steps in every algebraic development. Therefore, course emphasis is on the systematic incrementation and methods of instruction that address the development, refinement, and integration of students' sensory-cognitive abilities with the application and retention of algebraic problem solving and skills.
Topics include units on the four operations with integers and rational numbers, probability, number theory, ratio, proportion and percent, solving equations, and linear graphing. This course is designed for educational therapists, special educators, elementary and secondary classroom teachers, and college professors. Parents and those who consider themselves non-math majors are especially encouraged to enroll. Prior knowledge of algebra is not required.
These techniques are designed to reach the full diversity of learning styles. Extensive color-coding is a critical element of the program. Please bring 4 colored ball point pens or pencils in blue, green, red and black.
NEXT OFFERING:Pre-Algebra will return to Making Math Real's Calendar in the Spring of 2014.
Cost of the 8-day Pre-Algebra Course: $994 for tuition and reader, paid to Making Math Real Institute; $360 for optional 4 semester UC Extension academic units, paid to UC Regents on the first day of class.
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Easy Algebra 1.1 description
Master Algebra in 24 hours. This Tutorial. intended for mature students, covers the Algebra Topics taught in School and required for College - Numbers, Fractions, Linear Equations, Simultaneous Equations, Exponents, Quadratic Equations, Graphs and Polynomials. It makes Algebra easy by carefully explaining the Rules and providing examples showing how to apply them. Many people have trouble with Algebra because when it was taught in school, they werent ready to absorb the abstract Rules. And even checkers or baseball is difficult to understand if you dont know the Rules. But now, with maturity, you will have no difficulty learning the Algebra Rules. That is when Algebra becomes easy! Download the program and try it out. The first 3 Topics are FREE!
Having trouble doing your Math homework? This program can help you master basic skills like reducing, factorising, simplifying and solving equations. A step by step explanation of problems concerning Free Download
Interactive College Algebra course designed to ensure engaging, self-paced, and self-controlled e-learning process and help students to excel in their classes. Java- and web-based math course includes Free Download
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Algebra - 2nd edition
Summary: Algebra, Second Edition, by Michael Artin, discusses concrete topics of algebra in greater detail than most textbooks, preparing readers for the more abstract concepts. This book covers all of the topics that are important to the average mathematician, and are covered in the typical course. Linear algebra is tightly integrated throughout
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Description
Michael Sullivan's time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. The Enhanced with Graphing Utilities Serieshas evolved to meet today's course needs by integrating the usage of graphing calculator, active-learning, and technology in new ways to help students be successful in their course, as well as in their future endeavors.
In the Sixth Edition, new worksheets in MyMathLab—developed from the authors' experience in the classroom—provide mixed review for students who having trouble reconciling various topics, and also give students an opportunity to show their work. The "Are You Prepared?" section openers focus on students mastering the prerequisite material before beginning a new topic, and for the first time, those exercises are assignable in MyMathLab. Concept and Vocabulary exercises are also now assignable in MyMathLab as reading quizzes.
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Math Course Takes 'Real Life' Approach to Algebra
Educational courseware publisher American Education Corp. is taking a new approach to answering the age-old question, "What does algebra have to do with real life?" The company has announced the release of a new course for its A+nyWhere Learning System program. Algebra I: A Function Approach Part 1 is the first semester segment of a full-year algebra course geared to grades 9 and 10, and, in addition to the fundamental concepts and tools of algebra, the course aims to relate the material to "real life."
Taking the fundamentals and applying them to real-world situations using exercises in relevant scenarios allows students to realize the practical uses of linear and quadratic equations, graphs and coordinates, functions, and other algebraic concepts.
The A+nyWhere program is computer based, so students taking courses like Algebra I can use a number of tools incorporated into the software to aid in their assignments and overall comprehension of the material. These tools include onscreen standard and scientific calculators, pictures and diagrams, video tutorials, exercises, practice exams, and, for upper-level courses, interactive feedback
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focuses on the fundamental concepts of arithmetic, algebra, geometry and trigonometry needed by learners in technical trade programs. A wealth of exercises and applications, coded by trade area, include such trades as machine tool, plumbing, carpentry, electrician, auto mechanic, construction, electronics, metal-working, landscaping, drafting, manufacturing, HVAC, police science, food service, and many other occupational and vocational programs. The authors interviewed trades workers, apprentices, teachers, and training program directors to ensure realistic problems and applications and added over 100 new exercises to this edition. Chapter content includes arithmetic of whole numbers, fractions, decimal numbers, measurement, basic algebra, practical plane geometry, triangle trigonometry, and advanced algebra. For individuals who will need technical math skills to succeed in a wide variety of trades.
Table of Contents
Arithmetic of Whole Numbers
Fractions
Decimal Numbers
Ration, Proportion, and Percent
Measurement
Pre-Algebra
Basic Algebra
Pratical Plane Geometry
Solid Figures
Triangle Trigonometry
Advanced Algebra
Statistics Answers to Previews Answers
Index
Index of Applications
Table of Contents provided by Publisher. All Rights Reserved.
Excerpts
This book provides the practical mathematics skills needed in a wide variety of trade and technical areas, including electronics, auto mechanics, construction trades, air conditioning, machine technology, welding, drafting, and many other occupations. It is especially intended for students who have a poor math background and for adults who have been out of school for a time. Most of these students have had little success in mathematics, some openly fear it, and all need a direct, practical approach that emphasizes careful, complete explanations and actual on-the-job applications. This book is intended to provide practical help with real math, beginning at each student's own individual level of ability. Features Those who have difficulty with mathematics will find in this book several special features designed to make it most effective for them: Careful attention has been given toreadability.Reading specialists have helped plan both the written text and the visual organization. Adiagnostic pretestand performanceobjectiveskeyed to the text are included at the beginning of each unit. These clearly indicate the content of each unit and provide the student with a sense of direction. Each unit ends with aproblem setcovering the work of the unit. Theformatis clear and easy to follow. It respects the individual needs of each reader, providing immediate feedback at each step to ensure understanding and continued attention. The emphasis is onexplainingconcepts rather than simplypresentingthem. This is a practical presentation rather than a theoretical one. Special attention has been given toon-the-job math skills,using a wide variety of real problems and situations. Many problems parallel those that appear on professional and apprenticeship exams. The answers to all problems are given in the back of the book. A light, livelyconversational styleof writing and a pleasant, easy- to understand visual approach are used. The use of humor is designed to appeal to students who have in the past found mathematics to be dry and uninteresting. Seven editions and over two decades of experience with a wide variety of students indicate that this approach is successful--the book works and students learn, many of them experiencing success in mathematics for the first time. Flexibility of use was a major criterion in the design of the book. Field testing and extensive experience with the first five editions indicate that the book can be used successfully in a variety of course formats. It can be used as a textbook in traditional lecture-oriented courses. It is very effective in situations where an instructor wishes to modify a traditional course by devoting a portion of class time to independent study. The book is especially useful in programs of individualized or self-paced instruction, whether in a learning lab situation, with tutors, with audio tapes, or in totally independent study. Calculators Calculators are a necessary tool for workers in trade and technical areas, and we have recognized this by using calculators extensively in the text, both in fording numerical solutions to problems, including specific keystroke sequences, and in determining the values of transcendental functions. We have taken care to first explain all concepts and problem solving without the use of the calculator and to estimate and check answers. Many realistic problems included in the exercise sets involve large numbers, repeated calculations, and large quantities of information and are ideally suited to calculator use. They are representative of actual trades situations where a calculator is needed. Detailed instruction on the use of calculators is included in special sections at the end of appropriate chapters or is integrated into the text. Supplements An extensive package of supplementary
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Workshop Calculus integrates a review of basic precalculus concepts with the study of concepts encountered in a traditional, first semester calculus course: functions, limits, derivatives, integrals, and an introduction to integration techniques.
Active Learning Prepares Students for Calculus Designed to develop students confidence and critical thinking, this text offers a fresh and effective bridge to calculus. CLICK ON PICTURE FOR FULL DETAILS AND PRICES.
Enrich Your Students Calculus Experience Your students will directly experience the dynamic, geometric nature of calculus with the activities in this module. Available only in UK and Europe. Not available to US or other international customers.
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Links
- This article was written by one of the Stepping Stone Algebra Tutors. If you know of anyone who might be interested in reading tuition, please do get in
contact.
Algebra, once only studied by advanced mathematicians and scientists, is now taught to every seventh and eighth grade child across the United States. While the basics of algebra may seem, well basic, it no doubt took a great deal of intelligence to form the foundations of algebra today. These basic building blocks of algebra are being used today by students, professors, physicists, and algebra tutors around the world.
Algebra can be sourced back to the Egyptians and Babylonians. The earliest equations were linear, quadratic, or indeterminate. The Babylonians were capable of solving quadratic equations using very similar formulas that are used today, while Egyptians solved the equations using geometric solutions. Today, zero can be used as placeholder to differentiate between numbers. For instance, zero is used in 7018 to show that it is a different number than 718. The Babylonians had a similar method, except with a base of 60. It is also interesting to note that the Chinese mathematicians had a multiplicative system with a base of 10. This system was most likely contrived from the Chinese counting board, which is a checker board consisting of rows and columns.
In 3rd century AD, Diophantus, aka "The Father of Algebra", a Greek mathematician wrote Arithmetica, a math book that provided algebra help to other mathematicians of the time by providing many more solutions to algebraic problems, such as indeterminate equations. Brahmasphutasiddhanta, created by Brahmagupta, an Indian mathematician, was another piece of mathematical literature that supplied algebra help by completely describing the arithmetic solution to quadratic equations. By medieval times, mathematicians were able to multiply, divide, and solve for the square roots of polynomials. They also had knowledge of the binomial theorem. Additional algebra help and progress came in the 13th century when Italian mathematician Leonardo Fibonacci released an approximate solution on how to solve a cubic equation.
By 1799, the German mathematician, Carl Friedrich Gauss, published the proof for the theory of equations. The solution proved that for every polynomial equation, there was at least one root in the complex plane. At this point, algebra had entered its modern phase. With algebraic foundations now in place, research topics became more abstract. These abstract ideas, such as complex numbers, are the topics most students seek algebra help for because of their theoretical nature.
Finally, more recently, the German mathematician Hermann Grassmann started researching vectors, which lead J.W. Gibbs to incorporate vector algebra and physics. The discoveries made in modern algebra since then have continued to grow. Algebra continues to be applied to various technical fields. The progression of algebra is fascinating and if our future findings are anything like the past, there is an uncountable amount of algebraic solutions waiting to be discovered.
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Math Essentials: No-Nonsense Algebra {Review}
We received No-Nonsense Algebra from Math Essentials to review this summer. This book provides a method of instruction that is "short, concise, and self-contained." The lessons are clear and free of excess distraction to enable kids to really focus on what the lesson is covering. Easy-to-understand instructions are provided and each lesson provides appropriate practice problems as well as a short section of review to quickly cover previous lessons again.
I went through a section of this with my incoming 7th grader this year and she actually found it to be, not only helpful, but somewhat enjoyable. She asked to take it with us on our recent vacation and work on math "on the go."
Of course I said, "Yes."
The video lessons online are great. I usually prefer a hard copy of things like this by way of DVD/CD-Rom, but in this case it was really nice to be able to access the lessons from any computer at any time. The access code is included in every book, so we have the login information available at all times.
The book also provides chapter tests and a final exam. The answer key is included as well. All of this is available to you for only $27.95.
Math Essentials also provides skills practice books. We received Whole Numbers and Integers. Check out the Table of Contents and Sample Pages here.
My daughter really liked this one as well and I gave her freedom with it to complete lessons and self-check in the back. She appreciated brushing up on some of these basics over the summer. This book is available for $11.95. Right now, with any order for a Math Essentials item, customers will receive a Free A+ Math Homework kit, a $4.99 value.
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Glen Echo Algebra 1In American mathematics education, precalculus (or Algebra 3 in some areas), an advanced form of secondary school algebra, is a foundational mathematical discipline. It is also called Introduction to Analysis. In many schools, precalculus is actually two separate courses: Algebra and Trigonometry.
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MODERATORS
I've noticed that a good portion of actuaries were math majors, but reading through exam study-guides it seems like you don't need to know any math beyond calculus. Do actuaries need to know "higher" math like group theory, field theory, real analysis, etc.? Is knowledge of these subjects useful?
As some have pointed out - depends on what you do. Calculus? Some actuaries don't use much beyond basic algebra. Some use stochastic differential equations, generalized linear modeling, advanced statistical methods, you name it.
You also have to remember that "higher math" your referring to often doesn't deal explicitly with more messy statistics. With stats, you often have a lot of data but you don't know for sure the actual nature of the underlying system. You have to make guesses. The higher math you refer to often assumes the nature of the underlying system and looks at the implications of that.
A lot of the "higher math" involved in actuarial science is more about guessing the nature of the underlying system and constructing accurate models.
If math is the "science", then what we do is more along the lines of "engineering", if that analogy makes any sense.
Personally, I have never even used Calculus in my day to day work. HOWEVER, I will always say that the higher level math classes I took(group theory, real analysis, number theory, etc) taught me how to think. These classes taught me how to problem solve and think through problems which has helped me immensely at work and in exam taking.
Higher math as well as higher stats may be useful if you go into modelling or hedging. I remember seeing crazy looking formulas on some of the documentation, the ones I haven't seen since my study manuals.
I've been in retirement for about 6 years and the only time I needed to know brownian motion is to study for MFE and FETE. Besides that, never! It is more of a financial concept, i mainly deal with liabilities.
I was a pure math major - took all the pure courses from group/ring/field theory, to algebraic geometry, topology, real/complex analysis etc. I actually never took a stats or probability course in college, I'm a little ashamed to say.
No, I have never used these things in my work, knowledge of them may be useful, but I can't imagine any application for most of it in what actuaries do.
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Lesson 31: Logarithms
Course Topic(s):
Developmental Math | Logarithms
The lesson begins with an application problem to motivate the necessity and use of a logarithm. The formal definition linking logs and exponents is then introduced. Exercises in writing exponential equations as logarithms follows before a calculator based method for approximating logarithmic values is discussed. The common log, i.e. logs of base (10), is introduced and a procedure for solving common log equations with a calculator is presented, along with various caveats about proper syntax for the calculator. The lesson concludes with exponential modeling problems where logs may be employed to find the desired exponent.
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Functions Teacher Resources
Title
Resource Type
Views
Grade
Rating
Your high schoolers will be able to relate to this exponential model. In part 1, they create a table to model a situation, plot the data, understand the domain and range, and answer questions about the general function. In part 2, they look at an exponential function and see how changes to the function effect the graph.
Learners create functions from graphs. In this movement with functions lesson, students use motion detectors and create graphs from the movement. Afterward, they describe graphs and write equations for the graphs.
What is absolute value? What is an absolute value function? Emerging mathematicians solve equations containing variables inside an absolute value sign. They graph each function on a coordinate plane and identify the maximum and minimum values in the graph. This two-page worksheet contains detailed notes, examples, and instruction, as well as four problems.
Students solve linear equations algebraically and through graphing. In this algebra instructional activity, students identify the domain and range of each function. They create formulas to solve word problems.
Explore variables and variable expressions. Learners select pictures from a newspaper or magazine to describe an algebraic expression. They then write the word sentence under the picture and then translate the words to an algebraic expression. In groups, they match expressions using symbols. They play an "I Have, Who Has" game and use a mystery box to explore functions.
Upper graders find the domain and range of a function. They graph the given functions and identify the breaks, and missing points in the graph. Then find the domain and range and explain how it affects the graph using a calculator. They apply these concepts to solving real world scenarios.
Learners hop online to complete a self-assessment. Using the interactive tool, they solve 16 multiple choice problems. They graph inequalities, find linear equations passing through two points, solve piecewise functions, find the domain and range of a relation, and find the first three terms in a sequence. There's even a hint provided for each problem.
Play ball! High schoolers explore the concept of quadratic equations through modeling how shooting a basketball can be expressed as a quadratic function. They impose a coordinate grid on the path of a shooting basketball and determine points to model the data. Additionally, they enter data into lists and perform a quadratic regression on the data.
In this algebraic functions worksheet, learners write a function to determine the relationship between people and barrels of oil used. They research the population of the 10 largest cities in their state and use this functional relationship to calculate the number of barrels and gallons of oil used by each city.
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Be actively
involved in managing the learning process, the mathematics and your study
time.
Take responsibility for
studying, recognizing what you do and don't know, and knowing how to get
your Instructor to help you with what you don't know
Attend class every day
and take complete notes. Instructors formulate test questions based
on material and examples covered in class as well as those in the text.
Be an active
participant in the classroom. Get ahead in the book; try to work
some of the problems before they are covered in class. Anticipate
what the Instructor's next step will be.
Ask questions in class!
There are usually other students wanting to know the answers to the same
questions you have.
Go to office hours and
ask questions. The Instructor will be pleased to see that you are
interested, and you will be actively helping yourself.
Good study habits
throughout the semester make it easier to study for tests.
Studying Math
is Different from Studying Other Subjects
Math is learned by doing
problems. Do the homework. The problems help you learn the
formulas and techniques you do need to know, as well as improve your
problem-solving prowess.
A word of warning: Each
class builds on the previous ones, all semester long. You must keep
up with the Instructor: attend class, read the text and do homework every
day. Falling a day behind puts you at a disadvantage. Falling
a week behind puts you in deep trouble.
A word of
encouragement: Each class builds on the previous ones, all semester long.
You're always reviewing previous material as you do new material.
Many of the ideas hang together. Identifying and learning the key
concepts means you don't have to memorize as much.
College Math is
Different from High School Math
A College math
class meets less often and covers material at about twice the pace that a High
School course does. You are expected to absorb new material much more
quickly. Tests are probably spaced farther apart and so cover more
material than before. The Instructor may not even check your homework.
Take responsibility for
keeping up with the homework. Make sure you find out how to
do it.
You probably need to
spend more time studying per week - you do more of the learning outside
of class than in High School.
Tests may seem harder
just because they cover more material
Study Time
You may know a
rule of thumb about math (and other) classes: at least two hours of study time
per class hour. But this may not be enough!
Take as much time as
you need to do all the homework and to get complete understanding of the
material.
Form a study group.
Meet once or twice a week (also use the phone). Go over problems
you've had trouble with. Either someone else in the group will help
you, or you will discover you're all stuck on the same problems.
Then it's time to get help from your Instructor.
The more challenging
the material, the more time you should spend on it.
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Matrix of a Linear Map
In this lesson our instructor talks about matrix of a linear map. First, he discusses a helpful theorem and procedure for computing to matrix. Then he talks about property of matrix of a linear map. He ends the lesson with solutions to three complete example problems.
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Matrix of a Linear Map introduces concepts early in a familiar, concrete real number setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.
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Basic Nemeth Code
The Nemeth Code for Science and Mathematics includes all the Symbols a braille user needs for written math and science. By learning the basic Nemeth Code symbols presented in this course, you can help students who use braille develop math skills that will serve them throughout their school years and beyond. This course will not enable you to transcribe material from print to the Nemeth Code, however. Additional study and practice would be necessary before doing so. Prerequisite: "Contracted Braille" or the ability to read and write contracted (grade 2) braille.
Course BNC-111. LP.
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User rh - MathOverflowmost recent 30 from by RH for Linear Algebra Texts?RH2010-03-03T19:58:58Z2010-06-19T09:50:35Z<p>I rather like Linear Algebra Done Right, and depending on the type of students you are aiming the course for, I would recommend it over <strong>Hoffman and Kunze</strong>. Since you seemed worried that Axler might be too advanced, my feeling is that Hoffman and Kunze will definitely be (especially if these are students who have never been taught proof-based mathematics).</p>
<p>Of course, the big caveat here being that <strong>Axler</strong> avoids determinants at all costs, and this will put more on you to introduce them comprehensively.</p>
<p>I've never looked at it, but another one worth considering might be <strong>Halmos's Finite Dimensional Vector Spaces</strong>.</p>
by RH for What to look for in applicants to graduate programs (in mathematics)?RH2010-02-22T02:50:16Z2010-02-22T02:50:16Z<p>Can I ask for clarification on some of the responses?</p>
<p>Igor Belegradek and Paul are both very specific about which classes should be taken, and that "good grades" should be achieved. How does one define "good grades"? Does this mean all As? Mostly As with some Bs? Or perhaps As in undergraduate class with As or Bs in the graduate level classes taken?</p>
<p>(I believe Paul addressed the related question of what "good" GRE scores are.)</p>
<p>P.S. Based on my understanding, it would be more appropriate for this to be a comment on one of the answers but I can't do this without reputation points. So apologies if I am breaking the MO etiquette.</p>
<p><strong>Edit:</strong> Another question: Does it make any sort of impact to have been an undergraduate grader and/or course assistant?</p>
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Mathematics at St. Olaf
Practical - Popular - Visible - Active - Useful - Fun
Mathematics is all of those things--and more--at St. Olaf, where the mathematics program is recognized nationally for innovative and effective teaching. Our program was cited as an example of a successful undergraduate mathematics program by the Mathematical Association of America (Models That Work, Case Studies in Effective undergraduate Mathematics Programs) and St. Olaf ranks sixth in the nation as a producer of students who went on to complete Ph.D.'s in the mathematical sciences (Report on Undergraduate Origins of Recent [1991-95] Science and Engineering Doctorate Recipients).
One department, three programs
The St. Olaf Department of Mathematics, Statistics, and Computer Science houses three programs, described briefly below. Click the links for further information and details.
This concentration enables students to pursue statistics either as a primary interest or as a supplement to some other major. The statistics concentration - including course work in both theoretical and applied statistics - may be attached to any major. Typically, about 12-15 students complete a statistics concentration each year.
A computer science major was begun recently; the first graduates completed the program in 2005. (A computer science concentration was offered for many years previously.)
Areas of emphasis
Mathematics students choose various areas of emphasis:
Preparation for Graduate School Advanced courses provide breadth and depth for students intending to pursue graduate degrees in the mathematical sciences. Seminars and independent study provide opportunities for research-like experiences.
Applied Mathematics Courses offered in applied mathematics include statistics, computer science, differential equations, and optimization. The Mathematics Practicum has student teams working to solve real problems in industry and business.
Secondary School TeachingOne of the nation's largest undergraduate mathematics libraries, with more than 10,000 mathematics books and 80 journals, each with extensive back issues
Card catalog available from any campus terminal
Database support for inter-library loans
Grant Support
St. Olaf has attracted considerable support for its leadership in mathematics education at both college and pre-college levels. Projects supported by the National Science Foundation, the Fund for the Improvement of Post-Secondary Education and others include: Advanced Computation Laboratory, Computers in Geometry Classrooms, Post-Doctoral Teaching Fellow Program, Teaching with Symbolic Computer Systems, and the Minnesota Mathematics Mobilization.
Special Opportunities
Colloquium Series
Weekly presentations by mathematicians, statisticians, employers, alumni, and graduate school faculty on uses of mathematics beyond the classroom.
Examples:
Floods, Hot Potatoes, Counting to Infinity and Other Disasters of Network Routing
Mathematics and the Buckyball
MythMath: From Bumblebees and Snow to Chaos and Poincare
Mathematics and Medical Tomographs
Mathematics Practicum
During January, two or three teams of five students work for a month on real industrial problems and present their results to scientists and executives of the company that posed the problem.
Recent Practicum topics include:
Time-Efficient Suturing During Cardiac Surgery
Estimation of Minimum Freight Car Needs
Optimal Positioning of Manufacturing Equipment
Load Factors for Airline Scheduling
Federal Fairness Test for Benefit Plans
MAA Student Chapter
This organization for mathematics students arranges social and mathematical activities. Past events include a Halloween pumpkin-carving party, a pig roast and the Math-Bowl.
Mathematical Contests
Students compete in annual contests on calculus and other undergraduate mathematics. Prizes, fanfare, and a bronze plaque serve to recognize the winners.
An Opportunity for study abroad in one of the world's leading mathematical centers. St. Olaf has supplied the largest number of students enrolled in this program, which is open to all North American students of mathematics or computer science.
Actuarial Exams
St. Olaf is a test center for the Preliminary Actuarial Examinations. Regular review sessions are held during the spring term.
This lively weekly publication of fact, opinion, news, jokes, and misinformation keeps students and faculty informed of happenings in the Mathematics Department.
National Leadership
Members of the St. Olaf mathematics faculty not only keep up in their field, but also help lead collegiate mathematics through active research and writing. The professional record of St. Olaf mathematics faculty includes service in many capacities:
More than ten books, including: Counterexamples in Topology, Problem Solving Through Problems, Mathematics Today, Calculus for a New Century, A Course in Modern Geometries, The Wohascum County Problems Book, and Calculus from Graphical, Numerical, and Symbolic Points of View
Dozens of research papers in mathematics journals
Four national awards for expository writing
Over 10,000 Telegraphic Reviews for the American Mathematical Monthly
Numerous articles on mathematics and mathematics education in such publications as Science, ScientificAmerican, Education Week, Encyclopedia Britannica, and The Chronicle of Higher Education
Co-Director, Minnesota Mathematics Mobilization
President of the Mathematical Association of America
Editors-in-chief, problems editors, notes editor, and book reviews editors of the American Mathematical Monthly, Mathematics Magazine, and the Real Analysis Exchange
Associate Director of the William Lowell Putnam Mathematical Competition
President of the Minnesota Council of Teachers of Mathematics (MCTM)
Chair of the North Central Section of the Mathematical Association of America
Chairs of the New Mathematical Library Editorial Committee and the MAA Committee on the Undergraduate Program in Mathematics (CUPM)
North American Director of the Budapest Semester in Mathematics
Members of numerous committees
and councils of the Mathematical Association of America and the American Mathematical Society
Chair of the Council of Scientific Society Presidents (CSSP) and the Conference Board of the Mathematical Sciences (CBMS) and the Mathematical Sciences Education Board (MSEB)
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Are afraid of Algebra...?
Yes, Many kids are afraid of Algebra Exams and Homework.
So, try to understand the problems or the concepts from your Professor / Teacher / Tutor.
Discuss with your friends. Try Online. There are many more sites / Professors are helping kids online.
Send your problems we will solve or teach you live. Try YouTube. There are thousands of videos available on Algebra, Trigonometry, Calculus, Stat and many more.
There are few online Programs which helps you no matter what your standers are, no matter what math problems are. As of my experience i suggest These Algebra Solver, Algebra for Dummies, Algebra Help Software. There are many more out there. But the above programs will teach you in a unique way of Step-By-Step like your Math Professor with more patience and explain with complete description for every Step. You can try a trail version before purchase...
Another important thing to note about the algebra is the fact that his teachings are interconnected and in fact is based on the other. This means there must be continuity if they are university students retain the lessons of algebra. Once again, continuity is achieved if they are to see the importance of algebra in everyday life. If you are aware of the importance of algebra, then it will be able to relate to real events algebra lessons they have learned.
Yes Sam. Continuity is important in Math, especially in Algebra. If you miss your classes don't worry copy from your friends and discuss with them. If you still not clear about the problems, meet your school tutor. Try it in web.
As i mentioned in earlier posts, you can learn very easily and interactively... watch this video. How to Solve 5x ^2 + 9 -- 3x + 4x ^2 + 8x + 7
Please don't get me wrong, my teachers be great. If we just worked on those straightforward details a bit additional and were educated extra strictly be acing 6th grade. I am really stressed out because algebra 2 is necessary at my school in order to graduate. This is very disturbing, because I am good at any subject but math, I have 5 because and an F on my last report card, yes the F was on math, for both semesters
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Main menu
Maths
Mathematics is the most widely used subject in the world. Every career uses some sort of Maths. More importantly, doing Maths helps the mind to reason and organise complicated situations or problems into clear, simple, and logical steps.
Mathematics is a Core subject of the National Curriculum and our aim is to ensure that we foster an understanding and appreciation of Maths so students can use their skills in their everyday lives as well as essential exam success.
We deliver an extensive curriculum including:
Using and Applying Skills
Number and Algebra
Shape, Space and Measure
Handling Data
We use a variety of techniques to engage students in mathematics, including puzzles, challenges and games as well as traditional teaching.
Problem solving and critical thinking strategies are embedded into the Mathematics syllabus to develop pupils' ability to think independently. We endeavor to help our students develop a positive attitude to mathematics and to develop their understanding in a way that promotes confidence and enjoyment.
Skills that students obtained from math:
The ability to identify and analyze patterns
Logic and critical thinking skills
Ability to see relationships
Problem solving skills
Key Stage 4
In Year 9, pupils begin working towards their GCSE and have the opportunity to build on the excellent foundation provided in Key Stage 3 and tackle with confidence the GCSE syllabus.
All students follow the Edexcel Linear program and are taught to develop both calculator and non-calculator methods and to apply their skills to real-world problems wherever possible.
In Yr 11 students are assess through two examinations of equal weighting one calculator and one non calculator exam.
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AMATH 301: Beginning Scientific Computing
Instructor:
Eli Shlizerman
Guggenheim 418D
Course description
Introduction to use of computers to solve scientific and
engineering problems. Application of mathematical judgment in
selecting tools to solve problems and to communicate results.
MATLAB taught and used for numerical computation.
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The Animal Cell The Structure of The Animal Cell is discussed in this video. The purpose of this video is to explain the parts of the Animal Cell and give a brief overview on their function.
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Solving Equations - Pre-Algebra The instructor demonstrates how to solve one-step, two-step, and multi-step equations. Several examples are modeled gradually getting more complex with each. Video is good quality and good for all students as review or initial learning of the conceptThe Algebra Slide Song and Dance Students do a song and dance in a classroom about solving equations with addition and subtraction. It was created for an algebra class. (Run time 2:54) These are some of the lyrics for the song:
Alright we gonna do the basic steps You must isolate The Variable From the rest Of the equation Then use Inverse operations
Lets subtract now first X 5 Equals -13... So whats x equal? Well you add 5 To both side Author(s): No creator set
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Problem Solving in Mathematics Problemve equations, formulas and other math are exlained in this four minute video. This video moves very rapidly and so a replay and stopping the video may be of value. Author(s): No creator set
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Solving One-Step Equations Equations are fundamental to Algebra, and solving one step equations is necessary for students in order to learn how to solve two-step equations, and other multi-step equations. This video clip explains the difference between an equation and an expression. (1:15) Author(s): No creator set
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Solving Two-Step Equations Solving two-step equations will help introduce students to solving equations in multiple steps, a skill necessary in Algebra I and II. This video explains how to solve these types of equations by using additive and multiplicative inverses to isolate and solve for the variable. (00:46License information
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Multiplying Fractions and Mixed Numbers Watch Multiplying Fractions and Mixed Numbers. In this tutorial, students will learn how to multiply fractions and mixed numbers..Rational Inequalities, Part 1 In an easy conversational tone, the instructor uses the computer screen as his 'blackboard' (and different colors to emphasis his points) to demonstrate two ways to solve a rational inequality (or an inequality involving a fractional expression).
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Description
Addison Wesley | ISBN: 0321185587 | 11 edition (October 5, 2004) | 1380 pages | PDF | 68 Mb
The new edition of Thomas is a return to what Thomas has always been: the book with the best exercises. For the 11th edition, the authors have added exercises cut in the 10th edition, as well as, going back to the classic 5th and 6th editions for additional exercises and examples. The book's theme is that Calculus is about thinking; one cannot memorize it all. The exercises develop this theme as a pivot point between the lecture in class, and the understanding that comes with applying the ideas of Calculus. In addition, the table of contents has been refined to match the standard syllabus. Many of the examples have been trimmed of distractions and rewritten with a clear focus on the main ideas. The authors have also excised extraneous information in general and have made the technology much more transparent. The ambition of Thomas 11e is to teach the ideas of Calculus so that students will be able to apply them in new and novel ways, first in the exercises but ultimately in their careers. Every effort has been made to insure that all content in the new edition reinforces thinking and encourages deep understanding of the material. Thanks to the original uploaderThomas' Calculus (11
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Nazareth College of Rochester's math program focuses on problem solving. Mathematics is taught as a language of patterns, de-emphasizing rote learning and encouraging the integration of numerical, graphical, and symbolic approaches to problem solving. The Department wants all students to understand that mathematics is more than a collection of recipes for solving equations and that there often may be multiple correct answers to complex problems. This approach promotes critical thinking.
Nazareth students regularly compete in (and have won) the COMAP Mathematical Contest in Modeling, an international competition in which students spend a long weekend applying mathematics to the solution of a real-world problem. Our students are encouraged to take the William Lowell Putnam Mathematical Competition, the widely acknowledged benchmark in mathematics competitions. Many attend regional conferences on mathematics where they often give presentations of their own.
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Hi, A couple of days back I started solving my mathematics assignment on the topic Remedial Algebra. I am currently unable to finish the same since I am unfamiliar with the fundamentals of powers, difference of squares and radical equations. Would it be possible for anyone to help me with this?
Algebrator is one of the best resources that can render a helping hand to people like you. When I was a newbie, I took aid from Algebrator. Algebrator covers all the principles of Algebra 2. Rather than using the Algebrator as a step-by-step guide to solve all your homework assignments, you can use it as a coach that can give the fundamental principles of graphing parabolas, equivalent fractions and conversion of units. Once you understand the principles, you can go ahead and work out any tough question on College Algebra within minutes.
I checked out each one of them myself and that was when I came across Algebrator. I found it particularly appropriate for trigonometry, algebraic signs and exponential equations. It was actually also effortless to get started on this. Once you key in the problem, the program carries you all the way to the answer elucidating every step on its way. That's what makes it outstanding. By the time you arrive at the result, you already know how to crack the problems. I benefited from learning to crack the problems with Pre Algebra, Remedial Algebra and Intermediate algebra in algebra. I am also positive that you too will appreciate this program just as I did. Wouldn't you want to check this out?
complex fractions, percentages and matrices were a nightmare for me until I found Algebrator, which is really the best math program that I have ever come across. I have used it through several math classes – Algebra 2, College Algebra and Algebra 2. Simply typing in the algebra problem and clicking on Solve, Algebrator generates step-by-step solution to the problem, and my algebra homework would be ready. I highly recommend the program.
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Bedford3540761802. Vector calculus is the cornerstone of a vast amount of applied mathematics This is an undergraduate text. This is both concise and comprehensive in structure and f [more]
3540761802. Vector calculus is the cornerstone of a vast amount of applied mathematics This is an undergraduate text. This is both concise and comprehensive in structure and format; 8vo; 182 pages
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