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In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and other subjects. No advanced mathematical background is needed to follow thought-provoking discussions of such topics a... read more
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Fifty Challenging Problems in Probability with Solutions by Frederick Mosteller Remarkable puzzlers, graded in difficulty, illustrate elementary and advanced aspects of probability. These problems were selected for originality, general interest, or because they demonstrate valuable techniques. Also includes detailed solutions
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MAT-1050 - Elements of Mathematics
Designed for students preparing to teach at the preschool and elementary level. Overview of mathematical systems, including sets, natural numbers, integers, rational and irrational numbers, algorithms and computational methods. 3 class/2 lab hours.
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Fundamental skills of mathematics will be applied to such topics as functions, equations and inequalities, probability and statistics, logarithmic and exponential relationships, quadratic and polynomial ...
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The ideal review for your geometry course. More than 40 million students have trusted Schaum s Outlines for their expert knowledge and helpful solved problems. Written by a renowned expert in this field, Schaum's Outline of Geometry covers what you need to know for your [...]
The ideal review for your elementary mathematics course More than 40 million students have trusted Schaum's Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaum's Outlines cover everything from math [...]
. When you need just the essentials of elementary algebra, this Easy Outlines book is there to help. If you are looking for a quick nuts-and-bolts overview of elementary algebra, it's got to be Schaum's Easy Outline. This book is a pared-down, simplified, and tightly [...]
. When you need just the essentials of geometry, this Easy Outlines book is there to help. If you are looking for a quick nuts-and-bolts overview of geometry, it's got to be Schaum's Easy Outline. This book is a pared-down, simplified, and tightly focused version of its [...]
Takes you through elementary maths, including algebra and geometry. This easy-to-follow study guide provides sample problems that show you step-by-step how to solve the kind of problems you may find on your exams. It also includes practice problems (with answers supplied) [...]
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The best way to proceed would be to agree on a given level of proficiency and then exhibit the first item thereafter that not everybody can understand and explain what is hard in that item.
Or, a faster way, skip the prerequisite for the time being and just come up with the algebra item and, if need be, we can always backtrack to what it is resting on. ===
It seems like people can accept a small leap like "since we don't know the number of apples, let's just use an x for now to stand for the number of apples"; but there seems to be an uneasiness/discomfort/difficulty accepting that an expression like "0.05(2x-3)" with all its various parts can actually be seen as a single entity: the value of the nickels (say). It's like a chunking thing. Learning to build and/or interpret such expressions, and especially, to assemble them into relevant equations, seems rather more difficult for some reason.
So my guess would be: everybody can learn to do arithmetic and solve linear equations. Many (most?) people have a hard time learning to write algebraic expressions and assemble them into meaningful equations when faced with some sort of practical application. What makes this difficult is... well I really don't know.
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INTEGRAL tool for mastering ADVANCED CALCULUS
Interested in going further in calculus but don't where to begin? No problem! With Advanced Calculus Demystified, there's no limit to how much you will learn.
Beginning with an overview of functions of multiple variables and their graphs, this book covers the fundamentals, without spending too much time on rigorous proofs. Then you will move through more complex topics including partial derivatives, multiple integrals, parameterizations, vectors, and gradients, so you'll be able to solve difficult problems with ease. And, you can test yourself at the end of every chapter for calculated proof that you're mastering this subject, which is the gateway to many exciting areas of mathematics, science, and engineering.
This fast and easy guide offers:
Numerous detailed examples to illustrate basic concepts
Geometric interpretations of vector operations such as div, grad, and curl
Coverage of key integration theorems including Green's, Stokes', and Gauss'
Quizzes at the end of each chapter to reinforce learning
A time-saving approach to performing better on an exam or at work
Simple enough for a beginner, but challenging enough for a more advanced student, Advanced Calculus Demystified is one book you won't want to function without!
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Course Overview:
The first several weeks of this course will consist of a review of Algebra II - concepts that are a prerequisit to this Precalculus course. There will be a "review" quiz given, (probably Fri,
This course will roughly follow the text but will skip some sections and do some others out of order. This is so that the most important and required concepts will be covered.
The first several weeks of this course will consist of a review of Algebra II - concepts that are a prerequisit to this Precalculus course. There will be a "review" quiz given early in the course (probably Fri.,Pg XVI of the text's preface lists an optional student solutions manual (for odd numbered problems) for those who may wish this supplement,
The first chapter (Chapter R) of the text (pgs 1 - 57) is a review chapter for concepts that the student needs to be familiar with for this course. They include:
- Real numbers, notation
- exponents, scientific notation
- algebraic manipulation of polynomials
- factoring
- solving linear and quadratic polynomials
- algebraic manipulation of rational and irrational expressions
It will be assumed that the student is familiar with these concepts. However, I understand that familiarity does not necessarily mean that these concepts are fully baked in. Please feel free to ask questions in class or schedule office time if clarification of these concepts is needed.
NOTE:
The material covered in this course is very important to more advanced math as well as many areas of science, engineering, business, etc. Some think this material is "hard". However, I believe that "tedious, but important" is a better description. Many people think this is hard because they may get a lot of wrong answers. However, this is usually due to the student not faithfully carrying out the rules that they already know as opposed to them not knowing the material. Many times, playing "dumb computer" (i.e. simply doing all steps without skipping any) is the key to getting the correct answer.
Homework and Grading:
Homework will be assigned most days meaning that there will usually be 3 separate homework assignments assigned each week. All homework assigned on a given week are due the following Tuesday. I highly recommend that you don't wait until the night before it is due to start the homework, but instead, you work on it as soon as it is assigned. Not only will this help you to complete the homework, it will also help you to better understand the lectures. Roughly half the points for each assignment will be earned by simply putting in a good effort on the entire assignment. The other half of the points will be earned by accuracy. I DO NOT ACCEPT LATE HOMEWORK, NO EXCEPTIONS!! I will, however, not count your lowest homework score.
Homework Grading Specifics:
Each day's homework will be worth 20 points. Due to the volume, I will only be grading 3-4 randomly selected problems from each homework. Each graded problem will be worth 3 points with partial credit being awarded to incorrect answers that have reasonable work associated with them. These graded problems' total worth will be 9 or 12 points. The other 11 or 8 points will be awared based on eyeballing the rest of the student's homework. Full credit will be given if it appears that all questions were reasonably answered.
Students are encouraged to work together on homework. However, if I sense that someone is simply copying another's homework without doing the work, credit will be adjusted accordingly.
In class work/attendence: Attendance will NOT be taken but STRONGLY encouraged because:
1) on most days, I will work some of the EVEN numbered (those without answers in the back) homework problems on the board
2) on some days, I will assign a short one question problem, given 10 minutes before the end of the class period. Those who turn them in will get credit for this one problem. All of these problems added together will be worth 5% of the total grade.
Comprehensive Final: for most, this will count as exactly 25% of the total grade. If a student's final exam grade is significantly better than the earlier mideterm tests resulting in a border line final grade, I will award a higher final grade based on the fact that performance has improved.
For ALL Tests, Exams: No calculators, computers, phones, headphones, other electronics can be used in any way. Students may use such devices to help with homework but all homework must be hand written.
MAKE UP TEST POLICY:
Generally, a missed exam will result in a 0 given for that exam. However, sometimes events are so out of the student's control that a make up test attempt is warrented. In such a case, the student must contact the University Testing Center (255-3354), fill out their form, give at least a 24 hour notice and pay the associated $10 fee.
If a student knows of a commitment that conflicts with a given test, it is their responsibility to tell me as soon as this is known. If I am approached about something that the student had long known about only a day or two prior to the test, I will not be accomodating. I will judge the merit of whether or not a make up test attempt is warrented on a case by case basis. Be advised that I might require independent verification (such as a doctor's note) if I sense that the situation is anything but completely out of the student's control. Note that a sudden commitment the night before a test will generally not be sufficient cause; the student needs to be studying continuously instead of waiting until the night before a test.
Learning Resources
Math
Learning Center (MLC) Free tutoring service is available at the Math
Learning Center (MLC) located in EN 136. It is recommended that you use
this facility for questions regarding homework, computer algebra
systems, review for exams or any other course material that you are
having difficulty with. Please visit the MLC website for more information.
Supplemental Instruction
Other policies:
To make the
most of your class, you are required to attend every class session.
Students should notify (in advance) the instructor if they need to miss
more than one session. Supporting documentation may be required. Drop
dates: Please seek counseling from the Dean's office before dropping any
course and note the following important dates: Feb 6 – last day to
drop and receive a full tuition refund; Aor 5 – last day to drop
without special permission from the Dean.
Academic Dishonesty:
Academic
honesty is fundamental to the activities and principles of a university.
All members of the academic community must be confident that each
person's work has been responsibly and honorably acquired, developed,
and presented. Any effort to gain an advantage not given to all students
is dishonest whether or not the effort is successful. The academic
community regards academic dishonesty as an extremely serious matter,
with serious consequences that range from probation to expulsion. When
in doubt about plagiarism, paraphrasing, quoting, or collaboration,
consult the course instructor.
Disability Services:
If you are a student with
a disability and believe you will need accommodations for this class,
it is your responsibility to contact and register with the Disability
Services Office, and provide them with documentation of your disability,
so they can determine what accommodations are appropriate for your
situation. To avoid any delay in the receipt of accommodations, you
should contact the Disability Services Office as soon as possible.
Please note that accommodations are not retroactive, and that disability
accommodations cannot provided until an accommodation letter has been
given to me. Please contact Disability Services for more information
about receiving accommodations at Main Hall room 105, 719-255-3354 or
dservice@uccs.edu
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GraspMath Learning Systems Intermediate Algebra (8) VHS Combo
Please Note: Pricing and availability are subject to change without notice.
The Intermediate Algebra Video Tutor series consists of 8 videos containing approximately 13 hours of video instruction. Topics in this series include exponents, solving linear equations and inequalities and applications, polynomials, factoring, rational expressions, complex fractions, graphing linear equations and inequalities, radicals, rational exponents, solving quadratic equations. May of the topic titles are the same as for the beginning algebra series, but at a level consistent with Intermediate Algebra courses.
Video 1 Equations covered are at the Intermediate Algebra level of difficulty. Also covered are literal equations or equations involving several different symbols in which one in particular is to be isolated.
Applications that Lead to Linear Equations.
This segment covers a variety of intermediate level word problems including problems involving distance, speed, and time as well as problems involving interest rates.
Solving Linear Inequalities.
This segment covers solving linear inequalities by isolating the unknown using methods similar to those for linear equations. The reversal of inequality symbol when multiplying both sides of an inequality by a negative number is also covered. The problems covered here are at the Intermediate Algebra level of difficulty.
Solving Absolute Value Equations.
This segment covers the solution of equations in which one or more terms contain the absolute value of a linear expression in the unknown . The method of isolation of the absolute value term is used.
Video 2 -Compound Inequalities, Exponents, Polynomials
Compound Inequalities.
This segment covers the method of solving and graphing compound inequalities and pairs of inequalities in one unknown.
Solving Absolute Value Inequalities.
This segment covers the method of solving absolute value inequalities by isolating the absolute value term and reducing to a system of compound inequalities.
Exponents.
This segment covers the laws of exponents in relation to the basic operations on real numbers as well as the use of the laws of exponents to simplify or rearrange algebraic expressions. Negative exponents are also covered.
Addition, Subtraction and Multiplication of Polynomials.
This segment covers addition and subtraction of polynomials as well as removal of parentheses. Multiplication of polynomials is also covered.
Video 3 -Factoring Binomials & Trinomials, General Factors
Greatest Common Factor and Factoring Trinomials case of polynomials with four or more terms, the method of factoring by grouping is covered. The problems covered here are at the Intermediate Algebra level of difficulty.
Factoring Binomials The problems covered here are at the Intermediate Algebra level of difficulty.
General Factoring.
This segment covers factoring polynomials in general. In the case of binomials the difference of two perfect squares and the sum or difference of two cubes as well as binomials which can be treated by these methods are covered. In the case of trinomials the method of arranging terms in order of decreasing degree in order to determine the signs of the terms in the factors is covered. For polynomials with more than three terms factoring by grouping is covered. Polynomials in more than one variable are also covered.
Video 4 -Complex Fractions, Rational Expressions
Multiplication and Division of Rational Expressions.
This segment covers multiplication and division of rational expressions as well as reducing to lowest terms by factoring both numerator and denominator. In case of multiplication the use of cancellation before multiplication to simplify work is covered. The problems covered are at the Intermediate Algebra level.
Addition and Subtraction of Rational Expressions.
This segment covers addition and subtraction of rational expressions by finding the least common denominator after factoring all denominators. The problems covered here are at the Intermediate Algebra level of difficulty.
Complex Fractions.
This segment covers complex fractions and the short method of simplification by multiplying numerator and denominator by the least common denominator of all denominators in the terms of the numerator and denominator of the complex fraction. This segment also covers complex fractions in which negative exponents appear.
Division of Rational Expressions.
This segment covers the simplification of rational expressions by using long division of polynomials to divide the numerator by the denominator when the numerator has higher degree than the denominator.
Video 5 -Rational Expressions, Rational Exponents, Radicals
Equations Involving The problems covered are at the level of Intermediate Algebra.
Applications that Lead to Rational Expressions.
This segment covers a variety of applications that arise which lead to equations involving rational expressions. In particular, problems involving distance, rate and time, as well as word problems are covered. Also covered are problems with literal equations.
Rational Exponents.
This segment covers the meaning and usage of rational exponents and the simplification of algebraic expressions using the laws of exponents when rational exponents are involved. The problems covered here are at the Intermediate Algebra level of difficulty.
Video 6 -Radical Expressions and Equations.
Simplifying Radicals.
This segment covers the simplification of algebraic expressions involving radicals. This segment also covers the equivalence of radicals with fractional exponents as well as rationalizing denominators where these radicals are encountered in denominators.
Addition and Subtraction of Radical Expressions.
This segment covers the simplification of algebraic expressions with several terms involving radicals. The method of extraction of perfect roots from the various terms followed by collecting like terms is covered.
Multiplication and Division of Radical Expressions.
This segment covers multiplication and division of radical expressions and their simplification by extracting perfect roots. This segment also covers rationalizing radical expressions with binomial denominators by multiplying numerator and denominator by the appropriate conjugate of the denominator.
Radical Equations.
This segment covers the solution of equations with terms containing radicals via successive isolation of radicals and their removal by raising both sides of the equation to the appropriate power. The removal of extraneous solutions from the solution set by checking all solutions in the original equation is also covered.
Video 7 -Quadratic Equations, Intercepts, Distance Midpoint
Miscellaneous Quadratic Equations Solved by Factoring.
This segment covers a variety of equations, involving various previously studied algebraic expressions, which are reducible to quadratic equations which can then be solved by factoring. This segment also covers the method of solving equations by substituting new symbols for expressions which appear repeatedly in the same equation.
Solving Quadratic Equations by the Completing the Square.
This segment covers the solution of quadratic equations in which the unknowns can be collected into a single term which is the square of a binomial and then are solvable directly by roots. The technique of completing the square is covered to show that the preceding form can always be obtained.
Solving Quadratic Equations by the Quadratic Formula.
This segment covers the quadratic formula and its use in solving quadratic equations. This segment also covers the rearrangement of any quadratic into standard form to facilitate identification of appropriate coefficients as to their proper place in the quadratic formula for computation of solutions.
Applications that Lead to Quadratic Equations.
This segment covers various applications which lead to equations which after rearrangement and simplification become reduced to quadratic equations. This segment also covers the Pythagorean Theorem and applications to perimeter and area problems.
Video 8 -Slope, Simultaneous Equations.
Intercepts, distance and Slope.
This segment covers the rectangular coordinate system and intercept for linear equations in two unknowns. This segment also covers the calculation of the distance between pairs of points with given coordinates as well as the slope of the line segment connecting them.
Equations of Straight Lines.
This segment covers the slope-intercept and point-slope form for the equation of a line. The relationship of a slope to steepness and methods of calculating slope via rise over run as well as rearrangement into slope-intercept form is covered. Parallel and perpendicular lines are also covered. The problems covered are at the Intermediate Algebra level of difficulty.
Graphs of Linear Inequalities.
This segment covers graphing of linear inequalities by the technique of graphing the boundary lines and using test points off of the boundary lines to decide which regions to shade or include. This segment also covers intersection, union, and absolute value inequalities.
Simultaneous Equations.
This segment covers the solution of systems of linear equations using the elimination method as well as the substitution method. This segment also covers an application.
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Search Course Communities:
Course Communities
Lesson 43: Linear Inequalities in Two Variables
Course Topic(s):
Developmental Math | Linear Inequalities
The lesson begins with a definition of a linear inequality and then looks at individual points that satisfy the inequality to motivate the existence of a larger set of points that satisfy the inequality. The point test is then presented and a general procedure for graphing inequalities. The lesson concludes with systems of inequalities and application problems.
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Purpose
of the course
The purpose of
this course is to
introduce the equations and fundamental theorems of mathematical fluid
dynamics, and to then to
derive practical numerical techniques that can be used to solve a wide
variety of fluid problems. In addition, the numerical techniques
you will learn can also be applied to the partial differential
equations one encounters in many other fields of science and
engineering.
This course will be given in the form of two six-week modules, as
follows:
Mathematical Introduction to Fluid
Mechanics (CES 716)
We derive the Euler and Navier-Stokes equations from the first
principles of continuum mechanics. Mathematical properties of these
systems of equations are discussed, such as the boundary conditions,
potential and rotational flow and representation of the equations in
different coordinate systems. We also briefly consider shocks, boundary
layers and turbulence as well as the limits of small and large Reynolds
number. Finally, we survey analytical solutions of the Euler and
Navier-Stokes equations.
Incompressible Computational Fluid
Dynamics (CES 715)
We introduce techniques for the numerical solution of partial
differential equations, with a special emphasis on fluid
dynamics. We focus on finite volume techniques (as a special case
of finite elements). We are particularly interested in equations
with discontinuities (interface problems), efficient treatment of
boundary layers and high Reynolds number flows. Fundamental
aspects such as local and global truncation error, consistency,
convergence, stability, non-uniform grids and numerical oscillations
are introduced in the context of specific problems. The module finishes
with the derivation of a full staggered grid discretization of the
incompressible Navier--Stokes equations (with general boundary
conditions and pressure correction split step). Matlab computer
codes are used throughout the course to illustrate the material.
Text
The main text for this course is Principles
of computational fluid dynamics
by P. Wesseling
(Springer, 2001). Course
outline
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Curriculum Design: Pre-requisites/Co-requisites/Exclusions
The notion of a limit underlies a whole range of concepts that are really basic in mathematics, including sums of infinite series, continuity, differentiation and integration. After the more informal treatment in the first year, our aim now is to develop a really precise understanding of these notions and to provide fully watertight proofs of the theorems involving them. We also show how the theorems apply to give useful facts about specific functions such as exp, log, sin, cos, including some integrals and other unexpected identities.
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Systems of Equations and Problem Solving, Set 1
Excerpted from
Patterns, ratios, equality, algebraic functions, and variables are some of the concepts covered in this printable book for elementary students. You'll find a variety of materials to encourage your young students to learn math
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Larson's market-leading text, PRECALCULUS is known for delivering sound, consistently structured explanations and exercises of mathematical concepts ...Show synopsisLarson's market-leading text, PRECALCULUS is known for delivering sound, consistently structured explanations and exercises of mathematical concepts to expertly prepare students for the study of calculus. With the ninth edition, the author understanding of the skill sets to help students better prepare for tests. Available with InfoTrac Student Collections http: //gocengage.com/infotrac
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TI Calc Instructions: Matrix Operations, by Diane Mathios
Instructions are for Row Operations Only for TI-83, 83+, and 86.
Please note that:
For the TI-82 or TI-84+, use the instructions for the TI-83 & 83+. For a TI-82 or a TI-83 that is not a TI-83+, there is a separate matrix key; matrix is not reached by using the x-1 key.
The TI-85 should work somewhat similarly to the TI-86; consult your calculator's instruction manual
For the TI-89 , you must consult your calculator's instruction manual
Which calculator is best to use for this class? The instructor will demonstrate the TI-83, 83+, 84 in class. These calculators will be the easiest to learn. TI-86 is also acceptable, but the instructor not demonstrate it.
The TI-89 is acceptable for use in Math 11 but the TI-89 is NOT recommended. The instructor will not demonstrate or teach in class how to use a TI-89. It is harder to use than the recommended calculators. You will need to be independent and learn how to use it on your own. The instructor has a program that we will use during the quarter that she will download to students' TI 83, 83+, 84, 86 calculators and this program may not be available for the TI-89.
Older models such as the TI-82 and 85 have some of the same functionality as the TI-83,84,86, but may lack some of the required functions or operations. Again, the instructor has a program that we will use during the quarter that she will download to students' TI 83, 83+, 84, 86 calculators and this program may not be available for the TI-82 or TI-85.
The instructor can not help with calculators from other manufacturers, which may not be able to do the work, and can not run the program that will be given to students using the TI-83, 83+, 84, 86
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Get online tutoring here.
Calculus Homework Help
Calculus lies at the center of math and science. It is also easier for students to find this subject interesting compared to other areas of math. Before we have some fun, let's review the basic topics that are normally considered part of college calculus that we can help with:
FUNCTIONS AND MODELS
LIMITS
DERIVATIVES
APPLICATIONS OF DIFFERENTIATION
INTEGRALS
APPLICATIONS OF INTEGRATION
INVERSE FUNCTIONS
TECHNIQUES OF INTEGRATION
DIFFERENTIAL EQUATIONS
PARAMETRIC EQUATIONS AND POLAR COORDINATES
INFINITE SEQUENCES AND SERIES
VECTORS AND THE GEOMETRY OF SPACE
VECTOR FUNCTIONS
PARTIAL DERIVATIVES
MULTIPLE INTEGRALS
VECTOR CALCULUS
SECOND-ORDER DIFFERENTIAL EQUATIONS
An absolutely fabulous place to get instructive articles in calculus is matharticles.com. And, if you haven't seen the MIT calculus videos, you haven't lived. These are essential for anyone interested in calculus.
To fulfill our mission of educating students, our online tutoring centers are standing by 24/7, ready to provide calculus homework help to students who need extra practice.
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Study Guide for Stewart/Redlin/Watson/Panman's College Algebra: Concepts and Contexts
9780495387916
ISBN:
0495387916
Edition: 1 Pub Date: 2010 Publisher: Brooks Cole
Summary: Reinforces student understanding with detailed explanations, worked-out examples, and practice problems. Lists key ideas to master and builds problem-solving skills. There is a section in the Study Guide corresponding to each section in the textReinforces student understanding with detailed explanations, worked-out examples, and practice problems. Lists key ideas to master and builds problem-solving skills. There is a section in the Study Guide corresponding to each section in the text.[less]
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Stinson Beach Physics such as quantum mechanics or even classical mechanics make extensive use of the mathematical tools and concepts studied in linear algebra, and I have taken many of those! The fact that I use the tools of linear algebra on a regular basis, instead of just studying the theory, means that m...
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Welcome
If you are new to the resource, please read the Introduction, particularly the contents and navigation pages. Otherwise, go directly to a section using the tabs across the top of the screen.
Functional Skills in Mathematics is a set of resources designed to help mathematics teachers to give students the skills they will need to gain a Functional Skills qualification, and to use in later life. To see a full contents list, go to the table of contents.
To return to this front page, click on the Functional Skills in Mathematics title at the top of any screen.
If you would like to order a copy of
Functional Skills in Mathematics,
please
click here.
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Saxon Teacher provides comprehensive lesson instructions that feature complete solutions to every practice problem, problem set, and test problem, with step-by-step explanations and helpful hints. These Algebra 1 1 3rd Edition. Five Lesson CDs and 1 Test Solutions CD included.
Does this include the Solutions manual and if not do I need it if I purchase the homeschool kit with the Saxon teacher cds
This kit does not contain the Solutions Manual. However, the Saxon Teacher CDs contain step-by-step solutions to the practice problems, problem sets, and tests, so the Solutions Manual would be optional.
"DIVE" (Digital Interactive Video Educator) is an excellent tutorial, and uses different illustrations than those presented in the Saxon Textbook. It does not have solutions to the problem sets.
"Saxon Teacher" contains the lesson instructions, practice problems and problem sets as they are presented in the Saxon Textbook, with some additional commentary. "Saxon Teacher" can also serve as a solutions manual for the practices, lessons and tests.
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Book DescriptionProduct Description
From Amazon-vacation reading (for most), but Principia Mathematica will reward the dedicated student with a deeper understanding of how we got here. --Rob Lightner
Book Description
The great three-volume Principia Mathematica is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premisses and primitive ideas, and so to prove that mathematics is a development of logic.This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will of course wish to refer to the complete edition).
--This text refers to the
Paperback
edition.
First this is a monumental work and one of the most influential works of the 20th century. I am not giving it five stars: this book earned them. With that said I don't think is the most influential book of the 20th century because such a book doesn't exist. In my opinion that kind of debate is totally misleading.
However the five stars do not suggest that you should buy this book. With the exception of libraries and scholars specializing in Russell or related subjects, I can't see anybody else spending [this amount] on a copy of this work. That is unless they like to collect books. For a math or philosophy student the paperback copy to *56 is all you need.
Unless you are a mathematician, a logician or a philosopher with a strong background in logic and philosophy of mathematics and aware of the issues surrounding the problems in the foundations of mathematics at the beginning of the 20th century then you are not going to benefit from STUDYING this book. The emphasis in studying is important because this book needs to be studied not just read like some reviewers may suggest.
If you are not an expert in this area and you want to learn about the subject then you may want to start with Bertrand Russell's "Introduction to Mathematical Philosophy". It summarizes the major points of this work for the layman and is Russell at its best (he won a Nobel prize mostly due to this book). Read it with a critical mind and then you can continue reading Quine, Putnam, Brower, Heyting and the rest. You can get a good bibliography from Benacerraf and Putnam's "Philosophy of Mathematics".
Finally if you are a mathematician, a logician or a philosopher you already know about this book and you don't need this review. Moreover you know you can borrow a copy from the university library for study...that is unless you like to collect books.
I decided to write a review, because, when reading the existing ones,- I realized their incorrectness. Leaving out the "Customer from Christchurch New Zealand", the rest shows an evident shallowness of mind. The reader "La-la land" utilizes an enormous mass of epithets discrediting Russell and Whitehead, which could be valuable in a form, but instead,- he shows a stupid prejudice that must have learned in his Mathematical-logic "polytechnic" course. I will only refute his last thought( which is the base of his "thesis"), because the others refute themselves. He presents Russell as a "Fruitless Mathematician", and even more stupid, compares him with Hilbert, saying: " at least he proved himself worthy.....". Throughout all Mathematics history we have individuals with enormous logic-constructive aptitudes, who although creating fundamentals results, were unable to understand their significance. Two perfect examples are Newton and Leibniz, both creators of the "infinitesimal calculus". One went on to construct the modern mechanistic view of physics in his "Principia". The other, with a much more profound understanding of logic, a superficial "monadic-substantial" and teleological ontology. Newtonian physics was a major episode in modern science, and Leibniz "subject-predicate" logic is the first glance at mathematical-logic.But their incorrect understanding of the infinitesimal calculus made them see, in it, the proof of an omnipotent god: they both conceived a universe with its first cause as god, and the human aptitude is, within it, merely an "algorithmic" one, which could never fully calculate god's creation. Hilbert, also providing fundamental results in constructive knowledge, went on to expose a somewhat "Hegelian" conception of mathematics, giving an almost silly definition of numbers. Both of this errors cause enormous damage, which I don't have space to describe now. Russell's "Principia Mathematica", although written with the wrong "motivation"( that is: to reduce the whole of mathematics into axiomatic form, finding the "universal method"), achieved unquestionable logic-mathematical results: The most valuable and original, the "theory of descriptions". in an abridged explanation, these theory comprehends the next: "algorithmic" function in logic and mathematics. when you say, " this is black", the theory of descriptions shows that you are only saying something about "this", which is a subject-variable(x), and black is an element-predicate, calculable within the conjunct "this". The theory permits mathematical-logic understand algorithmic functions, and is, also, what makes possible via your computer processor to read codified information. The result is more than a "fruit". it gives you the possibility of grasping that, like any other mathematical fruit, men is able of creating it,- and of reading it(calculate it). these means: Mathematical creations are only valuable as a source of human power, not as mystic ontological formulae,- that stupid motivation in all pseudo "Mathematicians". In terms of actuality, the axiomatic system, the method, has been perfected, simplified, and transcended. If I had to recommend some books on the matter, I would say Tarski's: "Introduction to logic and to the methodology of the deductive sciences", Patrick Suppes:"axiomatic set theory", continued by the reading of the: "Gödel proofs" by Raymond Smullyan, some other text dealing whith "boolean algebra" such as: "logic as algebra" by Halmos. This would give any self-educated person, the basic models he needs to comprehend math-logic, the "method" with which he can possibly contribute to this "powerful trend of modern thought" as described by tarski. Remember that Russell and whitehead say in the introduction that they not claim having the most perfect axiomatic reduction, only that the one presented was enough to reduce mathematics into that form, which was, until godel, true, or at least "thought possible"(completely). Is important to undersatnd that "principia mathematica" made "possible" the incompleteness proofs of Godel: his original paper was named "on formally undecidable propositions of principia mathematica and related systems"(see dover edition), and although he uses mostly the axioms of peano in his system, if someone as Russel had not attempted successfully such axiomatic construction of math, godel would have never found or seen the incompleteness of arithmetic's. Something similar could be said of the later notions of completeness of first order logic, metamathematics, etc. The few works (few only in number) independent from principia may be the ones of: 1) the polish masters: Lukasiewicz, Lesniewski, and the last king Tarski. 2) the forgotten Richard Martin's and Rudolf Carnap's logic-syntaxic-semantic conception of math-logic. The rest walked, continued walking the path of principia. Individual example: Quine. ...
The notation of PM is hard to read by anyone who learned logic post 1960, say. The typesetting is archaic. Hundreds of theorems are proved, but it is not clear where they all lead. Russell and Whitehead are guilty of a number of major philosophical confusions, such as use and mention, between meta- and object language, and their confused notion of "propositional function." Their choice of axioms can be much improved upon. The PM theory of types and orders is a complicated horror; Chwistek, Ramsey, and others later showed that it could be radically simplified. R & W think they can substitute the intensional for the extensional, and ultimately define sets and relations in logical terms. PM does not have a clue about model theory or metatheory. There is no hint of proofs of consistency, completeness, categoricity, and Loewenheim-Skolem. In this sense, the fathers of modern logic are Skolem, Goedel, Tarski, and Church. And Goedel did indeed prove that there must exist mathematical truths that cannot be proved true using the axioms of PM, or any other finite set of axioms.
But this is still one of the greatest works of mathematics and philosophy of all time. The long prose introduction is a philosophical masterpiece. The collaboration between Russell and Whitehead may be the greatest scientific collaboration in British history. Whitehead, who was trained as a mathematician, went on to become one of the shrewder philosophers of the 20th century, and supervised Quine's PhD thesis. PM's treatment of the algebra of relations (a brilliant generalisation of Boolean algebra that has not received the study it deserves) is perhaps the most thorough ever.
Mathematical logic is indeed the abstract structure that underlies the digital electronics revolution. And PM is still perhaps the greatest work of math logic ever penned.
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Diana Fisher's Modeling Dynamic Systems: Lessons for a First Course, the
follow-up to her popular Lessons in
Mathematics: A Dynamic Approach, provides a set of tools that
enable educators at the secondary and college levels to teach a one-semester or
one-year course in System Dynamics. Developed for beginning modelers, the
lessons contained in this book can be used for a core curriculum or for
independent study.
Updated in 2011, the Third Edition incorporates the latest material that Diana uses to teach her own students. The following lessons are new to this edition:
Explaining a Feedback Loop
Transfer of Loop Dominance
Class Demonstration of News Article
Specifying Units
Introduction to Oscillations
Pollution Model introducing:
Sector maps (high-level feedback loop diagrams)
Extreme value testing
Systematic parameter testing
Starting a Model in Equilibrium
Using the Storytelling Feature of STELLA
Course materials meet National Science Education Standards (NSES) and National
Council of Teachers of Mathematics (NCTM) standards and are out-of-the-box
ready for use in your classroom today.
Enable students to understand the unintended consequences of real
world problems systemically.
Modeling has been used for years to help scientists and policy makers find
solutions to complex problems. It is one of the most valuable and useful
applications of mathematics. However, most models are difficult to understand
and require significant mathematics to interpret.
Systems Thinking software like
STELLA offers an opportunity to create visual models that actively engage
students to study a wide variety of problems. Creating a model, allows for
"real-time" analysis and a more stimulating environment to glean insights. Modeling
Dynamic Systems: Lessons for a First Course provides an easy-to-use
set of teaching materials that are paced gently enough for students to learn to
create dynamic models using STELLA software.
,
Diana published Lessons
in Mathematics: A Dynamic Approach in 2001 and Modeling Dynamic
Systems: Lessons for a First Course in 2005. She has worked in
industry as a software engineer and co-authored (in the 1980s) three
programming textbooks published by Computer Science Press.
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Reform in mathematics instruction at the college level has been slow to arrive (Dossey, Halvorson, & McCrone, 2008), and many institutions of higher learning still follow the calculus model, while fewer and fewer students need calculus for their chosen areas of study (Ganter & Barker, 2003). Instead, mathematics that is applicable and transferable to other disciplines is more useful to many of today's college students. The Introduction to the Mathematical Sciences course that was the subject of this research study is a standards-based laboratory class that integrates algebra, statistics, and computer science. It was designed for students at both the high school and college levels who have struggled in mathematics. The intent of the course is to provide students with mathematics that they will find useful in their future careers, or future classes. The course is intended to reflect the ideals of reform mathematics at the college level. The purpose of the study was to examine the implementation of this curriculum, and its impact on student thinking and learning of algebra.
In exploring the research questions, the researcher found that the Introduction to the Mathematical Sciences course provided a reform-instruction setting where students were able to demonstrate their understanding of algebra, statistics and computer science. The students showed skill at moving between a number of representations of algebra concepts, indicating they were developing deeper understanding of those concepts. One of the key components of this course that reflected reform ideals was the extensive discussion that took place in the course. This instance of the implementation of the Introduction to the Mathematical Sciences course provides an example of how reform instruction in line with the recommendations of NCTM, MAA and AMATYC (Baxter Hastings, et al., 2006) can be successful in helping students at the introductory college level gain understanding of mathematics. This research study describes a course that successfully plays out using reform instructional methods that are in sharp contrast to other college courses taught using traditional lecture style methods. High DWF rates among students who take college algebra (Lutzer, et al., 2005) indicate that the current model of instruction at the college level is not working. For students who lack confidence in their mathematical abilities and have seen little success in mathematics, this type of course may be a tool that can provide students the mathematical skills necessary to move forward in their studies and
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Function Analyzer Highlight the rationale behind symbolic operations used to solve a linear equation with this tool that displays changes in the graphic and area models of functions as you change the value of each symbolic element. Author(s): No creator set
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Algebra is Awesome! This project will help you understand patterns which is one of the foundations of algebra.Linear Algebra When wo Author(s): No creator set
College Algebra Preview - Patti Blanton This course includes the study of linear and quadratic equations; inequalities and their applications; polynomial, rational, exponential and logarithmic functions; and systems of equations.
This is the first in a series of lectures on College Algebra by Patti Blanton. To view the full course please visit and open Missouri State on iTunes U. Navigate to the Complete Courses section in iTunes U to find all the videos for this course. Author(s): No creator set
Children's Heart Conditions (Part 1 one of this two-part program addresses the following topics:
Infants and heart
Congenital heart defects
Genetic heart defects
Birt Author(s): No creator set
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Children's Heart Conditions (Part 2 two of this two-part program addresses the following topics:
Arrhythimia
Heart conduction system
Cardiac Ablation
Pacemakers
Defi Author(s): No creator set
Math Literature Connections: Patterns and Algebra Ideas and activities that use Two of Everything, One Grain of Rice and the King's Chessboard to introduce students to function machines and input/output tables. Links to appropriate templates are also provided. Author(s): No creator set
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Algebra: Growing Patterns Introduce elementary students to the concept of functions by investigating growing patterns. Visual patterns formed with manipulatives are especially effective for elementary students and allow them to concretely build understanding as they first reproduce, then extend the pattern to the next couple of stages. Author(s): No creator set
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Get Lucky and Algebra Jeopardy "Get Lucky" is a fast-paced thinking game that requires students to be creative in the ways that they can manipulate basic operators and randomly given integers to reach a "lucky number." "Algebra Jeopardy" is a team-based activity that tests the knowledge students have acquired in the classroom with review questions categorized by topic. The combination of these games is appropriate for students in 6th through 9th grade (Algebra 1). Author(s): Creator not set
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Quadratic Functions
4th six weeks
Targeted TEKS:
A.1A, A.2A,B, A.3A, A.4A,C, A.9A,B,C,D, A.10A, B
Quadratics Galore
As students move into quadratic equations, there are much more vocabulary and techniques to be learned involving solving equations. This PBL unit is designed to make the experience meaningful and present students with various ways to use quadratic functions. It also relates the new concepts with previously learned concepts.
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Just in Time Algebra for Students of Calculus in Management and the Lifesci your students having a problem in your calculus class? It's possible that calculus isn't really the problem-it may be the algebra that's giving them trouble. Sharp algebra skills are essential to mastering calculus, and Just-in-Time Algebra for Students of Calculus in Management and the Life Sciences is designed to bolster these skills exactly at the moment that students need them in calculus. The easy-to-use Table of Contents has the algebra topics arranged in the order that students need them as they study calculus. So all the information students need is right here-just in time!
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Product Synopsis
Oxford A Level Mathematics for Edexcel takes a completely fresh look at presenting the challenges of A Level. It specifically targets average students, with tactics designed to offer real chance of success to more students, as well as providing morestretch and challenge material. This Core book includes a background knowledge chapter to help bridge the gap between AS and A2 study, as well as a free CD containing a wealth of further practice material and worked solutions
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Welcome to the Math Circle
The Fall 2013 session will start on September 28th, 2013. There will be a very limited number of spots for new students. Please check back the web page in mid-late July for registration information.
Los Angeles Math Circle (LAMC) is a top-tier math circle open to elementary, middle and high school students interested in mathematics and eager to learn. LAMC is a program of the Department of Mathematics at UCLA and is supported by the National Science Foundation, the Boeing Employees Community Fund, Raytheon, a gift from the Glickman family, and math circle families donations.
Following the traditions of Russian and Eastern European math circles, the program focuses on showcasing the beauty of mathematics and its applications, improving problem solving skills, preparing students for a variety of contests and competitions, creating a social context for mathematically inclined students as well as attracting students to math-related careers.
The topics we cover are as varied as advanced plane geometry, elementary number theory, fractals, combinatorics, game theory for the older students, logic, counting techniques, basic combinatorics for the younger ones. The main goal is to learn wonderful mathematics not covered in a typical school curriculum but accessible to the mathematically inclined students. Another goal is to actively engage students in problem solving and to learn effective problem solving strategies. To get an idea of what we are doing, please look at the titles and descriptions of past meetings which are available on our "Circle calendar" for the current year and on our "Archive" page for previous years.
Math Circle Structure
In 2012-2013, Math Circle will have the following levels of participation:
High School Circle (grades 8-12; MS 6221), led by Mike Hall and Yingkun Li;
All Math Circle meetings take place on Sunday afternoons at UCLA.
Enrollment for Fall 2012
Please apply for Fall 2012 by going to "Apply to LAMC" on the left toolbar. Please submit your complete application before August 20th. We expect that the number of applicants will greatly exceed the number of spots we have in the math circle. Please be sure to answer all the questions in the application. While given some priority, previously enrolled students do not automatically get a spot in the math circle and need to go through the same application process.
Important Note: Math. Sci. Building Access
Starting in early April 2011, the Mathematical Science Building will be locked on Sundays. The glass doors on the 5th floor (entry from the breezeway with vending machines) should be unlocked during the times of the math circle. However, all other doors in the building will be locked. If you are accustomed to entering the building through other doors, please make sure that you know how to enter through the doors on the 5th floor. Please see our Directions Page for more information.
Please refer to FAQs if you have questions about the proper placement (choice of group) and other questions related to math circle.
Contact LAMC
If you have any questions or comments, please write to Dr. Olga Radko, director of the Los Angeles Math Circle, at radko@math.ucla.edu after consulting the FAQs.
If you would like to provide anonymous feedback on the circle please use "Contact us" form on the left toolbar. Keep in mind that if you want to receive an answer to your comments you need to provide a return address.
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This review of arithmetic and elementary algebra is designed to prepare the student to study MATH 100 (Mathematical Sampler) or MATH 101 (Finite Mathematics). The course is designed as a self-directed study experience. The student will have access to textbook explanations and online resources to gain mastery of the material. Appropriate testing is done with the tutors in the Mathematics Resource Center (MaRC). A nominal registration fee is charged.
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Groups
The Algebra One course begins with a fast-paced review of the previous year. The beauty, clarity, and utility of algebraic reasoning are explored through practical and not so practical challenges. We will conclude with a study of the quadratic formula, and introduce formal logical reasoning.
This section contains information for our Explorer Tournament El Toro Boat Building Project. Documents for this project are listed below. Not all documents are publicly available. For full access, login or create an account.
In eighth grade, students begin bulding functional furniture using
traditional tools and techniques. They often build a threee-legged stool, a
small table, or a bench. More complex use of mallots and gauges is required
in these projects, as well as a greatly expending set of other tools. Mortise
and tennon joints are used to join the legs to the top
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MATLAB for Electrical and Computer Engineering Students and Professionals: With Simulink
Author: Roland Priemer
Year: 2013
Format:Paperback
Product Code:
SBPC5010
ISBN: 978-1-61353-188-4
Pagination: 450 pp.
Stock Status: Pre-order
The
arrival date is
May 2013
Your account will only be charged when we ship your item.
£38.25 Pre-order price
£29.25 Member price
£45.00
Full price
Description
This book combines the teaching of the MATLAB programming language with the presentation and development of carefully selected electrical and computer engineering (ECE) fundamentals. This is what distinguishes it from other books concerned with MATLAB: it is directed specifically to ECE concerns. Students will see, quite explicitly, how and why MATLAB is well suited to solve practical ECE problems.
This book is intended primarily for the freshman or sophomore ECE major who has no programming experience, no background in EE or CE, and is required to learn MATLAB programming. It can be used for a course about MATLAB or an introduction to electrical and computer engineering, where learning MATLAB programming is strongly emphasized. A first course in calculus, usually taken concurrently, is essential.
The distinguishing feature of this book is that about 15% of this MATLAB book develops ECE fundamentals gradually, from very basic principles. Because these fundamentals are interwoven throughout, MATLAB can be applied to solve relevant, practical problems. The plentiful, in-depth example problems to which MATLAB is applied were carefully chosen so that results obtained with MATLAB also provide insights about the fundamentals.
With this "feedback approach" to learning MATLAB, ECE students also gain a head start in learning some core subjects in the EE and CE curricula. There are nearly 200 examples and over 80 programs that demonstrate how solutions of practical problems can be obtained with MATLAB. After using this book, the ECE student will be well prepared to apply MATLAB in all coursework that is commonly included in EE and CE curricula.
Book readership
Freshman and sophomore students in electrical and computer engineering curricula. Professional electrical and computer engineers needing to learn MATLAB or needing a refresher.
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In Section 4 we introduce the hyperbolic functions sinh, cosh and tanh, which are constructed from exponential functions. These hyperbolic functions share some of the properties of the trigonometric functions but, as you will see, their graphs are very different.
In Section 2 we describe how the graphs of polynomial and rational functions may be sketched by analysing their behaviour – for example, by using techniques of calculus. We assume that you are familiar with basic calculus and that its use is valid. In particular, we assume that the graphs of the functions under consideration consist of smooth curves.
In Section 1 we formally define real functions and describe how they may arise when we try to solve equations. We remind you of some basic real functions and their graphs, and describe how some of the properties of these functions are featured in their graphs.
Many problems are best studied by working with real functions, and the properties of real functions are often revealed most clearly by their graphs. Learning to sketch such graphs is therefore a useful skill, even though computer packages can now perform the task. Computers can plot many more points than can be plotted by hand, but simply 'joining up the dots' can sometimes give a misleading picture, so an understanding of how such graphs may be obtained remains important. The object of reminds you about powers of numbers, such as squares and square roots. In particular, powers of 10 are used to express large and small numbers in a convenient form, known as scientific notation, which is used by scientific calculators.
This unit is from our archive and is an adapted extract from Open mathematics (MU120) which is no longer taught by The Open University. If you want to study formally with us, you may wish to explore other courses we offerUp to now only those points with positive or zero coordinates have been considered. But the system can be made to cope with points involving negative coordinates, such as (−2, 3) or (−2, −3). Just as a number line can be extended to deal with negative numbers, the x-axis and y-axis can be extended to deal with negative coordinatesPie charts are representations that make it easy to compare proportions: in particular, they allow quick identification of very large proportions and very small proportions. They are generally based on large sets of data.
The pie chart below summarises the average weekly expenditure by a sample of families on food and drink. The whole circle represents 100% of the expenditure. The circle is then divided into 'segments', and the area of each segment represents a fraction or pe climate change draws attention to the power of human activity to transform the planet in its entirety, and it is brought into sharp focus by the predicament of low-lying islands like Tuvalu. As we have seen in this unit, the issue of rising sea level and other potential impacts of changing global climate also point to the transformations in the physical world that occur even without human influence. Oceanic islands provide a particularly cogent reminder that the living things wit project, or single, team consists of a group of people who come together as a distinct organisational unit in order to work on a project or projects. The team is often led by a project manager, though self-managing and self-organising arrangements are also found. Quite often, a team that has been successful on one project will stay together to work on subsequent projects. This is particularly common where an organisation engages repeatedly in projects of a broadly similar nature – forOnce a small number of chains have been started, propagation involves successive addition of monomer units to achieve chain growth. At each step the free radical is regenerated as it reacts with the double bond. So in the case of styrene the propagation step is
The free radical can also add on in
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Join the thousands of students that have used our Algebra Video Tutorials since 2004 to master the subject!
There is no easier way to learn Algebra than to have a calm teacher show you each and every step. We don't focus on shortcuts - we focus on you truly understanding the subject so that every step makes sense!
The Matrix Algebra Tutor is a 7 hour course spread over 2 DVD disks that teaches the student how to perform Matrix operations. These topics are usually taught at the end of a high school algebra sequence, in college algebra, or in a linear algebra class. Every topic in this course is taught by working example problems that begin with the easier problems and gradually progress to the harder problems. Every problem in taught in step by step detail ensuring that all students understand the content.
The skills learned in this course will aid the student in more advanced areas of math and science. These skills are used time again in more advanced courses such as Physics and Calculus. The teaching method employed on this DVD ensures that the student immediately gains confidence in his or her abilities and improves homework and exam taking skills.
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A Transition to Advanced Mathematics
A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically--to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems.
Book and DVD. A guide to advanced improvisation. This sequel to the best-selling improv book Truth in Comedy is designed to help improv performers move up to the more advanced levels of improvisation ...
Abstract theory remains an indispensable foundation for the study of concrete cases. It shows what the general picture should look like and provides results that are useful again and again. Despite ...
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0840048149
9780840048141
113317101X
9781133171010, delivering matchless flexibility to both traditional and modern practitioners. The Tenth Edition, as with previous editions, is suitable for both majors and non-majors alike. The text abounds with helpful examples, exercises, applications, and features to motivate further exploration. Portfolio profiles highlight the way actual professionals use math in their day-to-day business. Newly enhanced technology sections provide step-by-step instructions for solving examples and exercises in Excel 2010. Supported by a powerful array of supplements including Enhanced WebAssign, the new Tenth Edition enables students to make full use of their study time and maximize their chances of success in class. «Show less,... Show more»
Rent Finite Mathematics for the Managerial, Life, and Social Sciences 10th Edition today, or search our site for other Tan
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Contents
Mathematical language
Introduction
When we try to use ordinary language to explore mathematics, the words involved may not have a precise meaning, or may have more than one meaning. Many words have meanings that evolve as people adapt their understanding of them to accord with new experiences and new ideas. At any given time, one person's interpretation of language may differ from another person's interpretation, and this can lead to misunderstandings and confusion.
In mathematics we try to avoid these difficulties by expressing our thoughts in terms of well-defined mathematical objects. These objects can be anything from numbers and geometrical shapes to more complicated objects, usually constructed from numbers, points and functions. We discuss these objects using precise language which should be interpreted in the same way by everyone. In this unit we introduce the basic mathematical language needed to express a range of mathematical concepts.
Please note that this unit is presented through a series of downloadable PDF files.
This unit is an adapted extract from the Open University course
Pure mathematics
(M208)
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Due to popular demand by teachers, students, and professionals, we have brought back these essential works of mathematics and science. We'll be offering even more important reissues every month — stop by again soon for the latest updates.
To visit our main Math and Science Shop, please click here. And be sure to join our Math and Science Club for a 20% everyday discount, free newsletter, and other exclusive benefits.An Introduction to Algebraic Structures by Joseph Landin This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.
Relativity, Thermodynamics and Cosmology by Richard C. Tolman Landmark study discusses Einstein's theory, extends thermodynamics to special and general relativity, and also develops the applications of relativistic mechanics and thermodynamics to cosmological models.
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Applied Optics and Optical Design, Part One by A. E. Conrady Classic detailed treatment for practical designer. Fundamental concepts, systematic study and design of all types of optical systems. Reader can then design simpler optical systems without aid. Part One of Two.
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Complex Variables by Francis J. Flanigan Contents include calculus in the plane; harmonic functions in the plane; analytic functions and power series; singular points and Laurent series; and much more. Numerous problems and solutions. 1972 edition.
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A Concept of Limits by Donald W. Hight An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. Many exercises with solutions. 1966 edition.
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Concepts of Force by Max Jammer This work by a noted physicist traces conceptual development from ancient to modern times. Kepler's initiation, Newton's definition, subsequent reinterpretation — contrasting concepts of Leibniz, Boscovich, Kant with those of Mach, Kirchhoff, Hertz. "An excellent presentation." — Science.
Our Price:$12.95Elasticity by Robert William Soutas-Little A comprehensive survey of the methods and theories of linear elasticity, this three-part introductory treatment covers general theory, two-dimensional elasticity, and three-dimensional elasticity. Ideal text for a two-course sequence on elasticity. 1984 edition.
Electromagnetism by John C. Slater, Nathaniel H. Frank A basic introduction to electromagnetism, supplying the fundamentals of electrostatics and magnetostatics, in addition to a thorough investigation of electromagnetic theory. Numerous problems and references. Calculus and differential equations required. 1947
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Book Description: Erudite and entertaining overview follows development of mathematics from ancient Greeks, through Middle Ages and Renaissance to the present. Chapters focus on logic and mathematics, the number, the fundamental concept, differential calculus, the theory of probability, and much more. Exercises and problems.
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Math 141: Precalculus I
Common Course Number
Prior to Summer 2009, this course was known as Math 131; only the course number has changed.
Course Description
Math 141 is the first course in a two-quarter precalculus sequence that also includes Math 142. Math 141 focuses on the general nature of functions. Topics include: linear, quadratic, exponential, and logarithmic functions; and applications.
Who should take this course?
Generally, students seeking to take the 151–152–153 calculus sequence take the 141–142 precalculus sequence first. Some students in programs like business take this course (in place of Math 140) and then take Math 148 instead of Math 142. You should consult the planning sheet for your program and consult an advisor to determine if this sequence is appropriate for you.
Who is eligible to take this course?
The prerequisite for this course is Math 90 with a grade of 2.0 or higher. Students new to EdCC with an appropriately high Accuplacer score may also consider taking Math 141 used 142.
What else is required for this course?
Students are required to have a graphing calculator; the TI-83 Plus or TI-84 Plus is recommended.
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Difference and Differential Equations in Mathematical Modelling demonstrates the universality of mathematical techniques through a wide variety of applications. Learn how the same mathematical idea governs loan repayments, drug accumulation in tissues or growth of a population, or how the same argument can be used to find the trajectory of a dog pursuing a hare, the trajectory of a self-guided missile or the shape of a satellite dish. The author places equal importance on difference and differential equations, showing how they complement and intertwine in describing natural phenomena.
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A First Course in Computational Algebraic Geometry is designed for young students with some background in algebra who wish to perform their first experiments in computational geometry. Originating from a course taught at the African Institute for Mathematical Sciences, the book gives a compact presentation of the basic theory, with particular emphasis on explicit computational examples using the freely available computer algebra system, Singular. Readers will quickly gain the confidence to begin performing their own experiments.
way and using an easy to follow format, it will help boost your understanding and develop your analytical skills. Focusing on the core areas of numeracy, it will help you learn to answer questions without using of a calculator and...
This book makes quantitative finance (almost) easy! Its new
visual approach makes quantitative finance accessible to a broad
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Quantitative Techniques: Theory and Problems adopts a fresh and novel approach to the study of quantitative techniques, and provides a comprehensive coverage of the subject. Essentially designed for extensive practice and self-study, this book will serve as a tutor at home. Chapters contain theory in brief, numerous solved examples and exercises with exhibits and tables.
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The book is meant for an introductory course on Heat and Thermodynamics. Emphasis has been given to the fundamentals of thermodynamics. The book uses variety of diagrams, charts and learning aids to enable easy understanding of the subject. Solved numerical problems interspersed within the chapters will help the students to understand the physical significance of the mathematical derivations.
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Ankit1010 wrote:All right, Real Analysis is a proof-based course. If you have not had one of those before, it will be quite different from your other math classes. No longer will the professor tell you how to solve problems and then ask you to solve them. Now you will have to prove that the techniques to solve those problems are actually valid. You should be familiar with proof by induction, proof by contradiction, and proof by contraposition.
The course will start out covering thing that you've known since elementary school, but have probably never studied rigorously before. For example, in the section about field axioms, you might be asked to formally prove that 0·1=0. You might have to rigorously define what it means for a real number to be "positive", and prove that the positive numbers are closed under addition, multiplication, and division, but not subtraction.
From the list of topics you provide, it seems likely your course will not make you prove that such a thing as the real numbers actually exists. Instead it will implicitly take the stance, "If a complete ordered Archimedean field exists, these are the properties it must have."
Most of the course will stem from a few major ideas. One of these is the least upper bound property, meaning every bounded set of real numbers has a least upper bound in the reals. Another is trichotomy, meaning for any two real numbers x and y, exactly one of "x=y", "x<y", and "x>y" is true.
There will be a lot of topics dealing with limits from the ε-δ definition. This will probably be couched in the language of neighborhoods and balls, and likely will constitute your first introduction to the study of metric spaces. The course will start slowly, then progress quickly, until at the end you will be rigorously proving calculus theorems that you might not have seen before.
Qaanol wrote:And it really is a ton of fun. If you like that sort of thing, anyways.
Ben-oni wrote:Practice proofs. Look up any of the terms listed that your not familiar with. That should do you good for now.
Qaanol wrote:... AsI've actually done several proof-based courses before and am very comfortable with writing and understanding formal proofs. Let me clarify what I meant in the question - I want to know what textbooks/problem sets/video lectures/resources I can use to start learning the material that will be taught DURING the class, not the general areas I should cover for background knowledge. The fact is that my GPA that needs a lot of work, and next semester promises to be tough so I'm trying to effectively teach myself everything we do in class over the summer to get a head-start.
Understanding Analysis by Stephen Abbot is a very good book for self studies and the toc is suspiciously close to your course description. A good textbook in combination with wikipedia and will probably do the trick.
Alright, thanks for the advice! Understanding Analysis looks like a great book, I'll definitely pick up a copy, and I'll find out which text we'll be using for the class soon too. It will likely be either Principles of Mathematical Analysis by Rudin or Understanding Analysis. I love stack exchange, and that coupled with this forum for more serious difficulties should be enough to resolve any problems.
Ankit1010 wrote:I'm taking undergrad Real Analysis I at college next semester, and I want some advice on how I can start preparing for the course over summer since I need to do well on it.
I had a wonderful academic experience in that course. There were two factors I've identified.
1) I had a fabulous teacher. You have some control over that if there's more than one section and you can find reviews. This is difficult material ... and for someone who wants to do advanced math or physics, it's absolutely essential to nail this course. So get the best teacher you can.
And along these lines ... buddy up to the TA's. The TA's are grad students who still remember what it's like to not understand this material ... so they can be incredibly helpful. Join a study group. Go to TA office hours. Be friendly. Hang around with the other students. It really helps to grapple with this material with other people.
2) I took it during summer school and took nothing else. In fact I was taking an upper division computer science class and just dropped it. I did nothing but real analysis. And it really made a difference. This is a very labor-intensive course. You just have to do epsilon proofs till they come out your ears. Because the course involves concepts that are deep; and techniques that are precise. You really have to put some time into this class.
That would be my advice. Sign up with a good prof; hang out with the TA'S and other students; and clear the decks in the rest of your life so that you can spend all your time thinking about real analysis.
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Mathematics
The goal of this course is to build a solid foundation in algebraic methods and techniques to serve as a basis for further study. Directed toward students having minimal prior training in mathematics, the course of study begins with basic principles and progresses through the study of quadratic equations, graphing and the solution of systems of linear equations. Although designed for the beginning student, this course may also serve as a terminal course for those students desiring mainly to increase their confidence and proficiency in applying basic algebraic problem-solving concepts and techniques. Placement is by diagnostic testing.
MS 115
Quantitative Literacy
3 CR.HR.
MS111 OR MS242 OR MS141
MS 115
Quantitative Literacy
3 CR.HR.
MS111 OR MS242 OR MS141
Quantitative Literacy provides a college level experience that focuses on the process of interpreting and reasoning with quantitative information. Students are expected to build on prior understanding of mathematical models and applications, while integrating concepts from logic, algebra, geometry, probability and statistics. Understanding the language of mathematics, developing strategies and interpreting results, are learned via a context driven approach requiring a willingness to think about quantitative issues in new ways. The three credit course meets general education quantitative literacy requirement
MS 131
Logic and Problem Solving
3 CR.HR.
MS 131
Logic and Problem Solving
3 CR.HR.
This course is designed to develop logical thought processes and to lead to critical forms of reading and thinking. Topics include statement forms and types of statement connectives. Techniques of problem solving are taught.
MS 132
Probability and Statistics
3 CR.HR.
(MS111 OR MS141 OR MS242 OR MS331 OR MS232 Or MS 180 OR MS 181 OR MS 182)
MS 132
Probability and Statistics
3 CR.HR.
(MS111 OR MS141 OR MS242 OR MS331 OR MS232 Or MS 180 OR MS 181 OR MS 182)
This course is an introduction to the theory and application of probability and statistical analysis. Both descriptive and inferential techniques will be studied, with emphasis placed on statistical sampling and hypothesis testing. Also considered will be linear regression, contingency table analysis, and decision-making under uncertainty.
MS 141
Contemporary College Algebra
4 CR.HR.
MS 141
Contemporary College Algebra
4 CR.HR.
Contemporary College Algebra provides students a college level academic experience that emphasizes the use of algebra and functions in problem solving and modeling, provides a foundation in quantitative literacy, supplies the algebra and other mathematics needed in partner disciplines, and helps meet quantitative needs in, and outside of, academia. Students address problems presented as real world situations by creating and interpreting mathematical models. Solutions to the problems are formulated, validated, and analyzed using mental, paper and pencil, algebraic, and technology-based techniques as appropriate. Four credit hours.
MS 150
History of Mathematics
3 CR.HR.
MS 141, or MS 180 or MS 181 or MS 182
MS 150
History of Mathematics
3 CR.HR.
MS 141, or MS 180 or MS 181 or MS 182
This course introduces students to the development of mathematics from ancient to modern times, with emphasis on methods and techniques of particular times and cultures. The course also explores the connections between mathematics and other types of academic or artistic thought of a specific period, as well as the influence of mathematics on various societies.
MS 180
Precalculus with Trigonometry
4 CR.HR.
MS 180
Precalculus with Trigonometry
4 CR.HR.
This course is intended to prepare students for MS 181 Calculus with Applications as well as providing instruction in trigonometry to support subsequent studies in physics, chemistry, and mathematics. Emphasis is on the analysis of elementary functions and modeling, including polynomial and rational functions, exponential and logarithmic functions, and trigonometric functions. Topics in analytic trigonometry and analytic geometry are also included. Four credit hours.
MS 181
Calculus with Applications
4 CR.HR.
MS180
MS 181
Calculus with Applications
4 CR.HR.
MS180
This course provides an introduction to single variable calculus and its application. Emphasis is on conceptual understanding of the major ideas of calculus including limits as models of approximation, derivatives as models of change, and integrals as models of accumulation. Concepts are explored by combining, comparing and moving among graphical, numerical, and algebraic representations. This course serves as a prerequisite for MS182 Calculus II. Four credit hours.
MS 182
Calculus I I
4 CR.HR.
MS181
MS 182
Calculus I I
4 CR.HR.
MS181
This course is a continuation of MS181 Calculus with Applications. Prepares students for subsequent studies in mathematics, science, and business. Topics include concepts and applications of numerical integration, applications of integration, antidifferentiation, function approximation, improper integrals, and infinite series. Emphasis on concepts, complementing symbolic with graphical and numerical points of view. Integrates technology to support pedagogy and computation. Four credit hours.
MS 221
Number Theory
3 CR.HR.
MS 141 or MS 180 or MS 181 or MS 182
MS 221
Number Theory
3 CR.HR.
MS 141 or MS 180 or MS 181 or MS 182
In this course, students will explore the structure and properties of the Integers and some natural generalizations. Topics covered include unique factorization into primes, modular arithmetic, Fermat's Little Theorem and its applications, and may also include quadratic reciprocity, simple arithmetic functions, diophantine equations, factorization methods, primality testing, and cryptography.
MS 223
Research Design
3 CR.HR.
MS132
MS 223
Research Design
3 CR.HR.
MS132
This course introduces basic concepts and skills needed for understanding and conducting research in the social, educational and health sciences. Students will receive a basic introduction to the fundamentals of research – what it involves, what types exist, and how to design and conduct such research. Examined are the essential terms and concepts of research necessary for students to critically evaluate research literature, develop solid research questions, and plan simple research projects. Students will acquire foundation knowledge through readings and lecture. Active engagement with the research process will occur through class participation, exercises, literature reviews, development of research questions, and creation of inquiry strategies for answering research questions.
MS 230
Multivariable Calculus
4 CR.HR.
MS 182
MS 230
Multivariable Calculus
4 CR.HR.
MS 182
Extends the notions of single-variable Calculus to functions of several variables. Includes vector-valued functions, arc length, curvature, partial differentiation, the chain rule, and grad, div, curl, as well as iterated integrals.
MS 232
Finite Mathematics
3 CR.HR.
(MS111 OR MS141 OR MS242)
MS 232
Finite Mathematics
3 CR.HR.
(MS111 OR MS141 OR MS242)
In this the student studies the algebraic development of linear and nonlinear equations and inequalities. Topics include math of finance, analytic geometry, linear systems of equations and inequalities, matrix theory, and linear programming. This course is designed as a continuation for those students who have taken Ms 111.
MS 241
Linear Algebra with Applications
3 CR.HR.
MS 181
MS 241
Linear Algebra with Applications
3 CR.HR.
MS 181
This course begins with a generalized study of systems of linear equations, developing the notion of vectors and matrices. From these ideas naturally follows the study of vector spaces of dimension three or larger, including bases, eigenvalues, eigenvectors, and matrix representations of linear transformations and change of bases. Applications discussed may include computer graphics, facial recognition, (internet) search optimization, linear programming, cryptography, Leontief economic analysis.
MS 243
Trigonometry
1 CR.HR.
(MS141 OR MS242)
MS 243
Trigonometry
1 CR.HR.
(MS141 OR MS242)
This course is intended to round out the student's knowledge of basic mathematics through the study of trigonometry and its applications to solving triangles. Topics include trigonometric functions, radian measure, identities, law of sines, law of cosines, polar coordinates and complex numbers.
MS 258
Introduction to Differential Equations with Linear Algebra
4 CR.HR.
MS 182
MS 258
Introduction to Differential Equations with Linear Algebra
4 CR.HR.
MS 182
Differential Equations is the study of how to identify a function from equations involving the derivatives of the function. These types of equations arise naturally in a number of places, among them biological population models, radioactive decay, heat diffusion, motion. A variety of techniques will be explored, such as separation of variables, integrating factors, variation of parameters, undetermined coefficients, and the Laplace transform. This course also includes an introduction to elementary linear algebra.
MS 299
Topic/
1-6 variable CR.HR.
MS 299
Topic/
1-6 variable CR.HR.
This course is intended to provide the opportunity to offer introductory courses in mathematics that would not normally be a part of the Husson curriculum. As such the topics will depend upon the interests of students and faculty.
MS 332
Applied Statistics
3 CR.HR.
MS132
MS 332
Applied Statistics
3 CR.HR.
MS132
This course continues the development of statistical analysis begun in Ms 132. Following a brief review of the elementary ideas of descriptive and inferential statistics, a variety of intermediate-level topics and procedures will be studied, including analysis using the chi-square distribution, regression and correlation analysis, analysis of variation, time series analysis, decision theory, and others.
MS 345
Biostatistics
3 CR.HR.
MS223
MS 345
Biostatistics
3 CR.HR.
MS223
Biostatistics encompasses the application and use of statistical procedures for the purposes of obtaining a better understanding of variations in data and information on living systems. Students will become familiar with one, or more, statistical software packages which will have descriptive and analytic statistical capabilities as well as report writing capacity. This course will instruct students on how to use and interpret data and information through the application of the principles of statistical inference. Specific diseases and public health issues will be used as examples to illustrate the application and use of biostatistical principles.
MS 450
Modeling and Simulation
3 CR.HR.
MS 181, MS 182, MS 216
MS 450
Modeling and Simulation
3 CR.HR.
MS 181, MS 182, MS 216
This course introduces computer simulation as a research tool through its application to problems from calculus, differential equations, linear algebra, graph theory, dynamical systems, and physics.
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Series overview MathsWorks for Teachers has been developed to provide a coherent and contemporary framework for conceptualising and implementing aspects of middle and senior mathematics curricula. more...
Boost Your grades with this illustrated quick-study guide. You will use it from college all the way to graduate school and beyond. FREE chapters on Linear equations, Determinant, and more in the trial version. Clear and concise explanations. Difficult concepts are explained in simple terms. Illustrated with graphs and diagrams. Table of Contents. I.... more...
Drawn from the literature on the asymptotic behavior of random permanents and random matchings, this book presents a connection between the problem of an asymptotic behavior for a certain family of functionals on random matrices and the asymptotic results in the classical theory of the U-statisticsMatrices are effective tools for modelling and analysing dynamical systems. This book presents the basics of the Cayley-Hamilton theorem and elementary operations of polynomial and rational matrices. It covers topics such as: normal matrices; rational and algebraic polynomial matrix equations; and more. more...
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Curriculum Design: Pre-requisites/Co-requisites/Exclusions
The aim of this module is to build on the theory of groups as introduced in the 2nd year module MATH225: Groups and Rings. Emphasis will be given to finite groups. The most important results covered will be as follows:
The classification of finite abelian groups.
The orbit-stabilizer theorem.
The Jordan-Holder theorem.
The classification and symmetry groups of the Platonic solids.
Sylow's theorems.
We shall first consider a way of comparing the elements of a group and show how a group may be built up from smaller components using 'direct products'. Next we shall treat situations in whch
Educational Aims: General: Knowledge, Understanding and Skills
The aim of this module is to build on the theory of gorups as introduced in the 2nd year module MATH225: Groups and Rings. Emphasis will be given to finite groups. The most important results covered will be as follows:
The classification of finite abelian groups
The orbit-stabilizer theorem
the Jordan-Holder theorem
The classification and symmetry groups of the Platonic solids
Sylow's theorems.
We shall first consider a way of comparing the element of a group and show how a group may be built up from smaller components using 'direct products'. Then we shall show how a general group can be broken in to 'simple' pieces. Next we shall treat situations in which
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032156524X
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Students use number sense and
numeration to develop an understanding of the multiple uses of numbers in the real world,
the use of numbers to communicate mathematically, and the use of numbers in the
development of mathematical ideas.
relate trigonometric relationships to the
area of a triangle and to the general solutions of triangles.
apply the normal curve and its properties
to familiar contexts.
design a statistical experiment to study a
problem and communicate the outcomes, including dispersion.
use statistical methods, including scatter
plots and lines of best fit, to make predictions.
apply the conceptual foundation of limits,
infinite sequences and series, the area under a curve, rate of change, inverse variation,
and the slope of a tangent line to authentic problems in mathematics and other
disciplines.
determine optimization points on a graph.
use derivatives to find maximum, minimum,
and inflection points of a function.
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......
......Usually this involves doing lots of examples, discussing problem solving strategies and working through practice problems. Algebra is one of the fundamental tools used in theoretical physics. During my physics education it was necessary to become proficient in algebra.
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This edition of Making Drama provides a complete class text for students studying Drama in Years 7 and 8 across Australia and links closely with Creating Drama which is written for students in Years 9 and 10.
The student book contains three units which fully cover the three study areas prescri...
The Mathematical Methods (CAS) Units 3&4 Exam 2 Bound Notes series has been designed to provide students with a bound resource to take into Examination 2 for Mathematical Methods (CAS).
Summary content, hints and examples have been provided, as well as space for annotations and study notes, as...
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This elective course taught at the high school level is possibly the only one of its kind in the state of Texas. Usually most students do not take this course until their second year of college. Although the demands of this course will not be unreasonable, they are not to be taken lightly either. We will eventually solve problems that require two and possibly three pages of work and encompass algebra, trigonometry, chemistry, physics, biology and techniques of ODE in the same problem. We will start with the very basics, resolve any areas of weakness or concern that you may have and progress. You will find almost immediately that you will be able to describe a physical situation with an ODE, solve it and make predictions. I am certain that you will become excited about the fact that on your own you will be able to describe, using differential equations, and situations that you observe in daily life. For example, in the field of medicine and pharmacy, if a patient is to maintain a certain concentration of medication in the bloodstream and the body dissipates the medication at a known rate based on weight, at what time interval and amounts should additional medication be given to maintain the appropriate dose?
Most of the class time will be used to illustrate through examples the techniques for developing and solving differential equations. Critical thinking and NOT memorization will be emphasized in this course.
(1) Foundation concepts for high school mathematics. As presented in Grades K-8, the basic understandings of number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry; measurement; and probability and statistics are essential foundations for all work in high school mathematics. Students continue to build on this foundation as they expand their understanding through other mathematical experiences.
(2) Algebraic thinking and symbolic reasoning. Symbolic reasoning plays a critical role in algebra; symbols provide powerful ways to represent mathematical situations and to express generalizations. Students study algebraic concepts and the relationships among them to better understand the structure of algebra.
(3) Functions, equations, and their relationship. The study of functions, equations, and their relationship is central to all of mathematics. Students perceive functions and equations as means for analyzing and understanding a broad variety of relationships and as a useful tool for expressing generalizations.
(4) Relationship between algebra and geometry. Equations and functions are algebraic tools that can be used to represent geometric curves and figures; similarly, geometric figures can illustrate algebraic relationships. Students perceive the connections between algebra and geometry and use the tools of one to help solve problems in the other.
(5) Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools, and technology (including, but not limited to, calculators with graphing capabilities, data collection devices, and computers) to model mathematical situations to solve meaningful problems.
(6) Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problem-solving, language and communication, and reasoning (justification and proof) to make connections within and outside mathematics. Students also use multiple representations, technology, applications and modeling, and numerical fluency in problem-solving contexts.
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PREREQUISITE:
Placement, Grade of C or better in an elementary algebra course, or consent of
the Department
TEXT: Explorations in College Algebra, Kime and Clark, (2nd
Edition) and a graphing calculator resource manual.
SUPPLIES:Texas Instruments TI-83 Graphing
Calculator (note: If you are purchasing a calculator for this class, you are
required to purchase the TI-83. If you already have a graphing calculator,
consult your instructor about its acceptability)
EXPECTED
STUDENT COMPETENCIES TO BE ACQUIRED: The successful student at the end
of the course will be able produce well-written correct solutions for problems
similar to those assigned for homework in this course.
ASSIGNMENTS:
Homework will be assigned daily and will occasionally be collected as a check on
how you are keeping up. Although most of the homework assignments will not be
collected, that doesn't mean you don't have to do it! A major part of learning
mathematics involves DOING
mathematics! Also, homework is useful in preparing for the type of questions,
which may appear on quizzes or exams.Many
homework problems will be given on quizzes and some on tests.
Evaluations:There will be given two tests and one final
exam during this short summer term.There will also be given quizzes once or twice a week depending on
whether a test is given that week or not.
GRADING:
Your success in meeting the course objectives will be measured by your scores
on homework, quizzes, lab activities, two one-hour exams (June 10 and June 24),
and a cumulative final exam (July 2, 8:00AM).
The weights of the various components of your grade in
determining your final course gradeare shown below, along with the grade
scale for the course.
WEIGHTS:
GRADE SCALE
1. Two exams (50%)
90-100
A
70-74
C
2. Quizzes, homework (20%)
85-89
B+
65-69
D+
3. Cumulative Final Exam (30%)
80-84
B
60-64
D
75-79
C+
0-59
F
NOTES:
One quiz/homework
grade will be dropped to determine your final quiz average.They will be no makeup quizzes.There will be no makeup tests, except under
special (documented) circumstances.In
the case you cannot an exam at the scheduled time, contact the instructor as
soon as possible after (or before the test), to arrange a make up.Exams not made up within 2 days of the
scheduled date will be recorded 0.
SPECIAL NOTES:
If you have a physical, psychological, and/or learning disability which might affect
your performance in this class, please contact the Office of Disability
Services, 126A B&E, (803) 641-3609, and/or see me, as soon as possible. The
Disability Services Office will determine appropriate accommodations based on
medical documentation.
ATTENDANCE
POLICY: I may occasionally take attendance. It is highly recommended
that the student not miss any class, especially for the very fast pace the
summer sessions. However, the Attendance Policy established by the Department
of Mathematical Sciences states
that the maximum number of unexcused absences allowed in this class before a
penalty is imposed is four for a regular semester.
ACADEMIC CODE OF
HONESTY: Please read and review the Academic Code of Conduct relating to Academic
Honesty located in the Student Handbook. If you are found to be in violation of
this Code of Honesty, a grade of F(0) will be given
for the work. Additionally, a grade of F may be assigned for the course and/or
further sanctions may
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Intermediate Algebra - With 2 Cds - 10th edition
Summary: This concise and cumulative guide shows students the art of technical writing for a variety of contexts and institutions. Using examples from the business and non-corporate world, the book emphasizes transactional writing through practical explanations, real-world examples, and a variety of ''role-playing'' exercises. Each section builds on the next as readers learn a variety of models of style and format. This edition features a stronger emphasis on electronic commu...show morenication, integrated coverage of ethics, and more explanation of how to create technical documents that produce concrete results. ...show less
3.1 The Rectangular Coordinate System 3.2 The Slope of a Line 3.3 Linear Equations in Two Variables Summary Exercises on Slopes and Equations of Lines 3.4 Linear Inequalities in Two Variables 3.5 Introduction to Functions
Chapter 4: Systems of Linear Equations
4.1 Systems of Linear Equations in Two Variables 4.2 Systems of Linear Equations in Three Variables 4.3 Applications of Systems of Linear Equations 4.4 Solving Systems of Linear Equations by Matrix Methods
9.1 The Square Root Property and Completing the Square 9.2 The Quadratic Formula 9.3 Equations Quadratic in Form Summary Exercises on Solving Quadratic Equations 9.4 Formulas and Further Applications 9.5 Graphs of Quadratic Functions 9.6 More about Parabolas and Their Applications 9.7 Quadratic and Rational Inequalities
11.1 Additional Graphs of Functions 11.2 The Circle and the Ellipse 11.3 The Hyperbola and Functions Defined by Radicals 11.4 Nonlinear Systems of Equations 11.5 Second-Degree Inequalities and Systems of Inequalities0321443624
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Course Description:
We will first study the history of mathematics focusing on a few of the ``great proofs" in our textbook. In the second half of the course we will move to the 20th and 21st centuries, studying a few of the great developments that have revolutionized our field in the past hundred years.
This course is required of all students studying secondary mathematics education, so an important theme throughout this course will be the teaching of mathematics.
If you have special needs or problems, please be sure to speak to me or see Joan Stottlemyer in the Academic Resources Center about them as early as possible in the semester. There is additional information in the Carroll College catalog.
Textbook: Journey Through Genius by William Dunham.
Course Requirements:
You are responsible for leading two class periods. In the first period, you must take us through a chapter of ``Journey Through Genius," teaching the history, background, and context of the proof, and then putting a special focus on presenting the proof in a clear and understandable manner. In the second period you must choose some aspect of mathematics from the past century for us to study. This may be a person, a development, a proof, an algorithm; whatever interests you. Because our textbook does not cover 20th century mathematics, you will also have to select a reading assignment for this topic: an article, a book chapter, a reputable web page, or other resource. Eight days before your second presentation you must bring this assignment to me, so that I can xerox it and distribute it to the class, in order for them to read it in the week leading up to your presentation. This reading assignment must be substantial enough to require about an hour of study.
One of the most effective ways to design a mathematics lecture is to structure the time around a series of questions which are posed to the class, so I would like to you to design your presentations in this manner. At the beginning of your two class periods, you must turn in to me a typed list of these questions (at minimum eight questions) which will guide the class discussion through the topics. However if you simply ask questions of the entire class, often a few students will jump to answer them all. Thus throughout the course of each class period you must ask at least one specific question of every person in the room (and for a class this size, I would encourage you to try to ask several questions of every person). During class, you may use the blackboard, the overhead projector, or any other materials that you think will make the class fun and interesting: All I ask is that you make good use of class time.
During the weeks of the term when you are not presenting, you must spend at least one hour doing the reading and studying the proof to prepare for the discussion and then simply attend class and participate in the discussion. At the beginning of each class period you must sign in, and verify that you have spent at least one hour studying the reading assignment for that week. (Note that in order for everyone to have two presentations, two people will be doing their presentations during the time scheduled for our final examination: Monday, May 3rd, 1:00 - 2:45.)
Grading:
There are no examinations and no regular graded homework in this course. Instead you must simply fulfill the requirements above, so grading will be largely based on attendance.
To receive an A you can miss no more than one reading or have one prearranged absence throughout the term, and have no unarranged absences. If you have one unarranged absence or two missed readings/prearranged absences you will receive a B. If you have two unarranged absences or three missed readings/prearranged absences you will receive a C. If you have no more than three unarranged absences or four missed readings/prearranged absences you will receive a D. If you have more than three unarranged absences or more than four missed readings/prearranged absences you will receive an F.
Policies on academic integrity are in the Carroll College catalog.
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Math 2
Course Information
Math 2 students continue the study of the key topics from Math 1. Additional topics include quadratics, systems of equations, algebraic fractions, probability and statistics. Students will take the Algebra Regents examination in June.
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Aims & Learning Objectives:
To extend the students previous knowledge of mathematics and provide the basic
core of mathematical tools required throughout the engineering course. To
introduce the student to statistical techniques used for data analysis. To give
the student a sound basic knowledge of computer programming in C++ upon which
they can subsequently build. After taking this unit the student should be able
to: Employ elementary numerical methods for the solution of algebraic equations
and integration. Set up and solve differential equations of typical engineering
problems by analytical and numerical methods . Apply
rules of partial differentiation to small increment and change of variable
problems for functions of several variables. Solve simultaneous linear
equations. Find eigenvalues and eigenvectors of
matrices. Interpret experimental data, carry out elementary statistical
analysis and calculate best least-squares fit to data. Write well structured
simple programs in C++.
Content:
First and second order differential equations with step and sinusoidal input,
including simultaneous differential equations. Linear
algebra; vectors, matrices and determinants, Gaussian elimination, eigenvalues and eigenvectors.Newton-Raphson method, numerical integration, elementary nonlinear
equations. Statistical analysis: normal distribution, probability,
linear interpolation, curve fitting using least squares. C++: main variable
types, input, output. Procedures, control stuctures.
The course is divided into six components: ordinary
differential equations, linear equations, eigenvalues
and eigenvectors, introduction to numerical methods, curve fitting, and statistics.
The first two are covered by Glen Mullineux, the next two by Patrick Keough, and the last two by me. This webpage contains
the information pertaining to the last two. The general XX10052/118 page is here
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For more information, to browse and to order you can visit the specification pages via the links to the right or stay on this page for a taster on:
Help with AO2 and AO3
Did you know our GCSE Maths resources provide support for the new Assessment Objectives?, with AO2 worth approximately 25-35% of marks in the exam and AO3 approximately 15-25%, it's worth making sure you and your students have got to grip with these new assessment objectives! Visit our AO2 and AO3| page to find out how our teacher guides and student books can help you.
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Revision Guides and Workbooks
Edexcel's new revision resources are the smart choice for students revising for Edexcel GCSE Maths. With Student Workbooks for studying in class and Revision Guides for independent study, they provide hassle-free revision for students with no lengthy set-up time or confusing concepts.
Visit our GCSE Maths Revision| page to view samples and to get any Revision Guide or Workbook for the school price of £1.99 (RRP £3.99)
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ActiveLearn
Tailored to the Edexcel GCSE Maths Linear and Modular specifications, ActiveLearn provides online homework and revision practice and support for all students.
Resources for Post-16 GCSE
Edexcel GCSE Mathematics 16+ is a practical one year course focusing on the essential topics post-16 learners will need to know to fulfill their potential when taking GCSE Maths. Visit our Edexcel GCSE Mathematics 16+| page to find out more.
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Reviewing for the AP Statistics Exam with Fathom
Description
Are you looking for some review activities for the AP® Statistics Exam that will enhance students' understanding and refresh their memories? This webinar will focus on short and informative lessons using Fathom that will strengthen your students' skills in preparation for the three-hour exam. The lessons focus on concepts from throughout the AP® Statistics curriculum, from descriptive statistics through inference. The activities can be used in an AP® or general statistics class.
Presenter
Beth Benzing is a moderator of the Teaching Statistics using Fathom online course. She has been teaching AP® Statistics for 12 years and is a reader for the AP® Statistics exam. She has taught a statistics institute for the Math and Science Partnership Program at Arcadia University and will be teaching a statistics institute at West Chester University this summer. Beth sits on the board of a regional affiliate of NCTM in the Philadelphia area. She is a regular presenter at local, state, and national math conferences. She teaches at Strath Haven High School in Wallingford, PA, a southwest suburb of Philadelphia where she lives with her husband and three children.
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MATHEMATICAL PROBLEM SOLVING
by
James W. Wilson, Maria L. Fernandez, and Nelda Hadaway
Your problem may be modest; but if it challenges your
curiosity and brings into play your inventive faculties, and
if you solve it by your own means, you may experience the tension
and enjoy the triumph of discovery. Such experiences at a susceptible
age may create a taste for mental work and leave their imprint
on mind and character for a lifetime. (26, p. v.)
Problem solving has a special importance in the study of mathematics.
A primary goal of mathematics teaching and learning is to develop
the ability to solve a wide variety of complex mathematics problems.
Stanic and Kilpatrick (43) traced the role of problem solving
in school mathematics and illustrated a rich history of the topic.
To many mathematically literate people, mathematics is synonymous
with solving problems -- doing word problems, creating patterns,
interpreting figures, developing geometric constructions, proving
theorems, etc. On the other hand, persons not enthralled with
mathematics may describe any mathematics activity as problem
solving.
Learning to solve problems is the principal reason for studying
mathematics.
National Council of Supervisors of Mathematics (22)
When two people talk about mathematics problem solving, they
may not be talking about the same thing. The rhetoric of problem
solving has been so pervasive in the mathematics education of
the 1980s and 1990s that creative speakers and writers can put
a twist on whatever topic or activity they have in mind to call
it problem solving! Every exercise of problem solving research
has gone through some agony of defining mathematics problem solving.
Yet, words sometimes fail. Most people resort to a few examples
and a few nonexamples. Reitman (29) defined a problem as when
you have been given the description of something but do not yet
have anything that satisfies that description. Reitman's discussion
described a problem solver as a person perceiving and accepting
a goal without an immediate means of reaching the goal. Henderson
and Pingry (11) wrote that to be problem solving there must be
a goal, a blocking of that goal for the individual, and acceptance
of that goal by the individual. What is a problem for one student
may not be a problem for another -- either because there is no
blocking or no acceptance of the goal. Schoenfeld (33) also pointed
out that defining what is a problem is always relative to the
individual.
How long is the groove on one side of a long-play (33 1/3
rpm) phonograph record? Assume there is a single recording and
the Outer (beginning) groove is 5.75 inches from the center and
the Inner (ending) groove is 1.75 inches from the center. The
recording plays for 23 minutes.
Mathematics teachers talk about, write about, and act upon,
many different ideas under the heading of problem solving. Some
have in mind primarily the selection and presentation of "good"
problems to students. Some think of mathematics program goals
in which the curriculum is structured around problem content.
Others think of program goals in which the strategies and techniques
of problem solving are emphasized. Some discuss mathematics problem
solving in the context of a method of teaching, i.e., a problem
approach. Indeed, discussions of mathematics problem solving often
combine and blend several of these ideas.
In this chapter, we want to review and discuss the research on
how students in secondary schools can develop the ability to solve
a wide variety of complex problems. We will also address how instruction
can best develop this ability. A fundamental goal of all instruction
is to develop skills, knowledge, and abilities that transfer to
tasks not explicitly covered in the curriculum. Should instruction
emphasize the particular problem solving techniques or strategies
unique to each task? Will problem solving be enhanced by providing
instruction that demonstrates or develops problem solving techniques
or strategies useful in many tasks? We are particularly interested
in tasks that require mathematical thinking (34) or higher order
thinking skills (17). Throughout the chapter, we have chosen to
separate and delineate aspects of mathematics problem solving
when in fact the separations are pretty fuzzy for any of us.
Although this chapter deals with problem solving research at the
secondary level, there is a growing body of research focused on
young children's solutions to word problems (6,30). Readers should
also consult the problem solving chapters in the Elementary and
Middle School volumes.
Research on Problem Solving
Educational research is conducted within a variety of constraints
-- isolation of variables, availability of subjects, limitations
of research procedures, availability of resources, and balancing
of priorities. Various research methodologies are used in mathematics
education research including a clinical approach that is frequently
used to study problem solving. Typically, mathematical tasks or
problem situations are devised, and students are studied as they
perform the tasks. Often they are asked to talk aloud while working
or they are interviewed and asked to reflect on their experience
and especially their thinking processes. Waters (48) discusses
the advantages and disadvantages of four different methods of
measuring strategy use involving a clinical approach. Schoenfeld
(32) describes how a clinical approach may be used with pairs
of students in an interview. He indicates that "dialog between
students often serves to make managerial decisions overt, whereas
such decisions are rarely overt in single student protocols."
A nine-digit number is formed using each of the digits 1,2,3,...,9
exactly once. For n = 1,2,3,...,9, n divides the first n digits
of the number. Find the number.
The basis for most mathematics problem solving research for
secondary school students in the past 31 years can be found in
the writings of Polya (26,27,28), the field of cognitive psychology,
and specifically in cognitive science. Cognitive psychologists
and cognitive scientists seek to develop or validate theories
of human learning (9) whereas mathematics educators seek to understand
how their students interact with mathematics (33,40). The area
of cognitive science has particularly relied on computer simulations
of problem solving (25,50). If a computer program generates a
sequence of behaviors similar to the sequence for human subjects,
then that program is a model or theory of the behavior. Newell
and Simon (25), Larkin (18), and Bobrow (2) have provided simulations
of mathematical problem solving. These simulations may be used
to better understand mathematics problem solving.
Constructivist theories have received considerable acceptance
in mathematics education in recent years. In the constructivist
perspective, the learner must be actively involved in the construction
of one's own knowledge rather than passively receiving knowledge.
The teacher's responsibility is to arrange situations and contexts
within which the learner constructs appropriate knowledge (45,48).
Even though the constructivist view of mathematics learning is
appealing and the theory has formed the basis for many studies
at the elementary level, research at the secondary level is lacking.
Our review has not uncovered problem solving research at the secondary
level that has its basis in a constructivist perspective. However,
constructivism is consistent with current cognitive theories of
problem solving and mathematical views of problem solving involving
exploration, pattern finding, and mathematical thinking (36,15,20);
thus we urge that teachers and teacher educators become familiar
with constructivist views and evaluate these views for restructuring
their approaches to teaching, learning, and research dealing with
problem solving.
A Framework
It is useful to develop a framework to think about the processes
involved in mathematics problem solving. Most formulations of
a problem solving framework in U. S. textbooks attribute some
relationship to Polya's (26) problem solving stages. However,
it is important to note that Polya's "stages" were more
flexible than the "steps" often delineated in textbooks.
These stages were described as understanding the problem, making
a plan, carrying out the plan, and looking back. To Polya (28), problem solving was a major theme of doing mathematics
and "teaching students to think" was of primary importance.
"How to think" is a theme that underlies much of genuine
inquiry and problem solving in mathematics. However, care must
be taken so that efforts to teach students "how to think"
in mathematics problem solving do not get transformed into teaching
"what to think" or "what to do." This is,
in particular, a byproduct of an emphasis on procedural knowledge
about problem solving as seen in the linear frameworks of U. S.
mathematics textbooks (Figure 1) and the very limited problems/exercises
included in lessons.
Clearly, the linear nature of the models used in numerous textbooks
does not promote the spirit of Polya's stages and his goal of
teaching students to think. By their nature, all of these traditional
models have the following defects:
1. They depict problem solving as a linear process.
2. They present problem solving as a series of steps.
3. They imply that solving mathematics problems is a procedure
to be memorized, practiced, and habituated.
4. They lead to an emphasis on answer getting.
These linear formulations are not very consistent with genuine
problem solving activity. They may, however, be consistent with
how experienced problem solvers present their solutions and answers
after the problem solving is completed. In an analogous way, mathematicians
present their proofs in very concise terms, but the most elegant
of proofs may fail to convey the dynamic inquiry that went on
in constructing the proof.
Another aspect of problem solving that is seldom included in textbooks
is problem posing, or problem formulation. Although there has
been little research in this area, this activity has been gaining
considerable attention in U. S. mathematics education in recent
years. Brown and Walter (3) have provided the major work on problem
posing. Indeed, the examples and strategies they illustrate show
a powerful and dynamic side to problem posing activities. Polya
(26) did not talk specifically about problem posing, but much
of the spirit and format of problem posing is included in his
illustrations of looking back.
A framework is needed that emphasizes the dynamic and cyclic nature
of genuine problem solving. A student may begin with a problem
and engage in thought and activity to understand it. The student
attempts to make a plan and in the process may discover a need
to understand the problem better. Or when a plan has been formed,
the student may attempt to carry it out and be unable to do so.
The next activity may be attempting to make a new plan, or going
back to develop a new understanding of the problem, or posing
a new (possibly related) problem to work on.
The framework in Figure 2 is useful for illustrating the dynamic,
cyclic interpretation
of Polya's (26) stages. It has been used in a mathematics problem
solving course at the University of Georgia for many years. Any
of the arrows could describe student activity (thought) in the
process of solving mathematics problems. Clearly, genuine problem
solving experiences in mathematics can not be captured by the
outer, one-directional arrows alone. It is not a theoretical model.
Rather, it is a framework for discussing various pedagogical,
curricular, instructional, and learning issues involved with the
goals of mathematical problem solving in our schools.
Problem solving abilities, beliefs, attitudes, and performance
develop in contexts (36) and those contexts must be studied as
well as specific problem solving activities. We have chosen to
organize the remainder of this chapter around the topics of problem
solving as a process, problem solving as an instructional goal,
problem solving as an instructional method, beliefs about problem
solving, evaluation of problem solving, and technology and problem
solving.
Problem Solving as a Process
Garofola and Lester (10) have suggested that students are largely
unaware of the processes involved in problem solving and that
addressing this issue within problem solving instruction may be
important. We will discuss various areas of research pertaining
to the process of problem solving.
Domain Specific Knowledge
To become a good problem solver in mathematics, one must develop
a base of mathematics knowledge. How effective one is in organizing
that knowledge also contributes to successful problem solving.
Kantowski (13) found that those students with a good knowledge
base were most able to use the heuristics in geometry instruction.
Schoenfeld and Herrmann (38) found that novices attended to surface
features of problems whereas experts categorized problems on the
basis of the fundamental principles involved.
Silver (39) found that successful problem solvers were more likely
to categorize math problems on the basis of their underlying similarities
in mathematical structure. Wilson (50) found that general heuristics
had utility only when preceded by task specific heuristics. The
task specific heuristics were often specific to the problem domain,
such as the tactic most students develop in working with trigonometric
identities to "convert all expressions to functions of sine
and cosine and do algebraic simplification."
Algorithms
An algorithm is a procedure, applicable to a particular type
of exercise, which, if followed correctly, is guaranteed to give
you the answer to the exercise. Algorithms are important in mathematics
and our instruction must develop them but the process of carrying
out an algorithm, even a complicated one, is not problem solving.
The process of creating an algorithm, however, and generalizing
it to a specific set of applications can be problem solving. Thus
problem solving can be incorporated into the curriculum by having
students create their own algorithms. Research involving this
approach is currently more prevalent at the elementary level within
the context of constructivist theories.
Heuristics
Heuristics are kinds of information, available to students
in making decisions during problem solving, that are aids to the
generation of a solution, plausible in nature rather than prescriptive,
seldom providing infallible guidance, and variable in results.
Somewhat synonymous terms are strategies, techniques, and rules-of-thumb.
For example, admonitions to "simplify an algebraic expression
by removing parentheses," to "make a table," to
"restate the problem in your own words," or to "draw
a figure to suggest the line of argument for a proof" are
heuristic in nature. Out of context, they have no particular value,
but incorporated into situations of doing mathematics they can
be quite powerful (26,27,28).
Theories of mathematics problem solving (25,33,50) have placed
a major focus on the role of heuristics. Surely it seems that
providing explicit instruction on the development and use of heuristics
should enhance problem solving performance; yet it is not that
simple. Schoenfeld (35) and Lesh (19) have pointed out the limitations
of such a simplistic analysis. Theories must be enlarged to incorporate
classroom contexts, past knowledge and experience, and beliefs.
What Polya (26) describes in How to Solve It is far more
complex than any theories we have developed so far.
Mathematics instruction stressing heuristic processes has been
the focus of several studies. Kantowski (14) used heuristic instruction
to enhance the geometry problem solving performance of secondary
school students. Wilson (50) and Smith (42) examined contrasts
of general and task specific heuristics. These studies revealed
that task specific hueristic instruction was more effective than
general hueristic instruction. Jensen (12) used the heuristic
of subgoal generation to enable students to form problem solving
plans. He used thinking aloud, peer interaction, playing the role
of teacher, and direct instruction to develop students' abilities
to generate subgoals.
Managing It All
An extensive knowledge base of domain specific information,
algorithms, and a repertoire of heuristics are not sufficient
during problem solving. The student must also construct some decision
mechanism to select from among the available heuristics, or to
develop new ones, as problem situations are encountered. A major
theme of Polya's writing was to do mathematics, to reflect on
problems solved or attempted, and to think (27,28). Certainly
Polya expected students to engage in thinking about the various
tactics, patterns, techniques, and strategies available to them.
To build a theory of problem solving that approaches Polya's model,
a manager function must be incorporated into the system. Long
ago, Dewey (8), in How We Think, emphasized self-reflection in
the solving of problems.
Recent research has been much more explicit in attending to this
aspect of problem solving and the learning of mathematics. The
field of metacognition concerns thinking about one's own cognition.
Metacognition theory holds that such thought can monitor, direct,
and control one's cognitive processes (4,41). Schoenfeld (34)
described and demonstrated an executive or monitor component to
his problem solving theory. His problem solving courses included
explicit attention to a set of guidelines for reflecting about
the problem solving activities in which the students were engaged.
Clearly, effective problem solving instruction must provide the
students with an opportunity to reflect during problem solving
activities in a systematic and constructive way.
The Importance of Looking Back
Looking back may be the most important part of problem solving.
It is the set of activities that provides the primary opportunity
for students to learn from the problem. The phase was identified
by Polya (26) with admonitions to examine the solution by such
activities as checking the result, checking the argument, deriving
the result differently, using the result, or the method, for some
other problem, reinterpreting the problem, interpreting the result,
or stating a new problem to solve.
Teachers and researchers report, however, that developing the
disposition to look back is very hard to accomplish with students.
Kantowski (14) found little evidence among students of looking
back even though the instruction had stressed it. Wilson (51)
conducted a year long inservice mathematics problem solving course
for secondary teachers in which each participant developed materials
to implement some aspect of problem solving in their on-going
teaching assignment. During the debriefing session at the final
meeting, a teacher put it succinctly: "In schools, there
is no looking back." The discussion underscored the agreement
of all the participants that getting students to engage in looking
back activities was difficult. Some of the reasons cited were
entrenched beliefs that problem solving in mathematics is answer
getting; pressure to cover a prescribed course syllabus; testing
(or the absence of tests that measure processes); and student
frustration.
The importance of looking back, however, outweighs these difficulties.
Five activities essential to promote learning from problem solving
are developing and exploring problem contexts, extending problems,
extending solutions, extending processes, and developing self-reflection.
Teachers can easily incorporate the use of writing in mathematics
into the looking back phase of problem solving. It is what you
learn after you have solved the problem that really counts.
Problem Posing
Problem posing (3) and problem formulation (16) are logically
and philosophically appealing notions to mathematics educators
and teachers. Brown and Walter provide suggestions for implementing
these ideas. In particular, they discuss the "What-If-Not"
problem posing strategy that encourages the generation of new
problems by changing the conditions of a current problem. For
example, given a mathematics theorem or rule, students may be
asked to list its attributes. After a discussion of the attributes,
the teacher may ask "what if some or all of the given attributes
are not true?" Through this discussion, the students generate
new problems.
Brown and Walter provide a wide variety of situations implementing
this strategy including a discussion of the development of non-Euclidean
geometry. After many years of attempting to prove the parallel
postulate as a theorem, mathematicians began to ask "What
if it were not the case that through a given external point there
was exactly one line parallel to the given line? What if there
were two? None? What would that do to the structure of geometry?"
(p.47). Although these ideas seem promising, there is little explicit
research reported on problem posing.
Problem Solving as an Instructional Goal
What is mathematics?
If our answer to this question uses words like exploration,
inquiry, discovery, plausible reasoning, or problem solving, then
we are attending to the processes of mathematics. Most of us would
also make a content list like algebra, geometry, number, probability,
statistics, or calculus. Deep down, our answers to questions such
as What is mathematics? What do mathematicians do? What do mathematics
students do? Should the activities for mathematics students model
what mathematicians do? can affect how we approach mathematics
problems and how we teach mathematics.
The National Council of Teachers of Mathematics (NCTM) (23,24)
recommendations to make problem solving the focus of school mathematics
posed fundamental questions about the nature of school mathematics.
The art of problem solving is the heart of mathematics. Thus,
mathematics instruction should be designed so that students experience
mathematics as problem solving.
The National Council of Teachers of Mathematics recommends
that --
l. problem solving be the focus of school mathematics in the
1980s.
An Agenda for Action (23)
We strongly endorse the first recommendation of An Agenda for
Action. The initial standard of each of the three levels addresses
this goal.
Curriculum and Evaluation Standards (24)
Why Problem Solving?
The NCTM (23,24) has strongly endorsed the inclusion of problem
solving in school mathematics. There are many reasons for doing
this.
First, problem solving is a major part of mathematics. It is the
sum and substance of our discipline and to reduce the discipline
to a set of exercises and skills devoid of problem solving is
misrepresenting mathematics as a discipline and shortchanging
the students. Second, mathematics has many applications and often
those applications represent important problems in mathematics.
Our subject is used in the work, understanding, and communication
within other disciplines. Third, there is an intrinsic motivation
embedded in solving mathematics problems. We include problem solving
in school mathematics because it can stimulate the interest and
enthusiasm of the students. Fourth, problem solving can be fun.
Many of us do mathematics problems for recreation. Finally, problem
solving must be in the school mathematics curriculum to allow
students to develop the art of problem solving. This art is so
essential to understanding mathematics and appreciating mathematics
that it must be an instructional goal.
Teachers often provide strong rationale for not including problem
solving activities is school mathematics instruction. These include
arguments that problem solving is too difficult, problem solving
takes too much time, the school curriculum is very full and there
is no room for problem solving, problem solving will not be measured
and tested, mathematics is sequential and students must master
facts, procedures, and algorithms, appropriate mathematics problems
are not available, problem solving is not in the textbooks, and
basic facts must be mastered through drill and practice before
attempting the use of problem solving. We should note, however,
that the student benefits from incorporating problem solving into
the mathematics curriculum as discussed above outweigh this line
of reasoning. Also we should caution against claiming an emphasize
on problem solving when in fact the emphasis is on routine exercises.
From various studies involving problem solving instruction, Suydam
(44) concluded:
If problem solving is treated as "apply the procedure,"
then the students try to follow the rules in subsequent problems.
If you teach problem solving as an approach, where you must think
and can apply anything that works, then students are likely to
be less rigid. (p. 104)
Problem Solving as an Instructional Method
Problem solving as a method of teaching may be used to accomplish
the instructional goals of learning basic facts, concepts, and
procedures, as well as goals for problem solving within problem
contexts. For example, if students investigate the areas of all
triangles having a fixed perimeter of 60 units, the problem solving
activities should provide ample practice in computational skills
and use of formulas and procedures, as well as opportunities for
the conceptual development of the relationships between area and
perimeter. The "problem" might be to find the triangle
with the most area, the areas of triangles with integer sides,
or a triangle with area numerically equal to the perimeter. Thus
problem solving as a method of teaching can be used to introduce
concepts through lessons involving exploration and discovery.
The creation of an algorithm, and its refinement, is also a complex
problem solving task which can be accomplished through the problem
approach to teaching. Open ended problem solving often uses problem
contexts, where a sequence of related problems might be explored.
For example, the problems in the investigations in the insert evolved from considering
gardens of different shapes that could be enclosed with 100 yards
of fencing:
Suppose one had 100 yards of fencing to enclose a garden.
What shapes could be enclosed? What are the dimensions of each
and what is the area? Make a chart.
What triangular region with P = 100 has the most area?
Find all five triangular regions with P = 100 having integer
sides and integer area. (such as 29, 29, 42)
What rectangular regions could be enclosed? Areas? Organize a
table? Make a graph?
Which rectangular region has the most area? from a table? from
a graph? from algebra, using the arithmetic mean-geometric mean
inequality?
What is the area of a regular hexagon with P = 100?
What is the area of a regular octagon with P = 100?
What is the area of a regular n-gon with P = 100? Make a table
for n = 3 to 25. Make a graph. What happens to 1/n(tan 180/n)
as n increases?
What if part of the fencing is used to build a partition perpendicular
to a side? Consider a rectangular region with one partition?
With 2 partitions? with n partitions? (There is a surprise in
this one!!) What if the partition is a diagonal of the rectangle?
What is the maximum area of a sector of a circle with P = 100?
(Here is another surprise!!! -- could you believe it is r2 when
r = 25? How is this similar to a square being the maximum rectangle
and the central angle of the maximum sector being 2 radians?)
What about regions built along a natural boundary? For example
the maximum for both a rectangular region and a triangular region
built along a natural boundary with 100 yards of fencing is 1250
sq. yds. But the rectangle is not the maximum area four-sided
figure that can be built. What is the maximum-area four-sided
figure?
Many teachers in our workshops have reported success with a
"problem of the week" strategy. This is often associated
with a bulletin board in which a challenge problem is presented
on a regular basis (e.g., every Monday). The idea is to capitalize
on intrinsic motivation and accomplishment, to use competition
in a constructive way, and to extend the curriculum. Some teachers
have used schemes for granting "extra credit" to successful
students. The monthly calendar found in each issue of The Mathematics
Teacher is an excellent source of problems.
Whether the students encounter good mathematics problems depends
on the skill of the teacher to incorporate problems from various
sources (often not in textbooks). We encourage teachers to begin
building a resource book of problems oriented specifically to
a course in their on-going workload. Good problems can be found
in the Applications in Mathematics (AIM Project) materials
(21) consisting of video tapes, resource books and computer diskettes
published by the Mathematical Association of America. These problems
can often be extended or modified by teachers and students to
emphasize their interests. Problems of interest for teachers and
their students can also be developed through the use of The
Challenge of the Unknown materials (1) developed by the American
Association for the Advancement of Science. These materials consist
of tapes providing real situations from which mathematical problems
arise and a handbook of ideas and activities that can be used
to generate other problems.
Beliefs about Mathematics Problem Solving
The importance of students' (and teachers') beliefs about mathematics
problem solving lies in the assumption of some connection between
beliefs and behavior. Thus, it is argued, the beliefs of mathematics
students, mathematics teachers, parents, policy makers, and the
general public about the roles of problem solving in mathematics
become prerequisite or co-requisite to developing problem solving.
The Curriculum and Evaluation Standards makes the point
that "students need to view themselves as capable of using
their growing mathematical knowledge to make sense of new problem
situations in the world around them" (24, p. ix.). We prefer
to think of developing a sense of "can do" in our students
as they encounter mathematics problems.
Schoenfeld (36,37) reported results from a year-long study
of detailed observations, analysis of videotaped instruction,
and follow-up questionnaire data from two tenth-grade geometry
classes. These classes were in select high schools and the classes
were highly successful as determined by student performance on
the New York State Regent's examination. Students reported beliefs
that mathematics helps them to think clearly and they can be creative
in mathematics, yet, they also claimed that mathematics is learned
best by memorization. Similar contrasts have been reported for
the National Assessment (5). Indeed our conversations with teachers
and our observations portray an overwhelming predisposition of
secondary school mathematics students to view problem solving
as answer getting, view mathematics as a set of rules, and be
highly oriented to doing well on tests.
Schoenfeld (37) was able to tell us much more about the classes
in his study. He makes the following points.
The rhetoric of problem solving has become familiar over
the past decade. That rhetoric was frequently heard in the classes
we observed -- but the reality of those classrooms is that real
problems were few and far between . . . virtually all problems
the students were asked to solve were bite-size exercises designed
to achieve subject matter mastery: the exceptions were clearly
peripheral tasks that the students found enjoyable but that they
considered to be recreations or rewards rather than the substance
they were expected to learn . . . the advances in mathematics
education in the [past] decade . . . have been largely in our
acquiring a more enlightened goal structure, and having students
pick up the rhetoric -- but not the substance -- related to those
goals. (pp. 359-9)
Each of us needs to ask if the situation Schoenfeld describes
is similar to our own school. We must take care that espoused
beliefs about problem solving are consistent with a legitimately
implemented problem solving focus in school mathematics.
Technology and Problem Solving
The appropriate use of technology for many people has significant
identity with mathematics problem solving. This view emphasizes
the importance of technology as a tool for mathematics problem
solving. This is in contrast to uses of technology to deliver
instruction or for generating student feedback.
Programming as Problem Solving
In the past, problem solving research involving technology
has often dealt with programming as a major focus. This research
has often provided inconclusive results. Indeed, the development
of a computer program to perform a mathematical task can be a
challenging mathematical problem and can enhance the programmer's
understanding of the mathematics being used. Too often, however,
the focus is on programming skills rather than on using programming
to solve mathematics problems. There is a place for programming
within mathematics study, but the focus ought to be on the mathematics
problems and the use of the computer as a tool for mathematics
problem solving.
A ladder 5 meters long leans against a wall, reaching over
the top of a box that is 1 meter on each side. The box is against
the wall. What is the maximum height on the wall that the ladder
can reach? The side view is:
Assume the wall is perpendicular to the floor. Use your calculator
to find the maximum height to the nearest .01 meter.
Iteration
Iteration and recursion are concepts of mathematics made available
to the secondary school level by technology. Students may implement
iteration by writing a computer program, developing a procedure
for using a calculator, writing a sequence of decision steps,
or developing a classroom dramatization. The approximation of
roots of equations can be made operational with a calculator or
computer to carry out the iteration.
For example, the process for finding the three roots of
is not very approachable without iterative techniques. Iteration
is also useful when determining the maximum height, h, between
a chord and an arc of a circle when the length S of the arc and
the length L of the chord are known. This may call for solving
simultaneously and using iterative techniques to find the radius
r and and central angle ø in order to evaluate h = r -
r cos ø. Fractals can also be explored through the use
of iterative techniques and computer software.
Exploration
Technology can be used to enhance or make possible exploration
of conceptual or problem situations. For example, a function grapher
computer program or a graphics calculator can allow student exploration
of families of curves such as
for different values of a, b, and c.
A calculator can be used to explore sequences such as
for different values of a. In this way, technology introduces
a dynamic aspect to investigating mathematics.
Thomas (46) studied the use of computer graphic problem solving
activities to assist in the instruction of functions and transformational
geometry at the secondary school level. The students were challenged
to create a computer graphics design of a preselected picture
using graphs of functions and transformational geometry. Thomas
found these activities helped students to better understand function
concepts and improved student attitudes.
Evaluation of Problem Solving
As the emphasis on problem solving in mathematics classrooms
increases, the need for evaluation of progress and instruction
in problem solving becomes more pressing. It no longer suffices
for us to know which kinds of problems are correctly and incorrectly
solved by students. As Schoenfeld (36) describes:
All too often we focus on a narrow collection of well-defined
tasks and train students to execute those tasks in a routine,
if not algorithmic fashion. Then we test the students on tasks
that are very close to the ones they have been taught. If they
succeed on those problems, we and they congratulate each other
on the fact that they have learned some powerful mathematical
techniques. In fact, they may be able to use such techniques
mechanically while lacking some rudimentary thinking skills.
To allow them, and ourselves, to believe that they "understand"
the mathematics is deceptive and fraudulent. (p. 30)
Schoenfeld (31) indicates that capable mathematics students
when removed from the context of coursework have difficulty doing
what may be considered elementary mathematics for their level
of achievement. For example, he describes a situation in which
he gave a straightforward theorem from tenth grade plane geometry
to a group of junior and senior mathematics majors at the University
of California involved in a problem solving course. Of the eight
students solving this problem only two made any significant progress.
We need to focus on the teaching and learning of mathematics and,
in turn, problem solving using a holistic approach. As recommended
in the NCTM's An Agenda for Action (23), "the success
of mathematics programs and student learning [must] be evaluated
by a wider range of measures than conventional testing" (p.
1). Although this recommendation is widely accepted among mathematics
educators, there is a limited amount of research dealing with
the evaluation of problem solving within the classroom environment.
Classroom research: Ask your students to keep a
problem solving notebook in which they record on a weekly basis:
(1) their solution to a mathematics problem.
(2) a discussion of the strategies they used to solve the problem.
(3) a discussion of the mathematical similarities of this problem
with other problems they have solved.
(4) a discussion of possible extensions for the problem.
(5) an investigation of at least one of the extensions they discussed.
Use these notebooks to evaluate students' progress. Then
periodically throughout the year, analyze the students' overall
progress as well as their reactions to the notebooks in order
to asses the effectiveness of the evaluation process.
Some research dealing with the evaluation of problem solving
involves diagnosing students' cognitive processes by evaluating
the amount and type of help needed by an individual during a problem
solving activity. Campione, Brown, and Connell (4) term this method
of evaluation as dynamic assessment. Students are given mathematics
problems to solve. The assessor then begins to provide as little
help as necessary to the students throughout their problem solving
activity. The amount and type of help needed can provide good
insight into the students' problem solving abilities, as well
as their ability to learn and apply new principles. Trismen (47)
reported the use of hints to diagnosis student difficulties in
problem solving in high school algebra and plane geometry. Problems
were developed such that the methods of solutions where not readily
apparent to the students. A sequence of hints was then developed
for each item. According to Trismen, "the power of the hint
technique seems to lie in its ability to identify those particular
students in need of special kinds of help" (p. 371).
Campione and his colleagues (4) also discussed a method to help
monitor and evaluate the progress of a small cooperative group
during a problem solving session. A learning leader (sometimes
the teacher sometimes a student) guides the group in solving the
problem through the use of three boards: (1) a Planning Board,
where important information and ideas about the problem are recorded,
(2) a Representation Board, where diagrams illustrating the problems
are drawn, and (3) a Doing Board, where appropriate equations
are developed and the problem is solved. Through the use of this
method, the students are able to discuss and reflect on their
approaches by visually tracing their joint work. Campione and
his colleagues indicated that increased student engagement and
enthusiasm in problem solving, as well as, increased performance
resulted from the use of this method for solving problems.
Methods, such as the clinical approach discussed earlier, used
to gather data dealing with problem solving and individual's thinking
processes may also be used in the classroom to evaluate progress
in problem solving. Charles, Lester, and O'Daffer (7) describe
how we may incorporate these techniques into a classroom problem
solving evaluation program. For example, thinking aloud may be
canonically achieved within the classroom by placing the students
in cooperative groups. In this way, students may express their
problem solving strategies aloud and thus we may be able to assess
their thinking processes and attitudes unobtrusively. Charles
and his colleagues also discussed the use of interviews and student
self reports during which students are asked to reflect on their
problem solving experience a technique often used in problem solving
research. Other techniques which they describe involve methods
of scoring students' written work. Figure 3 illustrates a final
assignment used to assess teachers' learning in a problem solving
course that has been modified to be used with students at the
secondary level.
Testing, unfortunately, often drives the mathematics curriculum.
Most criterion referenced testing and most norm referenced testing
is antithetical to problem solving. Such testing emphasizes answer
getting. It leads to pressure to "cover" lots of material
and teachers feel pressured to forego problem solving. They may
know that problem solving is desirable and developing understanding
and using appropriate technology are worthwhile, but ... there
is not enough time for all of that and getting ready for the tests.
However, teachers dedicated to problem solving have been able
to incorporate problem solving into their mathematics curriculum
without bringing down students' scores on standardized tests.
Although test developers, such as the designers of the California
Assessment Program, are beginning to consider alternative test
questions, it will take time for these changes to occur. By committing
ourselves to problem solving within our classrooms, we will further
accentuate the need for changes in testing practices while providing
our students with invaluable mathematics experiences.
Looking Ahead ...
We are struck by the seemingly contradictory facts that there
is a vast literature on problem solving in mathematics and, yet,
there is a multitude of questions to be studied, developed, and
written about in order to make genuine problem solving activities
an integral part of mathematics instruction. Further, although many may view this as primarily a curriculum
question, and hence call for restructured textbooks and materials,
it is the mathematics teacher who must create the context for
problem solving to flourish and for students to become problem
solvers. The first one in the classroom to become a problem solver
must be the teacher.
Still Wondering About ...
The primary goal of most students in mathematics classes is
to see an algorithm that will give them the answer quickly. Students
and parents struggle with (and at times against) the idea that
math class can and should involve exploration, conjecturing, and
thinking. When students struggle with a problem, parents often
accuse them of not paying attention in class; "surely the
teacher showed you how to work the problem!" How can parents,
students, colleagues, and the public become more informed regarding
genuine problem solving? How can I as a mathematics teacher in
the secondary school help students and their parents understand
what real mathematics learning is all about?
Nelda Hadaway, James W. Wilson, and Maria L. Fernandez
References
*1. American Association for the Advancement of Science. (1986).
The challenge of the unknown. New York: Norton.
11. Henderson, K. B. & Pingry, R. E. (1953). Problem solving
in mathematics. In H. F. Fehr (Ed.), The learning of mathematics:
Its theory and practice (21st Yearbook of the National Council
of Teachers of Mathematics) (pp. 228-270). Washington, DC: National
Council of Teachers of Mathematics.
22. National Council of Supervisors of Mathematics. (1978). Position
paper on basic mathematical skills. Mathematics Teacher, 71(2),
147-52. (Reprinted from position paper distributed to members
January 1977.)
23. National Council of Teachers of Mathematics. (1980). An agenda
for action: Recommendations for school mathematics in the 1980s.
Reston, VA: The Author.
24. National Council of Teachers of Mathematics. (1989). Curriculum
and evaluation standards for school mathematics. Reston, VA: The
Author.
Nelda Hadaway received a B.S. Ed., an M. Ed., and
an Ed. S. from The University of Georgia in Athens, Georgia and
the Ph. D. from Georgia State University in Atlanta. She has taught
mathematics at Hunter College High School in the New YorkCity
and presently teaches mathematics at South Gwinnett High School
in Snellville, Georgia. She is interested in integrating writing
into the teaching of mathematics to enhance problem solving.
James W. Wilson is a Professor of Mathematics Education at The
University of Georgia. He has a B.S. and M.A. from Kansas State
Teachers College, M.S. from University of Notre Dame, and M.S.
and Ph.D. from Stanford University. He has been interested in
problem solving for many years. His doctoral research dealt with
problem solving and his Problem Solving in Mathematics course
is a regular offering at The University of Georgia. Over the years,
he has also been involved in various problem solving projects
including the U.S.-Japan Joint Seminar on Problem Solving in School
Mathematics.
Maria L. Fernandez is an Associate Professor of Mathematics Education
at Florida International University. She completed both a B.S. and M.S.
in Mathematics Education at Florida International University in
Miami, Florida and the Ph. D. at the University of Georgia. She previously taught at the University of Arizona and at Florida State University. She
is interested in incorporating problem solving into the mathematics
curriculum at all levels. While teaching mathematics at the secondary
level in Miami, she integrated problem solving into the curriculum
using various strategies. Her research interests involve mathematics
visualizations in problem solving.
|
Book
Review: How to Solve It: A New Aspect of
Mathematical Method
G. Polya. Princeton, NJ: Princeton University Press, 1957, Second Edition. Reviewed
by Jennifer Norton, Graduate Student Associate, TRC
Polya's How
to Solve It details the motives and procedures that lead to solutions
in mathematical problem solving and shows teachers how to help their students
learn how to solve problems. The interactive approach illustrated
in this text is designed to help students with their problem- solving
skills, while making sure they perform a reasonable amount of the work.
Teachers use questions to guide students effectively and unobtrusively,
and to enhance their problem-solving skills through imitation and practice.
The book is divided into four sections:
In the Classroom:
This section begins with a concise table that carries the reader through
the four phases of problem solving: 1) understanding the problem, 2) devising
a plan and recognizing the connection of parts of the problem, 3) carrying
out the plan, and 4) looking back: reexamining, discussing, and checking
the results in order to aid future problem solving. This section then
details these aspects of Polya's approach and walks the reader through
several examples.
How to Solve
It: An imaginary dialogue between a student and teacher illustrates
Polya's approach with respect to a particular mathematical problem.
Short Dictionary
Heuristic: The dictionary provides references for particular aspects
of problem solving, including such topics as the following: using analogies
to aid problem solving, introducing auxiliary elements to aid problem
solving, checking the result and deriving it differently, using the results
of earlier problems to solve new problems, decomposing and recombining
problems, thinking inductively, using notation, setting up equations,
varying problems, and recognizing signs of progress.
Problems,
Hints, Solutions: This section provides many sample problems to let
readers test their knowledge and understanding of the approach introduced
in this book. By encouraging the teacher/readers to participate in the
learning process from a student's perspective, Polya helps readers internalize
the approach and integrate it with their teaching skills.
Although the
first edition dates from 1945 and the author is writing to teachers of
mathematics, How to Solve It offers insights and practical solutions
for the difficult task of teaching students to solve problems in several
disciplines. If you find yourself solving problems for your students because
they can't do it themselves, or frustrated that you can't get them to
understand, try Polya's approach!
|
Related Articles
Calculators are rarely first on list of things college students enjoy buying. And yet, without a little bit of research, some students can end up spending several hundred dollars on the devices throughout their college career.
While no guide can cover every calculator, course and instructor requirement, here you will find compiled a few basic guidelines for getting the right calculator during your time at Parkland College.
To get the straight scoop, Buster sat down with Omar Adawi, Associate Professor in mathematics and physics, and KeikoKircher, a part-time instructor who also pulls double duty, teaching physics and math as well.
These first questions were addressed to Kircher:
Buster Bytes: What calculators are allowed for PHY 141?
KeikoKircher: Any calculator is allowed, since our goal is not to test your algebra skills.
BB: Are any calculators not allowed for PHY 141?
KK: There is none.
BB: Do you use one calculator in particular during class? If so, would having that calculator help students follow along?
KK: I don't use any during lectures, but if I do use one during discussion time, I would probably be using the TI-83. It may help students to use the same calculator just because I'm able to help them with it, but not because the calculator itself does a better job.
BB: I'm not sure if you teach other Physics courses, but if you do, would any of your answers change for those courses?
KK: I have taught PHY 143 as well, and my answers would be the same with that course.
BB: I believe you also teach math? Are any particular calculators required for those courses?
KK: In the math class that I teach, pre-algebra, they are not allowed to use any calculator unless I explicitly tell them to use one. They are required to buy a calculator that can deal with basic functions such as square roots and trigonometric functions for when they deal with those. But the calculator doesn't have to be as fancy as theTI series.
Similar questions were asked of Adawi:
Buster Bytes: Professor Adawi, you teach MAT 129, what calculators are allowed for that course?
Omar Adawi: Depending on the instructor, the TI-83+, TI - 84+ or TI-89 is allowed.
BB: Are any calculators not allowed for MAT 129? Are these answers the same for all sections?
OA: Again it depends on the instructor. For example if the required calculator is a TI-83+ or TI-84+ then a TI-89 would not be permitted on quizzes and exams.
BB: Do you use one calculator in particular during class? If so, would having that calculator help students follow along?
OA: In MAT 129 I use the TI-89. The students may use this calculator to carry out explorations or sketch graphs, etc. The use of the calculator enhances the learning process of the class material.
BB: Do you know of any different regulations for other courses?
OA: There are different regulations, especially for MAT 128 and lower level courses, but for Calculus 3 and above as well.
BB: Do you teach courses in any other department? Are any particular calculators required for those courses?
OA: I teach PHY 142 in the summers. There is no particular calculator required for this class but I recommend the TI-89, since the engineering students will need this calculator for their future engineering courses.
Hopefully this information will help making your calculator purchases a little easier. To save money, you might want to look ahead and try to pick a calculator that will work for upcoming classes in your program, as well.
Another great way to save money is to shop around. Often, used calculators can be found for a discount from other students who have taken the course and no longer need their calculator. Look to the bulletin boards around campus for notifications about calculators for sale.
Used calculators can also be found on Craigslist, eBay and Amazon. Amazon even offers a free Prime membership to college students, which provides free two day shipping for many purchases.
Wherever you find your calculator, make sure you "do your homework," when it comes to shopping for the best price. And if you don't need it after the course, why not get a little money back and pass on the savings to another student who needs it?
|
Book Description: This brief book presents an accessible treatment of multivariable calculus with an early emphasis on linear algebra as a tool. Its organization draws strong analogies with the basic ideas of elementary calculus (derivative, integral, and fundamental theorem). Traditional in approach, it is written with an assumption that the student reader may have computing facilities for two- and three-dimensional graphics, and for doing symbolic algebra. Chapter topics include coordinate and vector geometry, differentiation, applications of differentiation, integration, and fundamental theorems. For those with knowledge of introductory calculus in a wide range of disciplines including—but not limited to—mathematics, engineering, physics, chemistry, and economics.
Buyback (Sell directly to one of these merchants and get cash immediately)
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Final Review
Sample Topics and Questions
This is not an exclusive list. It is merely meant to highlight some
of the major topics covered since the second midterm. It also includes
topics that may be appropriately asked on the two midterms. Students are also
referred to the topics listed on the review pages for the first and
second midterms.
Avoid "Catastrophic cancellation" in certain expressions.
Find the next n intervals using the bisection method for
a function.
Given the time it takes to solve a certain sized system
via Gaussian elimination, how long does it take to solve a different
sized system.
Decompose a matrix into an LU-decomposition.
Find the normal equations for a linear system.
Use the Gauss-Seidel iteration method to find several
iterations for a linear system.
Use the trapezoidal rule to approximate the integral.
Use Richardson's extrapolation to get a better approximation.
How many panels are needed to get a certain degree of
accuracy via Simpson's rule?
Use Gaussian quadrature to evaluate an integral.
Create a new quadrature formula.
Change an n-th order ODE into a coupled system of first
order ODEs.
"Solve" an ODE-BVP by discretization techniques, i.e.,
set up the appropriate linear system in matrix form.
|
Elementary Linear Algebra Applications Version
9780471669593
ISBN:
0471669598
Edition: 9 Pub Date: 2005 Publisher: John Wiley & Sons Inc
Summary: This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation. The applications version features a wide ...variety of interesting, contemporary applications. Clear, accessible, step-by-step explanations make the material crystal clear. Established the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues
|
Description
By purchasing a value pack, you will save compared to purchasing these two books separately.
Target audience
Suitable for Year 10 students.
Series overview
We're proud to introduce the only series has been structured according to the latest research on how students learn mathematics and on how to avoid common misunderstandings, making it easy for you to provide an innovative and effective education to your students with Pearson Mathematics.
Built from the ground up for the Australian Curriculum, we've been able to base the series on the latest pedagogical research on how students learn best. We've combined carefully selected grading with thoughtful open-ended questions at the end of every exercise, based on research conducted by the lead writer of the Australian Mathematics Curriculum, Peter Sullivan. Through careful integration of all the sub-headings of the proficiency strand (fluency, understanding, reasoning, problem solving and open-ended questions) a full coverage of the curriculum has been achieved. Equipped as well with the 5e+ format (the engage, explore, elaborate, evaluate and extend model), Pearson Mathematics helps you to provide the right balance of scaffolding and openness for inquiry-based investigations.
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MAS170 Practical Calculus
In this course we learn how to define and evaluate derivatives and
integrals for functions which depend on more than one variable,
with an emphasis on functions of two variables, for which the main
ideas already appear. We also think about what it means to
approach a limit or to add up a sum with infinitely many terms,
but throughout the emphasis is on explicit examples and getting
answers.
Differential equation for continuous compound interest. Solution by
inspection and by separation of variables. Radioactive decay,
half-life. Newton's law of cooling. Other examples of separable
equations.
4. Partial derivatives (4 lectures)
Functions of two variables, their graphs, level curves and tangent
planes. Partial derivatives, their graphical interpretation and
evaluation. Jacobians, higher derivatives. Increments, the Chain Rule
and its applications, including to Laplace's equation.
5. Double integrals (5 lectures)
Review of the Fundamental Theorem of Calculus. Two-dimensional
integrals as volumes under graphs, their evaluation by double
integration, in either order. Change of variables, including to polar
coordinates. ∫−∞∞ e−[1/2]x2 dx.
6. Infinite series (5 lectures)
Infinite series of positive terms. Basic examples including
geometric
and harmonic series. Sum as a limit of partial sums. Numerical and
graphical illustration. Absolute convergence. Manipulating Maclaurin
series. Finding the radius of convergence.
|
Topics in Mathematics Algebra and Trigonometry7
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List Price:225 Our Price:209 ($ 3.97) (£ 2.38) You Save: 16
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Topics in Mathematics Algebra and Trigonometry Book Description
Contents:PART A : ALGEBRA
1*.
Mapping, Equivalence Relations and Partitions
2*.
Congruence Moduloer n
3 .
Matrices
4 .
Rank, Row Rank and Column Rank of a Matrix and Linear Equations
5 .
Characteristics Roots and Characteristic Vectors
SECTION II
6 .
Relations between the Roots and Co-efficient of an Equation
7 .
Transformations of Equations
8 .
Descarte's Rule of Signs
9 .
Solutions of General Cubic and Bi-quadratic Equations
SECTION III
10 .
Groups
11 .
Subgroups
12 .
Normal Subgroups
13 .
Cyclic Groups
14 .
Permutation Groups
15 .
Rings
PART B : TRIGONOMETRY
SECTION IV
16 .
DeMoivre's Theorem and its Applications
17 .
Expansion of Trigonometric Functions and Logarithms of a Complex Quantity
Popular Searches
The book Topics in Mathematics Algebra and Trigonometry by Dr Kulbhushan Prakash, Om P Chug, Parmanand Gupta
(author) is published or distributed by Laxmi [, 9788131802274].
This particular edition was published on or around 2008 date.
Topics in Mathematics Algebra and Trigonometry
|
Algebra And Trigonometry - 3rd edition
Summary: understa...show morend the material.
Features
Functions Early and Integrated: Functions are introduced right away in Chapter 1 to get students interested in a new topic. Equations and expressions are reviewed in the second chapter showing their connection to functions. This approach engages students from the start and gives them a taste of what they will learn in this course, instead of starting out with a review of concepts learned in previous courses.
Algebraic Visual Side-by-Sides: Examples are worked out both algebraically and visually to increase student understanding of the concepts. Additionally, seeing these solutions side-by-side helps students make the connection between algebraic manipulation and the graphical interpretation.
Zeros, Solutions, and x-Intercepts Theme: This theme allows students to reach a new level of mathematical comprehension through connecting the concepts of the real zeros of the function, the solutions of the associated equation, and the x-coordinates of the x-intercept of the graph of the function.
Technology Connection: In each chapter, optional Technology Connections guide students in the use of the graphing calculator as another way to check problems.
Review Icon: These notes reference an earlier, related section where a student can go to review a concept being used in the current section.
Study Tips: These occasional, brief reminders appear in the margin and promote effective study habits such as good note taking and exam preparation.
Connecting the Concepts: Comprehension is streamlined and retention is maximized when the student views a concept in a visual form, rather than a paragraph. Combining design and art, this feature highlights the importance of connecting concepts. Its visual aspect invites the student to stop and check that he or she has understood how the concepts within a section or several sections work together.
Visualizing the Graph: This feature asks students to match an equation with its graph. This focus on visualization and conceptual understanding appears in every chapter to help students see ''the big picture.''
Vocabulary Review: Appearing once per chapter in the Skill Maintenance portion of an exercise set, this feature checks and reviews students' understanding of the language of mathematics.
Classify the Function: With a focus on conceptual understanding, students are asked to identify a number of functions by their type (i. e., linear, quadratic, rational, and so forth). As students progress through the text, the variety of functions they know increases and these exercises become more challenging. These exercises appear with the review exercises in the Skill Maintenance portion of an exercise setBooks Squared Dallas, TX
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clearlyMost students find it difficult to determine exactly how much time, they should spend in activities in studying. This is particularly important right at the beginning of the study so as to make an effective study plan.
This is complicated even more by the fact that every chapter requires different amount of time. Even different subjects require different amounts of time in theory and problems.
The different questions that come to the mind of the student are:
How much time should be spent in reading from the textbook?
Are the notes from tuition/coaching enough? Can I manage without reading the textbook?
Is there anything to read from the textbook in Mathematics?
How much time should I spend in solved examples given in the IITJEE course material>
How much time should be allocated to a certain topic?
How much time should be spent on a problem that is not getting solved before looking at the solution or asking for help?
How much time should I spend in testing at home?
How should I calculate the total time required?
We have tried to answer these questions by giving an indicative time plan.
List of chapters (with recommended time slotted)
Topic
Total
Reading (textbook)
Solved examples
Conceptual problems
Exercises (problems)
Chapter test
Mathematics
1
Complex numbers
21
2
2
1
16
2
2
Quadratic equations
19
1
1
1
16
1
3
Logarithms
6
1
5
1
4
Progressions
10
1
2
1
6
2
5
Permutations and combinations
22
1
2
1
18
2
6
Trigonometry
35
2
2
1
30
2
7
Straight lines
18
2
3
1
12
3
8
Circles
21
2
4
1
14
4
9
Conic sections
34
4
4
1
25
4
10
Binomial theorem
33
2
3
1
27
3
11
Functions, Limits and Continuity
49
4
4
1
40
4
12
Differentiability and differentiation
19
1
4
1
13
4
13
Application of derivatives
33
1
3
1
28
3
14
Indefinite integration
10
1
3
1
5
3
15
Definite integration
10
1
3
1
5
3
16
Area under the curve
19
1
5
1
12
5
17
Differential equations
14
1
4
1
8
4
18
Determinants
23
1
5
1
16
5
19
Matrices
11
1
2
1
7
2
20
Probability
16
1
4
1
10
4
21
Vectors
13
1
3
1
8
3
22
Three dimensional geometry
10
2
2
1
5
2
Total
446
34
65
21
326
66
Physics
1
Units, dimensions, vectors and calculus
15
2
2.5
0.5
10
2
2
Kinematics
13
3
2.5
0.5
7
3
3
Laws of motion
18
2
2.5
0.5
13
2
4
Work, Power and Energy
17
2
2.5
0.5
12
2
5
Center of mass, linear momentum, collision
28
4
3
1
20
4
6
Rotational dynamics
33
4
3
1
25
4
7
Elasticity, fluid dynamics and properties of matter
35
4
3
1
27
4
8
Gravitation
16
2
1.5
0.5
12
2
9
Simple Harmonic Motion
21
3
2.5
0.5
15
3
10
Wave motion
23
4
2.5
0.5
16
4
11
Heat and Thermodynamics
48
5
5.5
2.5
35
5
12
Electrostatics
45
5
3.5
1.5
35
7
13
Electric current and resistance
28
4
3
1
20
4
14
Magnetism
27
4
2
1
20
4
15
Electromagnetic Induction and AC
18
3
2
1
12
3
16
Geometrical Optics
21
4
2
1
14
4
17
Wave Optics
18
4
2
1
11
4
18
Modern Physics
18
5
2
1
10
5
Total
442
64
47.5
16.5
314
66
Chemistry
1
Basic concepts of chemistry
18
3
2.5
0.5
12
2
2
Structure of atom
15.5
3
2.5
0
10
2
3
Periodic properties
10
3
1
6
2
4
Gas laws
21
4
2.5
0.5
14
3
5
Chemical bonding
15
3
2
10
2
6
Chemical energetics
18
3
2.5
0.5
12
2
7
Chemical equilibrium
20
4
1.5
0.5
14
3
8
Ionic equilibrium
23
4
1.5
0.5
17
3
9
Redox reactions
16
3
2.5
0.5
10
2
10
General organic chemistry
29
5
1.5
0.5
22
4
11
Hydrocarbons
16
4
12
3
12
Alcohols and ethers
13
3
10
2
13
Alkyl and aryl halides
13
5
8
4
14
Solutions
26
3
2.5
0.5
20
3
15
Solid state
21
3
2.5
0.5
15
2
16
Chemical kinetics
20
3
2.5
0.5
14
2
17
Electrochemistry
25.5
3
2.5
20
2
18
Nuclear chemistry
14.5
3
1.5
10
2
19
Functional groups containing nitrogen
14
4
10
3
20
Aldehydes and ketones
14
4
10
3
21
Carboxylic acids and their derivatives
19
4
15
3
22
s-Block elements
17
5
1.5
0.5
10
4
23
p-Block elements
24
5
1.5
0.5
17
4
24
d-Block elements
19
5
1.5
0.5
12
4
25
Metallurgy
19
5
1.5
0.5
12
4
26
Qualitative salt analysis
19
5
1.5
0.5
12
4
27
Coordination compounds
15
5
1.5
0.5
8
4
Total
494.5
104
40.5
8
342
78
Chapter tests
210
Full length tests
120
at least 20 tests of various formats, of 6 hrs each
Self assessment
30
Revision / other material
60
Total Time (Required)
1802.5
This is just a recommendation. Students can make changes to the study plan based on their proficiency in the subjects. The actual time spent by the student can vary by 10% – 15% depending on the student's personal style of study. Please consider that the time given here is the minimum that a student needs to spend. The total time spent in studying for IITJEE across 2 years should not be less than 10% of the given.
The biggest reason that students state for stopping the use of timetables is that its ineffective.
"It does not work"
"We cant follow the timetable. It makes us feel bad"
"I do better without a timetable"
"It creates pressure"
These are all valid reasons.
However, we face these problems because of the manner in which we use the timetable.
We have a habit of focusing on the failures. If we have been able to follow the timetable 80% of the time, we look at the 20% when we could not follow and declare it a failure.
In reality the 80% time that was effectively utilized made it a success. It is never possible to follow the timetable 100%. Timetable is just a tool to guide us in utilizing our time. It reminds us to start work when we want to. If the timetable is unsuitable, we should change it to suit our schedule.
However, this tool can only work if we look at its success in stead of the failure.
We feel bad only when we look at the failures.
It is the nature of the human psyche to expand whatever it focuses on. If we focus too much on the failure then we will only find failure.
In reality, failure does not exist. It is just another attempt to success. The attempt transforms into failure when we stop attempting.
In reality, we work on some kind of a timetable even without writing it. This timetable is etched in our heads. Since it is not written, there is no measurement possible.
When we write down the timetable, it will allow us exact measurement of the utilization of our time. You can hope to increase your performance only if you have a way to measure it. Without measurement, any change is performance is a mere perception. I tmay or may not reflect reality.
Please utilize the format below to plan your days.
Fill up the timetable with activities. A sample of these activities is
Wake up / Off to sleep – These times should be closest to our biological clock for maximum efficiency. The human body is designed to operate efficiently in the day time. Try to sleep by 12 midnight (latest).
School, Tuition/Coaching, Travel time
Brush, bath, toilet, Breakfast, Lunch, Dinner
Spend at least 7 hours in sleep every day
Take out a minimum of 45 minutes in physical activities like Sports, yoga, exercise everyday. You can club this activity with friends. SMS, talking with friends on cellphone etc shoul dbe limited to 30 minutes per day.
There are some weekdays when students have to attend both school and IIT JEE coaching / Tuition. This leaves very little time for self study.
There are days when we have the entire afternoon, after school, available for self study.
The weekdays are of particular importance. This is the only time, when students get a lot of time to cover all the pending work.
Unlike Class X, when students take it easy on weekends, IIT JEE preparation calls for extra studies on weekends.
Weekly planner
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
After filling in the time table, calculate the number of hours of self study, available per week. This should not be less than 30 hours. If you can study 30 hours per week regularly for 2 years, it is good.
As you can see, there is enough time available at home to study for IIT JEE.
However, students tend to take the 1st 4 months, after Class X, very easy. They lose out on the time available in Summer vacation of Class XI.
The schools also take it easy. They start picking up momentum after 15 July, which is too late. By this time, the half yearly exams are just around the corner. The results are bad and the panic sets in. This is the time where most students lose confidence.
If a student is serious about cracking IITJEE, it is important that he prepares an annual plan right in the beginning of Class XI in April. This will give him a headstart over everyone else.
Almost 50% of the available free time is lost if we dont utilize the summer vacations for coverage of course.
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Some ideas
The following ideas might help with your individual learning. You might like to start by trying ideas for your preferred learning mode (see the Learning Modes section), but you will learn best if you use a mixture of learning modes.
If you want more ideas to help you study, take a look at our workshops.
Visual
Auditory
Reading/Writing
Kinaesthetic
Look back over any previous mathematical concepts involved
read notes, write a list of any important points
review any diagrams, or put information in a 'concept map'
discuss the concepts with a fellow student, and ask any questions in a tutorial
make a concept map using seperate revision cards linked by string
Identify key words and concepts
use bullet points to list the key ideas, and write a sentence or two expanding on the detail of each; explain any diagrams or symbols in words
add the key words to a concept map, and study any diagrams used in the lecture to see how they show the key concepts
discuss with fellow students which the key concepts are, and why they are important
look for ways to make 2D or 3D models demonstrating key ideas and concepts
Use some examples to try to figure out what's going on
try drawing a diagram or graph showing the example, and look for ways to show different aspects of the definition (e.g. special cases, how it breaks down when assumptions are not met)
compare examples with the definition. If the examples follow a process, make a list of the different steps involved. Write down any similarities and differences between examples
work through any examples yourself - use your notes, but try the example yourself rather than just copying it out. It may also be possible to find/create interactive diagrams of the examples e.g. which show how changing a variable changes the example
work in a group to discuss examples and work through them. Try to get ideas from each other and use notes when you get stuck
Try a variety of problems to help you think about different applications of the concept
try as many problems as you can. Looking at similar examples might help you identify how you need to go about answering a question
annotate your work at the side of the page explaining fully why you've made each step
try to find any diagrams which will help you answer the questions. Looking at diagrams for similar examples may help
if possible, work in a group to discuss ideas for some of the questions. Make sure you get experience of trying some of the problems on your own, as it can be easy to rely on other students' knowledge and understanding
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Mathematics - Further
You need a strong grade A* at GCSE and a recommendation from your Year 11 teacher.
A love of mathematics - especially algebra - is absolutely essential! You also need to be willing and able to give over significant amounts of your free time. The main face-to-face study sessions take place for several hours each Thursday after school and are taught by a specialist teacher from the national Further Maths Network. There may also be some modules taught online.
What will I study and learn?
The course could really be called 'Wider Mathematics', as what is offered will result in a broadening of your mathematical skills and experience.
AS:
You will study the module Further Pure 1 and 2 other modules.
Further Pure 1
Complex numbers
Numerical methods
Parabolas and hyperbolas
Matrices
Series
Proof
The other 2 modules could be Mechanics, Statistics or Decision Maths modules, depending on your aptitude, interest and which modules you are studying in your Maths AS or A-Level. The plan is to tailor the modules to compliment your AS or A2 maths choices and suit your own career plans.
A2:
You will study 3 more modules in addition to the 3 studied in your AS Further Maths.
You will study either Further Pure 2 or Further Pure 3 plus 2 other modules.
Again, there is a lot of flexibility about these 2 modules; you will be able to choose from modules in Mechanics, Statistics, and Decision Maths or study an extra Further Pure module.
These are FP1, and 2 applied modules (decided individually as appropriate).
Each exam is 1½ hours long.
Then a further three exams in Year 13.
These are FP2 and two further applied modules or additional further pure modules.
Each exam is 1½ hours long.
How will it help me?
In addition to the benefits listed for the Core and Mechanics / Core and Statistics, studying Further Mathematics will broaden your mathematical experience and prepare you for the most demanding university entry requirements. Students who achieve success in Further Mathematics are recognised to have a powerful skill set and are likely to be in high demand with universities and employers.
Students of this calibre may also want to study STEP or AEA qualification to support applications to the most prestigious universities.
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Description
John Squires and Karen Wyrick have used their successes in the classroom and the lab to design the MyMathLab for Intermediate Algebra eCourse. This new MyMathLab® eCourse offers students a guided learning path through content that has been organized into smaller, more manageable portions. This course structure includes pre-made tutorials and assessments for every topic in the course, giving instructors an eCourse that can be easily set up and customized for a variety of learning environments.
Features
The Squires and Wyrick MyMathLab eCourses are a little different from most of the MyMathLab courses you might have seen! The eCourses are organized by mini-modules and topics, rather than by chapters and sections. Each mini-module covers one week's worth of content, allowing for more frequent assessment of developmental students. The eCourse asks students to complete three tasks for each topic:
1. Watch the Tutorial. Students will learn the content through these three-part, Flash-based tutorials created by the authors, rather than an eText.
In the Step-by-step videos, John Squires narrates as he works through each step in the solution process for the examples, while also pointing out important definitions, rules, and procedures along the way.
The video is followed by interactive Guided Examples that ask students to "click through" each step of the solution.
The tutorial concludes with a Study Guide that offers a concise summary of key definitions and procedures for the topic.
2. Check for conceptual understanding. After watching the tutorial and before moving on to the homework assignment, students answer four multiple-choice questions to ensure they grasp the key concepts.
3. Complete the homework. The majority of questions in every MyMathLab-based homework assignment offer MyMathLab's "View an Example" and "Help Me Solve This" features, but the final 3–5 questions in each assignment require students to solve the problem on their own, without any learning aids.
Additional Resources
A MyMathLab Notebook can be packaged with the Squires and Wyrick MyMathLab access kit or downloaded from the MyMathLab eCourse.This notebook shows key examples from the step-by-step videos and provides extra space for students to take notes. It also offers additional helpful hints and practice exercises for every topic in the eCourse. The notebook is three-hole punched so that students can insert it into their course binder and add additional notes, solutions for their homework exercises, and additional practice work as needed. A bound version is also available for instructors to provide an additional teaching resource for the classroom.
Two sample quizzes are also available for each mini-module, in addition to the concept checks and homework assignments that already accompany each tutorial,
Author
John Squires has been teaching math for over 20 years. He was the architect of the nationally acclaimed "Do the Math" program at Cleveland State Community College and is now head of the math department at Chattanooga State Community College, where he is implementing course redesign throughout the department. John is the 2010 Cross Scholar for the League for Innovation and the author of the 13th Cross Paper which focuses on course redesign. As a redesign scholar for The National Center for Academic Transformation (NCAT), John speaks frequently on course redesign and has worked with both colleges and high schools on using technology to improve student learning.
Karen Wyrick is the current chair of the math department at Cleveland State Community College and has been teaching math there for over 18 years. She is an outstanding instructor, as students have selected her as the college's best instructor more than once! Karen played an integral role in Cleveland State's Bellwether Award-winning "Do the Math" redesign project, and she speaks frequently on course redesign at colleges throughout the nation and also serves as a redesign scholar for The National Center for Academic Transformation (NCAT).
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Harrington
Announcements
Algebra II Honors Syllabus
Course: Algebra II Honors
Teacher: Mr. Harrington
Text: Algebra and TrigonometryAlgebra II Level I Syllabus
Course: Algebra II Level I
Teacher: Mr. Harrington
Text: Algebra II Applications, Equations, and GraphsApplied Geometry Syllabus
Course: Applied Geometry
Teacher: Mr. Harrington
Text: Informal Geometry
Room: 168
Website:
Email: sharrington@watertown.k12.ma.us
Objectives: Students will continue to develop math skills as well as preparing
for the MCAS exam. Students will learn angles, polygons, congruent
triangles, quadrilaterals, parallel lines, perimeter, area, and volume.
Students will learn to graph linear functions. MCAS practice will consist of
practice exams and computer application programs. A scientific calculator
will be needed.
Materials:
Scientific Calculator Recommended (TI30)
Spiral Notebook
Folder
Pen or Pencil 40%
Quiz Average 30%
Homework Average 30%
Make Up Policy:
Students will have the opportunity to make up each quiz or test. They will
have one week to make up the quiz/test. The maximum grade on a retake exam is
a 70.
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Academics
Mathematics 101. Calculus I
Calculus is the elegant language developed to model changes in nature and to formally discuss notions of the infinite and the infinitesimal. Topics include techniques of differentiation, the graphical relationship between a function and its derivatives, applications of the derivative, the Fundamental Theorem of Calculus, and integration by u-substitution. No previous experience with calculus is assumed.
Connections
Microeconomics becomes all the more interesting when techniques from calculus can be applied to many of the issues it addresses. In particular, the graphic representation of marginal analysis, continuity and optimization in microeconomics can be approached analytically through the tools of differentiation, the major topic in introductory calculus. Many examples and projects in the introduction…
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First year students often use a functional language in their introductory programming classes today. Experiences gained in this way allows them to build mathematical concepts quickly and properly. On the other hand, modern algebra systems, such as MATLAB, accelerate advanced calculation and offer an excellent platform for experimentation, but they do not facilitate understanding of fundamental concepts. It is proposed to use jointly the functional approach and a modern algebra system (in this instance, the MATLAB software). This would reduce a danger of creating a clutter of unrelated procedures in place of a coherent system of concepts.
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I teach a college level pre-calculus course. Most of the students have
calculators from the TI-83 family, but a handful have TI-86's, usually
purchased for a previous course at a different institution. Those who own the
TI-86's generally do not know much about how to use them, nor do I. I want all
the students to be able to do the equivalent of using the TI-83 sequential
mode to enter a recursive function formula and then find the output of a given
value for n, such as u (500).
Is there an easy way to do this on a TI-86? Thanks for any help anyone can
offer
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web2.0calc.com
Solve advanced problems in Physics, Mathematics and Engineering.
Scientific Calculator
web2.0calc.com supports advanced mathematical functions which are
useful for scientific calculations. Trigonometric, logarithmic and
exponential functions, floating point arithmetic, complex numbers
and support for large numbers is integrated. Most common functions
are accessible by buttons with mouseover usage tips.
Google+Facebook
Math Formula Display
Large Number Support
Equation Solver
Calculator Widgets
Free Math Help Forum
web2.0calc Quick Start Guide
This guide will give you informative instructions on how to use this calculator effectively.
Chapter 1: Mouse Input
Click the buttons to input a math formula or equation like on a pocket calculator.
Chapter 2: Keyboard Input
If you prefer keyboard input of math formulas, you can type directly into the input bar. Pressing ↵ starts the calculation.
1234
12.34
12e3
12*10^3
12e-3
12*10^-3
10+0x7a+0b1010
Chapter 3: Numbers
Various number formats are allowed see the above examples for more information.
sin(90)
sqrt(9)
sqrt(27, 3)
exp(2)
ln(e)
log(10)
log(343, 7)
Chapter 4: Functions
To calculate a function like 'sine' with an argument like 90, input the corresponding function name followed by the argument 90 in parentheses. Example: sin(90)
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mean Here is practical advice that transforms essay writing into a satisfying exp Geometry becomes painless—and even fun—once students learn the sub
The author demonstrates how solving geometric problems amounts to fitting parts together to solve interesting puzzles. Students discover relationships that exist between parallel and perpendicular lines; analyze the characteristics of distinct shapes such as circles, quadrilaterals, and triangles; and learn how geometric principles can solve real-world problems. Titles in Barron?s Painless Series are written especially for middle school and high school students who are having a difficult time with a specific subject. In many cases, a student is confused by the subject?s complexity and details.
Updated with many new references, this entertaining book advises students on ways to enliven their essay assignments with vivid images, avoid the dull passive voice, and construct smooth, well-crafted sentences that flow together to create unified themes. Short quizzes called ?Brain Ticklers? appear throughout the text. Titles in Barron?s Painless Series are written especially for middle school and high school students who are having a difficult time with a specific subject. In many cases, a student is confused by the subject?s complexity and details. Still other students simply finds a subjec
For students who are intimidated by all forms of math, here is a set of easy steps that lead to an understanding of elementary algebra. The author defines all terms, points out potential pitfalls in algebraic calculation, and makes problem solving a fun activity. New in this edition are painless approaches to understanding and graphing linear equations, solving systems of linear inequalities, and graphing quadratic equations. Barron?s popular Painless Series of study guides for middle school and high school students offer a lighthearted, often humorous approach to their subjects, transformin
Reading comprehension is a skill that all students must develop for academic success, especially as they advance to college and beyond. This book for junior and senior high school students asks them meaningful questions about their reading preferences and difficulties. For example— What kind of reader am I? Avid or reluctant? What can I do if I don't understand what I'm reading? How do I keep the information in my head? All students can profit from this book, but reluctant readers will find it especially helpful. Guided by the author, who is an experienced teacher, they learn
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MAA's Bestselling Books of 2008
December 16, 2008
Still trying to decide what to get the math enthusiast in your life? Let the MAA help. The following list highlights 2008's most popular books published by the MAA. The list covers a wide range of mathematical topics, so you should have no problem finding something perfect for everyone on your list. Further down this page, you'll find a list of all MAA books that have been designated "outstanding academic titles" by Choice magazine, published by the American Library Association. These books and more are all available at the MAA Bookstore.
Where did math come from? Who thought up all those algebra symbols, and why? What's the story behind ? ...negative numbers? ...the metric system? ...quadratic equations? ...sine and cosine? The 25 independent sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that's accessible to teachers, students, and anyone who is curious about the history of mathematical ideas.
This important addition to the New Mathematical Library series pays careful attention to applications of game theory in a wide variety of disciplines. The applications are treated in considerable depth. The book assumes only high school algebra, yet gently builds to mathematical thinking of some sophistication. Game Theory and Strategy might serve as an introduction to both axiomatic mathematical thinking and the fundamental process of mathematical modelling. It gives insight into both the nature of pure mathematics, and the way in which mathematics can be applied to real problems.
Number Theory Through Inquiry is an innovative textbook that leads students on a guided discovery of introductory number theory. The book has two equally significant goals. One goal is to help students develop mathematical thinking skills, particularly, theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for an independent study experience, or for a course designed as an introduction to abstract mathematics.
A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions (AMC) have been given for more than fifty years to millions of high school students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone taking the AMC exams or helping students prepare for them will find many useful ideas here.
Written for the mathematically literate reader, this book provides a glimpse of Euler in action. Following an introductory biographical sketch are chapters describing his contributions to eight different topics—number theory, logarithms, infinite series, analytic number theory, complex variables, algebra, geometry, and combinatorics. Each chapter begins with a prologue to establish the historical context and then proceeds to a detailed consideration of one or more Eulerian theorems on the subject at hand. Each chapter concludes with an epilogue surveying subsequent developments or addressing related questions that remain unanswered to this day.
Hard Problems is about the extraordinary gifted students who represented the United States in 2006 at the world's toughest math competition: the International Mathematical Olympiad (IMO). It is the story of six American high school students who competed with 500 others from 90 countries in Ljublijana, Slovenia. The film shows the dedication and perseverance of these remarkably talented students, the rigorous preparation they undertake, and the joy they get out of solving challenging math problems. It captures the spirit that infuses the mathematical quest at the highest level.
The second edition of this book introduces and develops some of the important and beautiful elementary mathematics needed for rational analysis of various gambling and game activities. Most of the standard casino games (roulette, craps, blackjack, keno), some social games (backgammon, poker, bridge) and various other activities (state lotteries, horse racing, etc.) are treated in ways that bring out their mathematical aspects. The mathematics developed ranges from the predictable concepts of probability, expectation, and binomial coefficients to some less well-known ideas of elementary game theory.
In the second edition of this MAA classic, exploration continues to be an essential component. More than 60 new exercises have been added, and the chapters on Infinite Summations, Differentiability and Continuity, and Convergence of Infinite Series have been reorganized to make it easier to identify the key ideas. A Radical Approach to Real Analysis is an introduction to real analysis, rooted in and informed by the historical issues that shaped its development. It can be used as a textbook, or as a resource for the instructor who prefers to teach a traditional course, or as a resource for the student who has been through a traditional course yet still does not understand what real analysis is about and why it was created.
Among the many beautiful and nontrivial theorems in geometry found hereThis volume is a compilation of articles from researchers and educators who use the history of mathematics to facilitate active learning in the classroom. The contributions range from simple devices such as the rectangular protractor that can be made in a geometry classroom, to elaborate models of descriptive geometry that can be used as a major project in a college mathematics course.
The derivative and the integral are the fundamental notions of calculus. Though there is essentially only one derivative, there is a variety of integrals, developed over the years for a variety of purposes, and this book describes them. No other single source treats all of the integrals of Cauchy, Riemann, Riemann-Stieltjes, Lebesgue, Lebesgue-Steiltjes, Henstock-Kurzweil, Weiner, and Feynman.
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poll unit MSXR209_1 you saw how some of the stages of a mathematical modelling process can be applied in the context of modelling pollution in the Great Lakes. In this unit you are asked to relate the stages of the mathematical modelling process to another practical example, this time modelling the skid marks caused by vehicle tyres. By considering the example you should be able to draw out and clarify your ideas of mathematical modelling.
This unit, the second in a series of five, builds a real-world system – the Great Lakes – where mathematical modelling has been used to understand what is happening and to predict what will happen if changes are made. The system concerned is extremely complex but, by keeping things as simple as possible, sufficient information will be extracted to allow a mathematical model of the system to be obtained.
Just as we usually take for granted the basic arithmetical operations with real numbers, so we usually assume that, given any positive real number a, there is a unique positive real number b = such that b2 = a. We now discuss the justification end of Section 1, we discussed the decimals
and asked whether it is possible to add and multiply these numbers to obtain another real number. We now explain how this can be done using the Least Upper Bound Property of examples just given, it was straightforward to guess the values of sup E and inf E. Sometimes, however, this is not the case. For example, if
then it can be shown that E is bounded above by 3, but it is not so easy to guess the least upper bound of E.
In such cases, it the set [0, 2) has no maximum element. However, [0, 2) has many upper bounds, for example, 2, 3, 3.5 and 157.1. Among all these upper bounds, the number 2 is the least upper bound because any number less than 2 is not an upper bound of [0, 2 you how to prove inequalities of various types. We use the rules for rearranging inequalities given in Section 2, and also other rules which enable us to deduce 'new inequalities from old'. We met the first such rule introduced you to some aspects of using a scientific or graphics calculator. However, in many ways, it has only scratched the surface. Hopefully your calculator will be your friend throughout your study of mathematics and beyond. Like any friend, you will get to know it better and appreciate its advantages as you become more familiar with it. Don't expect to know everything at the beginning. You may find the instruction booklet, or other help facility, a bit hard going to begin the list of advantages given, here is a word of warning: a calculator is not a substitute for a brain! Even when you are using your calculator, you will still need to sort out what calculation to do to get the answer to a particular problem. However skilled you are at using your calculator, if you do the wrong sum, you will get the wrong answer. The phrase 'garbage in, garbage out' applies just as much to calculators as to computers. Your calculator is just that – a calculator! aspects of the calculator are straightforward to use. Calculations are entered on the screen in the same order as you would write them down. More complicated mathematical functions and features are also reasonably intuitive, and there are 'escape' mechanisms, so that you can explore without worrying about how you will get back to where you were calculator will give you information about any number that you have entered: for example, its square or cube, its square root or cube root. It will also give you information about a whole list of numbers: for example, the mean (average) or the highest value in the list
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Description
The Bittinger Graphs and Models Series helps students "see the math" and learn algebra by making connections between mathematical concepts and their real-world applications. The authors use a variety of tools and techniques—including side-by-side algebraic and graphical solutions and graphing calculators, when appropriate—to engage and motivate all types of learners. Abundant applications, many of which use real data, provide a context for learning and understanding the math.
Table of Contents
Preface
1. Basics of Algebra and Graphing
1.1 Some Basics of Algebra
1.2 Operations with Real Numbers
1.3 Equivalent Algebraic Expressions
1.4 Exponential Notation and Scientific Notation
Mid-Chapter Review
1.5 Graphs
1.6 Solving Equations and Formulas
1.7 Introduction to Problem Solving and Models
Summary and Review
Test
2. Functions, Linear Equations, and Models
2.1 Functions
2.2 Linear Functions: Slope, Graphs, and Models
2.3 Another Look at Linear Graphs
2.4 Introduction to Curve Fitting: Point-Slope Form
Mid-Chapter Review
2.5 The Algebra of Functions
Summary and Review
Test
3. Systems of Linear Equations and Problem Solving
3.1 Systems of Equations in Two Variables
3.2 Solving by Substitution or Elimination
3.3 Solving Applications: Systems of Two Equations
Mid-Chapter Review
3.4 Systems of Equations in Three Variables
3.5 Solving Applications: Systems of Three Equations
3.6 Elimination Using Matrices
3.7 Determinants and Cramer's Rule
3.8 Business and Economics Applications
Summary and Review
Test
Cumulative Review: Chapters 1—3
4. Inequalities
4.1 Inequalities and Applications
4.2 Solving Equations and Inequalities by Graphing
4.3 Intersections, Unions, and Compound Inequalities
4.4 Absolute-Value Equations and Inequalities
Mid-Chapter Review
4.5 Inequalities in Two Variables
Summary and Review
Test
5. Polynomials and Polynomial Functions
5.1 Introduction to Polynomials and Polynomial Functions
5.2 Multiplication of Polynomials
5.3 Polynomial Equations and Factoring
5.4 Trinomials of the Type x2 + bx + c
5.5 Trinomials of the Type ax2 + bx + c
5.6 Perfect-Square Trinomials and Differences of Squares
5.7 Sums or Differences of Cubes
Mid-Chapter Review
5.8 Applications of Polynomial Equations
Summary and Review
Test
6. Rational Expressions, Equations, and Functions
6.1 Rational Expressions and Functions: Multiplying and Dividing
6.2 Rational Expressions and Functions: Adding and Subtracting
6.3 Complex Rational Expressions
Mid-Chapter Review
6.4 Rational Equations
6.5 Applications Using Rational Equations
6.6 Division of Polynomials
6.7 Synthetic Division
6.8 Formulas, Applications, and Variation
Summary and Review
Test
Cumulative Review: Chapters 1—6
7. Exponents and Radical Functions
7.1 Radical Expressions, Functions, and Models
7.2 Rational Numbers as Exponents
7.3 Multiplying Radical Expressions
7.4 Dividing Radical Expressions
7.5 Expressions Containing Several Radical Terms
Mid-Chapter Review
7.6 Solving Radical Equations
7.7 The Distance Formula, the Midpoint Formula, and Other Applications
7.8 The Complex Numbers
Summary and Review
Test
8. Quadratic Functions and Equations
8.1 Quadratic Equations
8.2 The Quadratic Formula
8.3 Studying Solutions of Quadratic Equations
8.4 Studying Solutions of Quadratic Equations
8.5 Equations Reducible to Quadratic
Mid-Chapter Review
8.6 Quadratic Functions and Their Graphs
8.7 More About Graphing Quadratic Functions
8.8 Problem Solving and Quadratic Functions
8.9 Polynomial Inequalities and Rational Inequalities
Summary and Review
Test
9. Exponential Functions and Logarithmic Functions
9.1 Composite Functions and Inverse Functions
9.2 Exponential Functions
9.3 Logarithmic Functions
9.4 Properties of Logarithmic Functions
Mid-Chapter Review
9.5 Natural Logarithms and Changing Bases
9.6 Solving Exponential and Logarithmic Equations
9.7 Applications of Exponential and Logarithmic Functions
Summary and Review
Test
Cumulative Review: Chapters 1—9
10. Conic Sections
10.1 Conic Sections: Parabolas and Circles
10.2 Conic Sections: Ellipses
10.3 Conic Sections: Hyperbolas
Mid-Chapter Review
10.4 Nonlinear Systems of Equations
Summary and Review
Test
11. Sequences, Series, and the Binomial Theorem
11.1 Sequences and Series
11.2 Arithmetic Sequences and Series
11.3 Geometric Sequences and Series
Mid-Chapter Review
11.4 The Binomial Theorem
Summary and Review
Test
Cumulative Review: Chapters 1-11
Answers
Glossary
Photo Credits
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Download
Next: Expresiones Variables
Chapter 1: Ecuaciones y Funciones
Chapter Outline
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Chapter Summary
Description
This chapter covers evaluating algebraic expressions, order of operations, using verbal models to write equations, solving problems using equations, inequalities, identifying the domain and range of a function, and graphs of functions.
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Math
Mathematics enables the student to acquire self-discipline and logical/critical thinking skills. In fact, the study of mathematics is necessary to enable the student to reason logically in all aspects of her life. The progression of courses offered by the department provides the student with the opportunity to discover and strengthen her mathematical skills, and to achieve her highest potential. These goals are achieved by:
In our era of increasing technology, the study of mathematics is more important than ever before. Mathematics is directly related to Science and Computer Technology. Both Science and Technology are dependent upon the logic and symbolic manipulation that are integral parts of mathematics.
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Algebra Models are designed to model algebraic concepts through an area model! Your students will see abstract algebraic ideas and concepts come to life as they combine like terms, build rectangles and squares, use substitution to solve linear equations, find factors and quotients, determine area and perimeter, multiply binomials, factor trinomials and much more. Algebra Models can be incorporated into any Pre-Algebra or Algebra I curriculum and can be used with any existing algebra manipulative resource materials.
Set of 41 tiles includes twenty unit tiles, eight X tiles, four X˛ tiles, two XY tiles, five Y tiles, and two Y˛ tiles.
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Complete description
The Indispensable Source of Information for all those who use Mathematics in Their Work...This is undoubtedly the most comprehensive, up-to-date and authoritative mathematics encyclopaedia available today. Translated from the Russian, edited, annotated and updated by about 200 Western mathematicians, all specialists in their respective fields, the 10-volume Encyclopaedia of Mathematics contains nearly 7000 articles together with a wealth of complementary information. Explanations of differences in terminology are of historical interest and help to bridge the gap between Western and Soviet approaches to mathematics. The Encyclopaedia of Mathematics will help you: find the precise definition of a given concept loop up and verify terminology find the precise statement of a theorem reach the information you need via AMS classification number and/or keywords/phrases check the precise names of concepts and theorems find reference literature for a given field find out about applications of a concept and its links with other concepts
Top page
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Algebra Combat, players alternate turns to see who can solve sets of single-variable linear equations with the best time and accuracy. Equations are randomly generated in one of four difficulty levels. All solutions are integers less than 40 and presented as multiple choice.
Beginners may need to jot down a step or two on a piece of paper. More advanced players will be able to solve these problems on the fly. With continued gameplay, students develop increased confidence with entry level algebraic expressions, negative integers, and quick mental calculations.
Both practice and competition modes are included. All rounds contain 5 equations to solve. Scores and times are provided following each round. A "Current Rankings" score tally also follows each competition round. Best rounds of all time are entered into the "Top Fighters" hall of fame along with the player's name, time, score, and difficulty level played.
In keeping with the cage fight theme, players are encouraged to give their fighters a cool name and type in a little "trash talk" before each round. All trash talk messages are then delivered to the opposing player at the beginning of his or her turn… ensuring matches are both spirited and entertaining.
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30 Free Web Tools and Open Source Software for Students
"Free Web-Based and Open Source Software Mathematics and
Modeling Tools:
"15. GNU Octave is an open source high-level interpreted
language intended for numerical computations. It provides
capabilities for the numerical solution of linear and nonlinear
problems, and for performing other numerical experiments. GNU
Octave also provides extensive graphics capabilities for data
visualization and manipulation. The current version is Version
3.4.0 and it is available for Linux, Mac OS X and other projects
have contributed to a Windows binary distribution of Octave and a
binary distribution of Octave for Sun systems. There is also a
collection of contributed packages for Octave available.
"16. Graphing Calculator from e-Tutor is an online Web tool that
lets students enter functions of x using a standard mathematical
format. Students simply type one or more equations into the Graph
box on the site to use the graphing calculator.
"17. Mathway is an online tool that provides students with the
tools they need to solve their math problems. Mathway solves
problems from the following subjects: Basic Math, Pre-Algebra,
Algebra, Trigonometry, Precalculus, Calculus and Statistics.
"18. Sage is a free open-source mathematics software suite
system licensed under the GPL. It combines the power of many
existing open-source packages into a common Python-based interface.
Sage mathematical software is designed for research and teaching.
It is a viable free open source alternative to Magma, Maple,
Mathematica and Matlab."
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Mathematics for Economics and Business
Rebecca Taylor Simon Hawkins
ISBN: 0077107861 Copyright year: 2008
Welcome to the Online Learning Centre for Mathematics for Economics and Business, 1st European edition
Mathematics for Economics and Business by Rebecca Taylor and Simon Hawkins is an introductory level text aimed at undergraduates requiring an understanding of mathematics. For many students embarking on an economics or business course, the level of mathematics required to
understand key topics can at first seem daunting. This student friendly text takes a step-by-step approach to explaining mathematical principles and applying these to an economic and business context. The range of study tools employed throughout the text caters for different learning styles and levels of understanding, encouraging students to take an active role in their learning of the subject. This edition features:
Coverage of core mathematical principles found in economics and business courses, assuming little prior knowledge of the subject
Student notes provided in boxes within each chapter as a useful quick reference
tool, summarising key terms and providing tips to help understanding
Worked examples, to consolidate learning and demonstrate the mathematical
principles as applied in an economic and business context
Quick Problem boxes to test understanding and application of the mathematical
principles taught in each chapter. Answers are provided at the end of the chapter so that students can check progress
The book is accompanied by a range of supplementary resources designed to provide students with the support they need to gain an understanding of mathematical principles.
On this OLC you can find a host of information about the book, as well as a range of downloadable supplements for students and lecturers.
THE STUDENT CENTRE
The Student Centre contains material to accompany the study of Mathematics for Economics and Business. This material includes:
Additional exercises for students
Web links
Excel-based exercises
Self test questions
Click on the menu to the left of this page to view these resources.
Chapter-by-chapter resources may be viewed by clicking on the drop-down list.
THE LECTURER CENTRE
The Lecturer Centre for this title contains a host of downloadable material
for lecturers who adopt Mathematics for Economics and Business. The material found in the Lecturer Centre includes:
Seminar exercises
Teaching suggestions
Solutions to additional exercises in the student centre
PowerPoints
Solutions to questions in the book
Mock exam with answers
Accessing the lecturer centreRequest lecturer copy If you are considering using Mathematics for Economics and Business for course adoption, you can request a complementary
Click on the link at the base of this page to return to the Information Centre.
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Did You Know??
Integrating Visual Learning into Mathematics - Conclusion
Geogebra is a visual teaching of 2D geometry. It is an interactive geometrical engine that allows students to modify the values of each independent variable as how they want to. As you can see from the screenshot of the program taken below, as values are entered into the column of variables on the left, the geometrical shape and lines formed on the right are altered accordingly. This allows students to have a very clear understanding of exactly how each different variable affects the outcome of the graph.
Being able to modify the values at will allows students to better understand the relationship between individual variables and the overall graph.
In stark contrast, the conventional method of hand-drawing or sketching geographical figures with pen and paper are much less convenient. Students cannot change the values of each variable independently and have to mentally calculate the equation of each line before being able to plot the points on the graph paper. It is also much harder for students to mentally visualise the relationship between the variables and the geometrical graph, impeding their progress in the topic.
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Algebra 2/Trigonometry Math Resources are a
collection of on-line resources
designed to be used
by students and teachers (parents) in the study and review of a
second course in
high school algebra with trigonometry.
MathBits Presents: "Alge2Caching" and "TrigCaching" There are 10 hidden internet boxes waiting to be found.
Your ability to find each box will be determined by your skill at answering mathematical questions at the Algebra 2 or Trigonometry levels.
A certificate is available at the end of the journey indicating that you have successfully found all 10 boxes. Good luck!!
Teachers: Have your students search for the boxes together as a class activity (especially during review), or assign the problems as extra credit or independent study.
A list of the topics covered in each game can be
found on the Directions page.Answer Keys for Teachers: e-mail Roberts@MathBits.com from a school email address.Answer Keys for Parents: Register with MathBits.com. Click here to register.(one week holding period on parental registering)
Math & the Movies Resources Worksheets at Alg2/Trig level: • I Love Lucy •Star Wars Episode 1 • Star Trek: The Trouble w/Tribbles •The Englishman Who Went Up
a Hill But Came Down a Mountain •October Sky • Proof and more! Answers available for teachers
and parents by request.
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An Introduction to Twistor Theory
Author: , Date: 02 Apr 2010, Views: ,
S. A. Huggett, K. P. Tod, quot;An Introduction to Twistor Theoryquot; Cambridge University Press | 2009 | ISBN: 0521456894, 0521451574 | 192 pages | File type: PDF | 1,3 mb This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. It will be valuable also to the physicist as an introduction to some of the mathematics that has proved useful in these areas, and to the mathematician as an example of where sheaf cohomology and complex manifold theory can be used in physics
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Modeling of Curves and Surfaces with MATLAB (Repost)
This concise text on geometry with applications in a variety of disciplines is devoted to three main geometrical topics: curves, surfaces, and polyhedra. It presents elementary methods for analytical modeling and their visualization, as well as demonstrating the potential of symbolic computational tools to support the development of analytical solutions.
The author systematically examines powerful tools including 2D and 3D animation of geometric images, transformations, shadows and colors, and then further studies more complex geometrical modeling problems related to analysis and differential equations. With over 150 stimulating exercises and problems, this text integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format. The book is also well-illustrated, with over 300 figures reproducible using Matlab programs.
This text greatly extends the author's previous title, "Geometry of Curves and Surfaces with Maple" (Birkhauser, 2000), and has a different focus. In addition to being applications-driven and motivated by numerous examples and exercises from real-world fields such as physics, engineering, biology, computer science, and IT, the book also contains more than 60 percent new material, including new sections with a geometric view of dynamical systems and PDEs, fractals, and surfaces-splines.
This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines, engineers, computer scientists, and instructors of applied mathematics.
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Author's Description
Math Center Level 1 - Math software for students
Math software for students studying precalculus. Can be enteresting for teachers teaching precalculus. Math Center Level 1 consists of Graphing calculator 2D, Advanced Calculator, and Simple Calculator called from the Control Panel.
Simple calculator is a general purpose calculator which combines use simplicity and calculation power. It handles simple arithmetic operations and complex formulas.
Advanced Calculator is a step farther in complexity comparing to the Simple Calculator. The Advanced Calculator has two editing windows. One is for editing x, and the second is for editing f(x). In the x window you can enter any number or formula which contains numbers. In the f(x) window you can enter formulas containing numbers and formulas containing x. First, x will be calculated. Then the result for x will be substituted into the formula for f(x). The presence of two editing windows demands switching between windows. You can do it by clicking buttons "go to x" and "go to f(x)", or by clicking inside the window. If you forget to enter x, then the x=1 will be assumed. If you forget to enter f(x), then f(x)=x will be assumed.
Advanced Calculator works in scientific mode. All numbers in internal calculations are treated in scientific format, like 1.23456789012345E+2 for 123.456789012345
Graphing Calculator 2D has two panels.
The Left Panel has the Magnifying Square represented by Small Square with gray border on the Left Panel. It is 16 times smaller than the Left Panel. The Right Panel shows content of the Magnifying Square magnified 16 times. You can press button "zoom +". Then the Left and Right Panels will be zoomed twice each. Maximum zoom is 8 (tree clicks of "zoom +"). After that you can click "zoom -". Clicking button "C" (for Center) on Zoom returns picture to starting position with no zoom and Magnifying Square at the center of Left Panel.
Math Center Level 1 1.0.0.1 is licensed as Shareware for the Windows operating system / platform. Math Center Level 1Math Center Level 1 Tvalx. Please be aware that we do NOT provide Math Center Level 1 cracks, serial numbers, registration codes or any forms of pirated software downloads.
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The Math Department at CVCC offers a variety of courses for students depending on their career goals. Courses range in number from MAT 050 to MAT 285. Class numbers that begin with 0, such as MAT 060, are considered developmental courses and do not count as credits earned toward graduation, nor do they count toward a student's GPA. Class numbers that begin with 1 or 2, such as MAT 121 or MAT 273, are considered either technical or college transfer.
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MAT-121 College Algebra
A college-level algebra course that provides an understanding of algebraic concepts, processes and practical applications. Topics include linear equations and inequalities, quadratic equations, systems of equations and inequalities, complex numbers, exponential and logarithmic expressions, and functions and basic probability.
Advisory: it is advisable to have knowledge in a course equivalent to MAT-115 Intermediate are only permitted to take one of the following courses: MAT-119, MAT-121 or MAT-128. BSBA and ASBA students should not take MAT-121. BSAST and ASAST students should take MAT-121 and MAT-129.
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Keywords:
Background Tutorials
Numerical and Algebraic Expressions
There is a bunch of vocabulary that you just need to know when it comes to algebra, and coefficient is one of the key words that you have to feel 100% comfortable with. Check out the tutorial and let us know if you want to learn more about coefficients!
Definitions of Linear Systems
A system of equations is a set of equations with the same variables. If the equations are all linear, then you have a system of linear equations! To solve a system of equations, you need to figure out the variable values that solve all the equations involved. This tutorial will introduce you to these systems.
Matrix Definitions
Matrices can help solve all sorts of problems! This tutorial explains what a matrix is and how to find the dimensions of a matrix
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The course teaches students algebraic concepts and math skills for a strong base in the math concepts for MHS graduation requirements and to strive for proficiency on the Missouri EOC Algebra examWe will begin working Algebra concepts. The class will move at the students' pace. It is the first class in the Algebra 1A/1B seriesThis class will welcome our freshmen to MHS. We will begin the year in academy to learn the expectations and information about being the best Spartan we can be. We will finish our year working in RTI groups and improving our math skills through lessons, team work, and hands on learning sessions.
Intermediate Algebra will expand on Algebra and Geometry concepts to build students' math abilities and understanding prior to College Algebra
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Research in Physical Applied Mathematics
Physical Applied Mathematics is a term which generally refers to the study of mathematical problems with direct physical application. This area of research is intrinsically interdisciplinary. In addition to mathematical analysis, it requires a deep understanding of the underlying applications area, and usually requires knowledge and experience in numerical computation. The Program's affiliated faculty have a wide variety of expertise in various areas of application, e.g. atmospheric and fluid dynamics, theoretical physics, plasma physics, genetic structure etc. The course requirements of the Program are designed to provide students with a foundation for their study (analysis and computation). The Program also requires supplemental courses in one of the science or engineering fields which are needed to begin doing thesis research in physical applied mathematics.
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Search Digital Classroom Resources:
Flash Tools for Developers (AS3): Graphing curves in the plane
Flash CS3 (Actionscript 3.0) templates and classes for graphing functions in one variable as well as parametric curves in rectangular or polar coordinates.
Digital Classroom Resources
Actionscript 3 Tutorials
by Doug Ensley, Barbara Kaskosz
Overview
Doug Ensley
Shippensburg University
Barbara Kaskosz
University of Rhode Island
ActionScript 3.0 is new; it is exciting, fast, and fully object-oriented. Flash CS3 authoring environment and ActionScript 3.0 provide a great tool for educators in mathematics and sciences to create their own, custmized web-based learning aids. Most of available samples, books, and articles on ActionScript 3.0 (AS3) are not written with mathematical applications in mind and Flash's great potential in that respect is only now being realized. This is where our MathDL Flash Forum and this collection of tutorials come in. You will find here a collection of ActionScript 3.0 and Flash CS3 tutorials prepared with a mathematics educator in mind. We will help you learn AS3 through creating mathematical objects and applets.
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0486284336
9780486284330
How to Solve Mathematical Problems: Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions. Carefully and clearly written, this indispensable guide will help students in every discipline avoid countless hours of frustration and wasted effort. «Show less
Rent How to Solve Mathematical Problems today, or search our site for other Wickelgren Logic
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With a new
foreword by Dan Rockmore, Chair of the Department of Mathematics
at Dartmouth College
Translated
from Japanese
by Alan Gleason
Second Edition
Published 2012
426 pages
Paperback, fully illustrated
ISBN 978-0-9643504-3-4
$29.95
The
student authors take the reader along on their adventure of discovery,
creating an interactive work that gradually moves from the very basics
("What is a right triangle?") to the more complicated mathematics of
trigonometry, exponentiation, differentiation, and integration. This
is done in a way that is not only easy to understand, but actually fun!
While it is user-friendly
enough even for those who are "math phobic," Who is Fourier?
has been enjoyed by many people in the math and science fields. The
largest percentage of our readers are professors and engineers, with
business people and students following closely. It is a must-have for
anyone interested in mathematics, physics, engineering, or complex science.
Over 60,000 copies have sold in Japan since the original publication!
"An
approach to the teaching of elementary Fourier series that
is innovative, conceptual and appealingly informal."
--Dr.
John Allen Paulos, author of Innumeracy
Want to take a
look at Who is Fourier? for yourself? Barnes & Noble and
Amazon.com typically carry our books, or you can special order it from
your favorite bookstore!
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