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Twelfth graders explore the concept of limits. In this calculus lesson, 12th graders investigate the limit rules for both finite and infinite limits through the use of the TI-89 calculator. The worksheet includes examples for each rule and a section for students to try other examples.
Students practice calculating and analyzing Riemann sums and illustrate when Riemann sums will over/under-approximate a definite integral. They view how the convergence of Riemann sums as the number of subintervals get larger.
Students explore the area under a curve. In this calculus lesson plan, students investigate Riemann sums as they employ technology to discover that if enough Riemann sums are used. Students then determine whether the area under a curve can be calculated with the required degree of precision. TI-nspire and appropriate applications are required.
Young scholars read an article on how calculus is used in the real world. In this calculus lesson, students draw a correlation between the Battle of Trafalgar and calculus. The purpose of this article is the show everyday uses for calculus in the real world.
In this numerical integration activity, students approximate the value of an integral using the methods taught in the class. They use left-hand Riemann sums, right-hand Riemann sums, the midpoint method and the trapezoidal ruleTwelfth graders explore differential equations. For this calculus lesson, 12th graders explore Euler's Methods of solving differential equations. Students use the symbolic capacity of the TI-89 to compare Euler's Method of numeric solutions to a graphical solution.
Students find patterns in a sequence. In this sequences and series lesson, students use their calculator to find the sequence of partial sums. They graph functions and explore convergent series. Students approximate alternating series.
Students review integrals and how they apply to solving equations. In this calculus lesson plan, students assess their knowledge of derivatives, rate of change, and lines tangent to a curve. This assignment contains two version of the same test concept.
Twelfth graders assess their knowledge of trig functions and their properties. For this calculus lesson, 12th graders take a test on derivatives, trig functions, and the quotient rule. There are 2 different versions of the same test available.
Students use the derivative and integral to solve problems involving areas. For this calculus lesson, students calculate the area under a curve as they follow a robot off road making different curves along the drive. They use Riemann Sums and Trapezoidal rules to solve the problem.
Students read about AP calculus online. In this calculus lesson, students learn real life usage for calculus. They read about instructors and their experience teaching and incorporating calculus into the real world.
Twelfth graders investigate derivatives. In this calculus lesson plan, 12th graders use technology to explore the basic derivatives and how to choose the proper formula to use them. The lesson plan requires the use of the TI-89 or Voyage and the appropriate application.
Students practice the concept of graphing associated to a function with its derivative. They define the concepts of increasing and decreasing function behavior and explore graphical and symbolic designs to show why the derivative can be used as an indicator for the behavior.
Students assess transformations to remove integral symbols as well as to simplify expressions. They explore the Symbolic Math Guide to assist them in solving indefinite integration by parts. This lesson includes partial fractions, sum/difference and scalar product transformations. |
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This Textbook
Overview
Through a unique problem-solving approach that enables non-math majors to see math at work in the contemporary world, this highly accessible text helps students develop techniques and methods that will be invaluable to them throughout their lives and careers. Special examples are presented in a two-column format with the easy-to-remember instructions, RSTUV (Read, Select, Think of a plan, Use the techniques, and Verify). More than 500 examples and 4100 carefully developed exercises cover a wide range of topics and provide both instructor and student with flexibility in choosing computational, drill, or conceptual problems. Real-world applications motivate students and hold their interest.
A strong technology focus in the Seventh Edition, featuring new Web It Exercises, encourages students to apply their knowledge using the most up-to-date web links maintained by the author on a text-linked site. Also on the web site are downloadable PowerPoint slides as well as new lecture and practice test videos. Additional features include Collaborative Learning sections, Graph It margin notes, and Skill Checker.
Editorial Reviews
Booknews
New edition of a text which introduces mathematical concepts that are used in our contemporary world, relating these ideas to areas such as sociology, business and psychology. The redesigned format provides new examples and exercises, and each chapter contains special features such as a preview, "getting started," "in other words," problem-solving sections, and research questions. Rather than the more abstract and theoretical aspects, the understanding and use of concepts is emphasized. Annotation c. by Book News, Inc., Portland, Or.
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Meet the Author
Ignacio Bello attended the University of South Florida (USF), where he earned a B.A. and M.A. in Mathematics. He began teaching at USF in 1967, and in 1971 he became a member of the faculty and Coordinator of the Math and Sciences Department ay Hillsborough Community College (HCC). Professor Bello instituted the USF/HCC remedial program, which started with 17 students taking Intermediate Algebra and grew to more than 800 students with courses covering Developmental English, Reading, and Mathematics. In addition to Topics in Contemporary Mathematics, Professor Bello has written many other books that span the mathematics curriculum, many of which have been translated to Spanish. Professor Bello is featured in three television programs on the award-winning Education Channel. He helped create and develop the USF Mathematics department website, which serves as support for the Finite Math, College Algebra, Intermediate Algebra, Introductory Algebra, and CLAST classes at USF. Professor Bello is a member of the Mathematical Association of America (MAA) and the American Mathematical Association of Two-Year Colleges (AMATYC). He has given many presentations regarding the teaching of mathematics at the local, state, and national |
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Description
The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction.
The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.
Reviews
"This beautifully written text is unlike any other in statistical science. It starts at the level of a first undergraduate course in linear algebra, and takes the student all the way up to the graduate level, including Hilbert spaces. It is extremely well crafted and proceeds up through that theory at a very good pace. The book is compactly written and mathematically rigorous, yet the style is lively as well as engaging. This elegant, sophisticated work will serve upper-level and graduate statistics education well. All and all a book I wish I could have written." |
Whether you're a hobbyist or a budding game design pro, your objective is probably the same: To create the coolest games possible using today's increasingly sophisticated technology. To do that, however, you need to understand some basic math and physics concepts. Not to worry: You don't need to go to night school if you get this handy guide! Through clear, step-by-step instructions, author Wendy Stahler covers the trigonometry snippets, vector operations, and 1D/2D/3D motion you need to improve your level of game development. Each chapter includes exercises to make the learning stick, and Visualization Experience sections are sprinkled throughout that walk you through a demo of the chapter's content. By the end of the volume, you'll have a thorough understanding of all of the math and physics concepts, principles, and formulas you need to control and enhance your user's gaming experience.
Table of Contents
Errata |
RHIT - Department of Mathematics
Computer Use Policy - public version
This document is shortened public version of the departmental
computer policy for freshman and sophomore courses. The math-only version
contains some historical background as well as implementation information
of interest to the mathematics department.
Guiding principles
The policy will applies to the following courses:
MA111, MA112, MA113 (MA101, MA102)
MA221, MA222
MA223
The policy will be consistent with and support our goals for student
learning at the foundational level. These are:
become competent users of mathematics,
appreciate mathematics as an intellectual endeavor in its own right
become familiar with basic mathematical and statistical thinking and
modeling,
understand the use of mathematics in other disciplines, and become
competent at the application of mathematics to these disciplines,
become effective problem solvers,
become competent in using the computer as an aid to mathematical modeling
and computation, and
develop communication skills appropriate in a mathematical context.
The computer packages used are:
MA111, MA112, MA113 - Maple
MA211, MA222 - Maple
MA223 - Minitab
Following the "competent users of mathematics" and become competent in
using the computer as an aid ... ", each course will have a minimal
set of by hands fundamentals and by computer use fundamentals that each
student must master.
In addition, the student will need to develop the following computer
learning objectives
become familiar with basic mathematical and statistical
thinking and modeling,
become effective problem solvers
report writing
develop communication skills appropriate in a mathematical
context.
Students will learn appropriate use of the computer as they progress
through the 6 courses. In the initial classes hands-on class time will be
devoted to helping students gain experience with the above. In later classes
students will be expected to gain their understanding on their own, through
classroom demonstration and handouts. and less frequent classroom sessions.
The six basic classes are our shot at developing computer skill in mathematics.
Evaluation
Each course will have components of the course that will evaluate competence
in by hands skills and computer skills. Examples of these are: |
Lessons from the HistoryofMathematics Tom Osler Rowan University Is Mathematics a Humanity or a Science? Humanities The branch of learning regarded as having primarily a cultural character and use, including languages, literature, history and philosophy.
Assignment: pp. 6-8 #1-46 Finding & Describing Patterns Geometry, like much ofmathematics and science, developed when people began recognizing and describing patterns. ... you will study many amazing patterns that were discovered by people throughout history and all around the world.
Students must take approved courses from 7 of 10 knowledge and skills areas to attain a SUNY baccalaureate degree: Mathematics, ... American History, Western Civilization, Other World Civilizations, Humanities, The Arts, Foreign Language, ...
Phase 1 learning areas due are English, mathematics, science and history P(K)–12. The curriculum for these areas are due for final publication later this year. Phase 2 learning areas are the arts, geography and languages.
Historyofmathematics from the point of view of Cognitive Science Historical approach to mathematics with elements from both Cognitive Science and Sociology of Scientific Knowledge A look at practice from the historiographical point of view cognitive practice historico-psychological ...
Chapter 1 Oh, So Mysterious Egyptian Mathematics! Primitive Man Hunter/gatherers Counted Simple Notches on wolf bone Groups of pebbles and stones Development of a simple grouping system Early Civilizations Humans discovered agriculture Need for a calendar Trading or bartering of services and ...
4.1 Extreme Values of Functions Greg Kelly, Hanford High School, Richland, Washington Borax Plant, Boron, ... we still study the methods to increase our understanding of functions and the mathematics involved. They are sometimes called global extremes.
Combined over All Subjects: Reading, Mathematics, Writing, Science, and Social Studies. Student Groups: ... World Geography; World History; US History. English Language Learners (English and Spanish tests): Students in US schools Year 1 - Year 3 excluded.
se ≈ 1.33, 11.255 < y < 16 ... xk are independent variables b is the y-intercept y is the dependent variable * Because the mathematics associated with this concept is complicated, technology is generally used to calculate the multiple regression equation.
English Baccalaureate (EBacc) for English, Mathematics, History or Geography, two sciences and an ancient or modern foreign language. GCSE reforms – linear assessment and SPaG Ofqual has confirmed the following changes to all GCSEs in England: ... |
Featured Research
from universities, journals, and other organizations
The aftermath of calculator use in college classrooms
Date:
November 12, 2012
Source:
University of Pittsburgh
Summary:
Math instructors promoting calculator usage in college classrooms may want to rethink their teaching strategies, experts say. They have proposed the need for further research regarding calculators' role in the classroom after conducting a limited study with undergraduate engineering students.
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Math instructors promoting calculator usage in college classrooms may want to rethink their teaching strategies, says Samuel King, postdoctoral student in the University of Pittsburgh's Learning Research & Development Center. King has proposed the need for further research regarding calculators' role in the classroom after conducting a limited study with undergraduate engineering students published in the British Journal of Educational Technology.
"We really can't assume that calculators are helping students," said King. "The goal is to understand the core concepts during the lecture. What we found is that use of calculators isn't necessarily helping in that regard."
Together with Carol Robinson, coauthor and director of the Mathematics Education Centre at Loughborough University in England, King examined whether the inherent characteristics of the mathematics questions presented to students facilitated a deep or surface approach to learning. Using a limited sample size, they interviewed 10 second-year undergraduate students enrolled in a competitive engineering program. The students were given a number of mathematical questions related to sine waves -- a mathematical function that describes a smooth repetitive oscillation -- and were allowed to use calculators to answer them. More than half of the students adopted the option of using the calculators to solve the problem.
"Instead of being able to accurately represent or visualize a sine wave, these students adopted a trial-and-error method by entering values into a calculator to determine which of the four answers provided was correct," said King. "It was apparent that the students who adopted this approach had limited understanding of the concept, as none of them attempted to sketch the sine wave after they worked out one or two values."
After completing the problems, the students were interviewed about their process. A student who had used a calculator noted that she struggled with the answer because she couldn't remember the "rules" regarding sine and it was "easier" to use a calculator. In contrast, a student who did not use a calculator was asked why someone might have a problem answering this question. The student said he didn't see a reason for a problem. However, he noted that one may have trouble visualizing a sine wave if he/she is told not to use a calculator.
"The limited evidence we collected about the largely procedural use of calculators as a substitute for the mathematical thinking presented indicates that there might be a need to rethink how and when calculators may be used in classes -- especially at the undergraduate level," said King. "Are these tools really helping to prepare students or are the students using the tools as a way to bypass information that is difficult to understand? Our evidence suggests the latter, and we encourage more research be done in this area."
King also suggests that relevant research should be done investigating the correlation between how and why students use calculators to evaluate the types of learning approaches that students adopt toward problem solving in mathematicsMay 21, 2012 — Discipline-based education research has generated insights that could help improve undergraduate education in science and engineering, but these findings have not yet prompted widespread changes in |
Description new Precalculus eText by Eric Schulz, William Briggs, and Lyle Cochran strengthens the connection between precalculus and calculus in a way that's never been done before. The eText seamlessly integrates narrative text, interactive figures, and instructive author videos to immerse students in a rich learning environment. |
More About
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Overview
Compact and easy-to-use, Math for Nurses is a pocket-sized guide/reference to dosage calculation and drug administration. It includes a review of basic math skills, measurement systems, and drug calculations/preparations. Math for Nurses helps students to calculate dosages accurately and improve the accuracy of drug delivery. The author uses a step-by-step approach with frequent examples to illustrate problem-solving and practical applications. Readers will find it great for use in the clinical setting or as a study aid. Practice problems throughout the text and end-of-chapter and end-of-unit review questions will aid students' application and recall of material. A handy pull-out card contains basic equivalents, conversion factors, and math formulas.
Editorial Reviews
From The Critics
Reviewer: Shari J. Lynn, RN, MSN (Johns Hopkins University School of Nursing) Description: This drug calculation reference for students and nurses covers all aspects of drug calculation and includes a laminated reference card. The original edition was published in 1987. Purpose: The purpose is to create an easy to use drug reference to assist nurses and students in proper dosage calculations, thus reducing medication errors. The objectives are worthy as this is a much needed guide. Audience: This book is written for nurses and students. The author is a credible source. Features: The pocket guide covers drug administration, various systems of measurement, dosage calculation, and problem solving techniques. Basic conversions are well covered, as is how to read drug labels. Example problems assist the reader in gaining greater knowledge in dealing with dosage calculations and problem solving. Assessment: This is a very comprehensive reference. It begins with basic math, instead of assuming that the reader has previously mastered this knowledge. This is a much needed update 8, 2003
Fantistic Book
I got this book to help me with the Math on the Pharm. Tech Test...and it DID! I passed the test after studing this book + a class I took over the internet. It was great math support...I studied and worked every problem...till I knew how to work the problems just by looking at the problem AND I PASSED. Great BOOK!
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. |
How To Teach with DWFK Precalculus
Chapter 2: Polynomial, Power, and Rational Functions
With the complete vocabulary of functions available to use, the course now turns to a closer focus on particular classes of functions, beginning with polynomials, power functions, and rational functions. Since concepts like asymptotes and end behavior have already been introduced (as well as lines and a first look at parabolas), the presentation has been streamlined, combining two chapters from the previous edition and adding an extended treatment of power functions. There is more algebra in the book from here on, but the graphical and numerical models are continually mentioned in order to reinforce the connections.
Note that the first three sections introduce the function types "with modeling," in keeping with the emphasis on modeling that will be found throughout the course.
Section 2.1 Linear and Quadratic Functions with Modeling
Objectives
Students will be able to construct and graph linear and quadratic functions and use them to model behavior in real world problems.
Key Ideas
Average rate of change
Linear correlation (positive or negative)
Axis of symmetry of a parabola
Linear depreciation
Coefficient
Linear function
Correlation coefficient
Polynomial function
Degree of a polynomial
Quadratic function
Free-fall
Vertex of a parabola
Teaching Tips
Emphasizing a linear function as a function with a constant rate of change is an important "pre-calculus" feature of this section. We also exploit the regression capabilities of the calculators to fit linear and quadratic functions to data.
Teachers should be careful about assuming that their students have seen this material. The underlying algebra (e.g., linear functions, vertex of a parabola) might be familiar to some students, but the context in which it is presented will be new to most. We would expect classes to have the impression that they are covering new ground here.
Technology Tips
Many students will have calculators that give two forms of the linear regression line: one in the form y = ax + b and one in the form y = a + bx. They might be interested to learn why this redundancy is there. Statisticians are accustomed to the y = a + bx form, so that is what the earlier graphing calculators were programmed to give. When more statistics began to be incorporated into high school algebra, complaints started coming in from algebra teachers that b should be the y-intercept, not the slope. (Need we say why?) Later calculator models were therefore programmed to give an a + bx option for the statisticians and an ax + b option for the algebraists – take your pick!
Note that the quadratic regression gives a value of R2 (the coefficient of determination) rather than values of r2 and r (the linear correlation coefficient). That is because linear correlation is not appropriate with quadratic regression. See the remarks following Example 1 in Section 1.6. Top
Section 2.2 Power Functions with Modeling
Objectives
Students will be able to construct and graph power functions of the form and use them to model behavior in real world problems.
Key Ideas
Concave down
Direct Variation
Concave up
Inverse variation
Constant of proportion
Monomial function
Constant of variation
Power function
Teaching Tips
Although half of the "ten basic functions" of Section 1.3 are actually power functions, it took the addition of "power regression" on calculators to earn them the status of their own section in the textbook. Working through this section will leave you wondering why it took so long. Some nice topics like direct and inverse variation and concavity fit comfortably into a unified treatment of this important class of functions.
Example 2 introduces in the manner of the basic functions. It is a good review of the functions concepts to see if students can verify their properties.
Concavity (discussed in the paragraphs following Example 3) is a geometric property of curves that was not introduced in Section 1.2. Knowing the geometric meaning of concavity will help students in calculus when they analyze it as an application of the second derivative.
Technology Tips
Pay heed to the marginal warning about power regression alongside Example 6. Linear and quadratic regressions can be performed on any set of ordered pairs, but power regressions will fail if all values of x and y are not positive. Several of the other regression models have similar restrictions on x and/or y. (These restrictions are specified in the catalog of regression types on page 138, although they are easy to miss until one actually tries to use the regressions in specific cases.)
Section 2.3 Polynomial Functions of Higher Degree with Modeling
Objectives
Student will be able to graph polynomial functions of degree higher than 2 using graphing technology. They will be able to use the technology to find zeros and relative extrema, analyze end behavior, fit curves to data, and solve modeling problems.
Key Ideas
Coefficient
Multiplicity of a zero of a polynomial
Cubic function
Polynomial interpolation
Intermediate Value Theorem
Quartic function
Leading term of a polynomial
Term of a polynomial
Teaching Tips
Although there are formulas for solving cubic and quartic polynomial equations algebraically, they are complicated and must be broken down into different cases. It is not possible to solve a general quintic (5th degree) equation algebraically (a result proved by Niels Henrik Abel at the age of 19), so most modern algebra courses draw the line at the quadratic formula when it comes to exact algebraic solutions. We therefore jump from linear and quadratic polynomials to a section on all the rest, about which there is algebraically less to say until we have acquired the tools of calculus.
The emphasis here is on exploring end behavior, zeros, and relative extrema using grapher technology. Some students will have used graphers to find extrema in their algebra courses (as such problems now appear regularly in textbooks), but few will have seen the connection between a polynomial's leading term and its end behavior.
Since cubic and quartic regression appear on current calculators, we include some data analysis involving polynomial interpolation. In actual practice, polynomials of higher degree are applied to real-world data less frequently than linear and quadratic models.
Technology Tips
Pay heed to the technology tip on page 189 about how to change horizontal and vertical scales on a calculator when analyzing the graph of a polynomial. "Zooming" in and out will usually change horizontal and vertical scales by equal factors, distorting the shape of the graph—a possible source of frustration for students trying to study end behavior or search for zeros.
Exercise 75 in this section is an excellent use of graphing calculators to foreshadow differential calculus. The fact that a smooth curve can be locally approximated by its tangent line at a point underlies most applications of the derivative. Top
Section 2.4 Real Zeros of Polynomial Functions
Objectives
Students will be able to divide polynomials using long division or synthetic division. They will be able to analyze the zeros of polynomials using the Factor Theorem, the Rational Zeros Theorem, and the Upper and Lower Bounds tests.
Key Ideas
Factor Theorem
Remainder Theorem
Polynomial division
Synthetic division
Rational Zeros Theorem
Upper and lower bound tests for real zeros
Teaching Tips
This section contains a few algebraic approaches that have been traditionally used to find zeros of polynomials of degree higher than 2. While they are beautiful results of historical significance, the fact that they can only be used in carefully-constructed cases has caused them to be upstaged in practice by the more generally-applicable technological approach of the previous section.
Students who plan to compete in mathematics competitions will need to know these results well, as they are needed for solving many of the carefully-constructed problems that appear on such examinations. The degree to which this section is emphasized will probably depend on the extent to which the teacher reveres these classical results, but all teachers should keep in mind that there are, realistically, more essential topics yet to come.
Technology Tips
In is an interesting merger of the modern and the classical, the calculator comes in handy for applying the Rational Zeros Theorem. The most tedious aspect of applying the theorem has always been to "check" the many candidates to see which work. Not only can the calculator be used for those evaluations, but a quick graph can be used to reject most of the candidates before one bothers evaluating them.
Be sure to restrict calculator usage where appropriate. For example, exercises 49—56 should be done algebraically, with the calculator used only as a check.
Section 2.5 Complex Numbers
Objectives
Students will be able to add, subtract, multiply, and divide complex numbers and write the results in standard form. They will be able to evaluate reciprocals and absolute values of complex numbers and find complex zeros of quadratic functions.
Key Ideas
Absolute value (modulus) of a complex number
Imaginary number
Additive identity
Imaginary unit (i)
Additive inverse
Multiplicative identity
Complex conjugate
Multiplicative inverse (reciprocal)
Complex number
Real and imaginary axes
Complex plane
Real and imaginary parts of a number
Discriminant of a quadratic equation
Standard (a + bi) form
Teaching Tips
The emphasis in a precalculus course is on real-valued functions of real numbers, since those are the functions that can be graphed in the Cartesian plane. Nonetheless, it is natural to discuss complex numbers in a couple of precalculus contexts, one of them being the zeros of polynomial functions. (The other involves trigonometry and will appear in Section 6.5).
This section covers the basic algebra of complex numbers, something that all students should know by the time they get to calculus — despite the fact that they will have little opportunity to use it during their first two calculus courses.
After covering the absolute value of a complex number as thoroughly as you wish, you can bet your students any amount of money that at least one of them, when asked to find on the final exam, will respond with a + bi. You will win.
Technology Tips
Modern calculators will do the algebra of complex numbers. If you really want your students to learn how to manipulate complex numbers with pencil and paper (and you probably should), you will want to prohibit the use of calculators on all exercises in this section.
Before going on to Section 2.6, ask students to explain how the existence of complex zeros limits the calculator's ability to solve equations. It's a good review of many of the important equation-solving concepts covered up to this point. (Some calculators will actually find the complex zeros, which makes for an interesting extension of the conversation.) Top
Section 2.6 Complex Zeros and the Fundamental Theorem of Algebras
Objectives
Students will understand the Fundamental Theorem of Algebra and the Linear Factorization Theorem and be able to use them to find real and complex zeros of polynomials with real coefficients.
Key Ideas
Complex conjugate zeros
Irreducible over the reals
Fundamental Theorem of Algebra
Linear Factorization Theorem
Teaching Tips
Although the proof of the Fundamental Theorem of Algebra is well beyond the scope of this course, any precalculus student should be able to understand its statement and implications (one implication being the Linear Factorization Theorem). When deciding how much time to spend covering this section, be advised that the comments in "Teaching Tips" for Section 2.4 apply equally here.
Technology Tips
"A Word About Proof" following Example 10 in Section 1.1 mentioned the importance of the Fundamental Theorem of Algebra for doing computer (or calculator) searches for zeros of functions. Once we have found n zeros for a polynomial of degree n, this is the theorem that tells us to stop searching. Similarly, until we have found n zeros (including complex and/or repeated zeros), this is the theorem that tells us to keep searching.
This is another section in which the manipulative exercises should be solved algebraically, then verified graphically. Students who solve graphically will miss out on the applications of the theorems. Top
Section 2.7 Rational Functions and Equations
Objectives
Students will be able to describe and produce the graphs of rational functions, identify their horizontal and vertical asymptotes, and analyze their end behavior. Students will be able to model real-world problems with rational functions and solve the resulting equations, identifying extraneous solutions when they occur.
Key Ideas
Rational function
Teaching Tips
This section is a good review of many of the function concepts of Chapter 1 and should be approached in that spirit. Asymptotes, zeros, and intercepts can be found algebraically and then used to give a full geometric picture (graph) of the function's behavior. Also, since rational functions arise quite naturally in real-world applications, there are some good modeling problems in the examples and exercises.
Technology Tips
Although calculators are not specifically prohibited in most of the Section 2.7 Exercises, the clear intent of Exercises 1—48 is that they not be done with graphing calculators. Students should be able to make the connection between the geometric behavior and the algebraic expressions without actually seeing the graphs. Top
Section 2.8 Solving Inequalities in One Variable
Objectives
Students will be able to solve inequalities involving polynomials and rational functions, both algebraically and graphically. They will be able to model real-world problems with such inequalities and solve them.
Key Ideas
Rational inequality
Sign chart
Teaching Tips
This section is more important than it looks, as creating sign graphs for functions is a skill required in several contexts in a calculus course. Students might be used to "plugging in" numbers to determine the sign of a function on an interval, but we feel that the method illustrated in this section is better for several reasons. First, it is a waste of time to compute an actual value when all that is needed is its sign, and second, analyzing sign changes at zeros reinforces the useful notion that a polynomial graph "behaves" near a zero like a monomial graph behaves near x = 0. For example, the graph of
behaves near x = -1 like the parabola behaves near 0 (so there is no sign change there), while it behaves near x = 2 like the cubic behaves close to 0 (so there is a sign change there).
Technology Tips
Students often forget how simple it can be to solve inequalities algebraically. An inequality like
used to be worthy of being a bonus problem on a mathematics competition. Such inequalities can be solved today at a glance with a graphing calculator. |
Description:
This online course includes elements from an undergraduate seminar on mathematical problem solving. The material will help students develop their mathematical and problem solving skills. A few topics that are covered include probability, generating mathematical functions and polynomials. Course materials include student assignments and solutions. MIT presents OpenCourseWare as free educational material online. No registration or enrollment is required to use the materials. |
M-MODEL8 is a full simulation of traditional engineering mechanics homework solutions including free-body diagram...
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M-MODEL8 is a full simulation of traditional engineering mechanics homework solutions including free-body diagram construction, variable listing and mathematical modelling. It is a free-form solution unlike other online homework systems that are linear processes based upon multi-choice, short answer, pair matching and etc. responses. M-MODEL8 focusses upon model building and leaves equation solving and answer production, at the discretion of the instructor, to internal equation solvers. An intelligent tutor, hints/tips, helps, grading and error checker systems are always available to students to provide instant feedback, coaching, motivation, reflection and intellectual development. Instructors may use the included authoring tools to modify the provided problems or create their own problems.
Animation software for an introductory Dynamics course has been developed. This interactive software is unique because each...
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In the mechanics of materials course, students are challenged to develop problem-solving skills necessary for the design of...
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In the mechanics of materials course, students are challenged to develop problem-solving skills necessary for the design of machines and structures. MDSolids is multi-faceted software that offers students numerical, descriptive, and visual results and details that illustrate and explain many types of problems involving stress and strain, axial members, beams, columns, torsion members, truss analysis, and section properties calculations. MDSolids is a flexible and versatile tool that helps the student with the specific problem that he or she is interested in rather than compelling the student to consider a problem that is posed by the software. MDSolids' graphical user interface makes the software visually appealing, easy-to-use, and very intuitive, so that students can focus on the problem-solving concepts rather than on the operation of the software. Named Premier Courseware of 1998. Requires Windows 95/98 or Windows NT 4.0. Requires 800 x 600 monitor resolution.Premier Award WinnerTUES NSF Projects - Transforming Undergraduate Education in STEMThis is a free textbook offered by BookBoon.'A First Course on Aerodynamics is designed to introduce the basics of...
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This is a free textbook offered by BookBoon.'A First Course on Aerodynamics is designed to introduce the basics of aerodynamics to the unfamiliar reader. This text avoids lengthy and complicated derivations, focusing on primary equations and fundamental concepts. Detailed figures and explanations of important mathematical equations are interspersed throughout the text. This e-book can be downloaded free of charge.The field of aerodynamics studies the motion of air around an object, such as an aircraft. After introducing fundamental concepts such as fluid flow, Thin Airfoil Theory, and Finite Wing Theory, A First Course on Aerodynamics presents the fundamentals of three key topics: Inviscid Compressible Flow, Viscous Flow, and wind tunnels. Important subtopics include one dimensional flow, quasi one dimensional flow, oblique shocks and expansion waves, boundary layer, and low speed and supersonic speed wind tunnels.Following each chapter are multiple choice questions, designed to help the reader put theoretical concepts into practice and identify equations that are vital to the continued study of aerodynamics. A list of references for further reading is included at the end of the text.'
This is a free textbook offered by BookBoon.'The level of knowledge content given in this book is designed for the students...
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This is a free textbook offered by BookBoon.'The level of knowledge content given in this book is designed for the students who have completed elementary mechanics of solids for stresses and strains associated with various geometries including simple trusses, beams, shafts, columns, etc. At the successful completion of understanding the content, the students will be able to reach a stage where they can do self-directed learning at any further advanced level in the area of mechanics of solids. The emphasis is given on the fundamental concepts for students to quickly follow through for an advanced level if required in the future. Fracture mechanics is included in this book with necessary preliminary steps for those who might have had difficulties with the subject in the past.'
This is a free textbook offered by BookBoon.'This book is written on the base of a lecture course taught by the author at the...
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This is a free textbook offered by BookBoon.'This book is written on the base of a lecture course taught by the author at the Faculty of Mechanical Engineering and Marine Technology at the Rostock University in Germany. The course contains fourteen lectures which include main principles of ship manoeuvrability. Experimental, theoretical and numerical methods used in the ship theory are presented in a clear and simple form. Each chapter is supplied with exercises which can be solved either analytically or using software provided by the author. An optional chapter is devoted to wing in ground effect dynamics. The only prerequisite for the course is the knowledge of general fluid dynamics.'
This is a free textbook offered by BookBoon.'In this book on Natural (or, Free) convection, many problems of practical...
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This is a free textbook offered by BookBoon.'In this book on Natural (or, Free) convection, many problems of practical interest are solved using Mathcad, Engineering Equation Solver (EES) and EXCEL.As done in other books in this series, viz. "Software Solutions to Problems on Heat Transfer", much emphasis is given on the use of these software to conduct parametric analysis and present graphical representation of results.In 'Natural or free convection', fluid movement is caused because of density differences in the fluid due to temperature differences, under the influence of gravity. Obviously, as compared to Forced convection, the heat transfer coefficient is lower in the case of Natural convection.Still, Natural convection is one of the important modes of heat transfer used in practice since there are no moving parts and as a result, there is an increased reliability.We shall solve problems of Natural convection involving following geometries: Vertical plates and cylinders, horizontal plates, cylinders and spheres, different types of enclosed spaces, rotating cylinders, disks and spheres. We will also consider important problems of Natural convection from finned surfaces, and cases of combined Natural and Forced convection.'
This is a free textbook offered by BookBoon.'A good knowledge of Fluid mechanics is essential for Chemical, Mechanical and...
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This is a free textbook offered by BookBoon.'A good knowledge of Fluid mechanics is essential for Chemical, Mechanical and Civil engineers. As a result it is taught at a very early stage in degree courses on those disciplines.A First Course in Fluid Mechanics covers the basics of the engineering fluid mechanics without delving into deeper more mathematical concepts.Building from most basic concepts such as physical properties of fluids, it covers the topics in fluid statics and dynamics. Hydrostatic pressure, buoyancy and forces on immersed bodies are discussed under fluid statics.Under fluid dynamics, Bernoulli's principle is introduced. Furthermore, the nature of fluid flows is discussed in engineering context. Laminar and turbulent flows in pipes are explained in detail.Finally hydraulic design is discussed paying attention to pump capacity calculations.This textbook is levelled at first year undergraduate students, Radiation |
Algebra
Do your students attempt to memorize facts and mimic examples to make it through algebra? James Stewart, author of the worldwide, best-selling ...Show synopsisDo your students attempt to memorize facts and mimic examples to make it through algebra? James Stewart, author of the worldwide, best-selling calculus texts, saw this scenario time and again in his classes. So, along with longtime coauthors Lothar Redlin and Saleem Watson, he wrote "College Algebra, 6/e, International Edition" specifically to help students learn to think mathematically and to develop genuine problem-solving skills. Comprehensive and evenly-paced, the text has helped hundreds of thousands of students. Incorporating technology, real-world applications, and additional useful pedagogy, the sixth edition promises to help more students than ever build conceptual understanding and a core of fundamental skills.Hide synopsis
Description:Good. Hardcover. May include moderately worn cover, writing,...Good. Hardcover. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9781111990169-4Fine. Hardcover. Almost new condition. SKU: 9781111990169-2-0-3...Fine. Hardcover. Almost new condition. SKU: 9781111990169-2 |
ALEX Lesson Plans
Title: Family Ties: Parabolas
Description:
This 18: Solve quadratic equations in one variable. [A-REI4] [MA2013] AL1 (9-12) 21: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. [A-REI72 (9-12) 6: (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. [N-CN9] [MA2013] AL2 (9-12) 32: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9] [MA2013] ALC (9-12) 6: Use the extreme value of a given quadratic function to solve applied problems. (Alabama) [MA2013] ALT (9-12) 4: Solve quadratic equations with real coefficients that have complex solutions. [N-CN7] [MA2013] ALT (9-12) 6: (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. [N-CN9 AM1 (9-12) 11: (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Understand the importance of using complex numbers in graphing functions on the Cartesian or complex plane. [N-CN9] (Alabama)
Subject: Mathematics (9 - 12), or Technology Education (9 - 12) Title: Family Ties: Parabolas Description: This
Title: 'There's Gold in Them There Hills'
Description:
StudentsStandard(s): [S1] (6) 10: Describe components of the universe and their relationships to each other, including stars, planets and their moons, solar systems, and galaxies. [S1] (6) 10: Describe components of the universe and their relationships to each other, including stars, planets and their moons, solar systems, and galaxies (9 - 12), or Science (6) Title: 'There's Gold in Them There Hills' Description: Students
Title: Exponential Growth and Decay
Description:
This 30: Graph functions expressed symbolically, and show key features of the graph, by hand in ALC (9-12) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [MA2013] ALT (9-12) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE 25: Compare effects of parameter changes on graphs of transcendental functions. (Alabama)
Subject: Mathematics (9 - 12) Title: Exponential Growth and Decay Description: This
Title: Density
Description:
DStandard(s): [S1] (8) 1: Identify steps within the scientific process. [S1] CHE (9-12) 1: Differentiate among pure substances, mixtures, elements, and compounds. [S1] ENV (9-12) 1: Identify the influence of human population, technology, and cultural and industrial changes on the environment. 15: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [A-CED4] [MA2013] AL1 (9-12) 17: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [A-REI ALC (9-12) 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama)
Subject: Mathematics (9 - 12), or Science (8 - 12) Title: Density Description: D
Title: Math is Functional
Description:
This 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama) AL1 (9-12) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [F-LE1] [MA2013] AL1 (9-12) 30: Calculate and interpret 14: Use digital tools to defend solutions to authentic problems. [MA2013] AL1 (9-12) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2]
Subject: Mathematics (9 - 12), or Technology Education (9 - 12) Title: Math is Functional Description: This
Title: You Mean ANYTHING To The Zero Power Is One?
Description:
This lesson is a technology-based project to reinforce concepts related to the Exponential Function. It can be used in conjunction with any textbook practice set. Construction of computer models of several Exponential Functions will promote meaningful learning rather than memorization ALC (9-12) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay 2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. [N-RN2] [MA2013] AL1 (9-12) 13 9: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* [A-SSE3]
Subject: Mathematics (9 - 12), or Technology Education (9 - 12) Title: You Mean ANYTHING To The Zero Power Is One? Description: This lesson is a technology-based project to reinforce concepts related to the Exponential Function. It can be used in conjunction with any textbook practice set. Construction of computer models of several Exponential Functions will promote meaningful learning rather than memorization.
Title: Creating a Payroll Spreadsheet
Description:
Spreadsheet software allows you to calculate numbers arranged in rows and columns for specific financial tasks. This activity allows students to create an "Employee Work/Pay Schedule" spreadsheet to reinforce spreadsheet skills. Students will practice spreadsheet skills by entering data, creating formulas, and using formatting commands.
Standard(s):TC2] CA2 (9-12) 5: Utilize advanced features of spreadsheet software, including creating charts and graphs,
sorting and filtering data, creating formulas, and applying functions.
Title: Swimming Pool Math
Description:
Students will use a swimming pool example to practice finding perimeter and area of different rectangles.
Standard(s): ALC (9-12) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama) ALC (9-12) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems 5: Define appropriate quantities for the purpose of descriptive modeling. [N-Q28) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems. [8-G9]
Thinkfinity Lesson Plans
Title: Finding Our Top Speed
Description:
This
Standard(s): [S1] (6) 11: Describe units used to measure distance in space, including astronomical units and light years. [MA2013] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5 Finding Our Top Speed Description: This Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Title: Apple Pie Recording Chart
Description:
This reproducible activity sheet, from an Illuminations lesson, prompts students to use strings and rulers to measure and record the distance around several round objects, as well as the distance across the middle of those objects.
Standard(s): [MA2013] (6) 1: Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6-RP1 20: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. [7-SP Apple Pie Recording Chart Description: This reproducible activity sheet, from an Illuminations lesson, prompts students to use strings and rulers to measure and record the distance around several round objects, as well as the distance across the middle of those objects. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Title: Building Bridges
Description:
In
Subject: Mathematics,Professional Development Title: Building Bridges Description: In Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Title: Gallery Walk
Description:
In Gallery Walk Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Graphing What
Description:
This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs.
Standard(s): [MA2013] (6) 17: Use variables to represent numbers, and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. [6-EE6] [MA2013] (6) 20: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. [6-EE9 Graphing WhatTitle: Least Squares Regression
Description:
In seen Least Squares Regression Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Think of a Graph
Description:
This reproducible transparency, from an Illuminations lesson, asks students to sketch a graph in which the side length of a square is graphed on the horizontal axis and the perimeter of the square is graphed on the vertical axis model Think of a Graph Description: This reproducible transparency, from an Illuminations lesson, asks students to sketch a graph in which the side length of a square is graphed on the horizontal axis and the perimeter of the square is graphed on the vertical axis. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Egg Launch Contest
Description:
Students 33: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9]
Subject: Mathematics Title: Egg Launch Contest Description: Students Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Bathtub Water Levels
Description:
In relate the slope and y-intercept of the least squares regression line to the real-life data. They also interpret the correlation coefficient of the least squares regression line. This lesson incorporates an interactive regression line applet Bathtub Water Levels Description: In relate the slope and y-intercept of the least squares regression line to the real-life data. They also interpret the correlation coefficient of the least squares regression line. This lesson incorporates an interactive regression line applet. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: The Effects of Outliers
Description:
This
Subject: Mathematics Title: The Effects of Outliers Description: This Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Exploring Linear Data
Description:
In this lesson, from Illuminations, students model linear data in a variety of settings. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.
Standard(s): [S1] (8) 1: Identify steps within the scientific process. [MA2013] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5 variables Exploring Linear Data Description: In this lesson, from Illuminations, students model linear data in a variety of settings. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
Title: Traveling Distances
Description:
In linear Traveling Distances Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Do You Hear What I Hear?
Description:
In this lesson, from Illuminations, students explore the dynamics of a sound wave. Students use an interactive Java applet to view the effects of changing the initial string displacement and the initial tension.
Standard(s): [S1] (8) 12: Classify waves as mechanical or electromagnetic. 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [S-ID6 31: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F-IF8 ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1 ALT (9-12) 40: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* [F-TF5] [MA2013] PRE (9-12) 26: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses. (Alabama)
Subject: Mathematics,Science Title: Do You Hear What I Hear? Description: In this lesson, from Illuminations, students explore the dynamics of a sound wave. Students use an interactive Java applet to view the effects of changing the initial string displacement and the initial tension. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Automobile Mileage: Comparing and Contrasting
Description:
In measurement Automobile Mileage: Comparing and Contrasting Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Graph Chart
Description:
Using Title: Graph Chart Description: Using Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Analyzing the Data
Description:
In
Standard(s):S1] PHY (9-12) 7: Describe properties of reflection, refraction, and diffraction.,Science Title: Analyzing the Data Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: How Should I Move?
Description:
In Title: How Should I Move? Description: In strategiesTitle: Exact Ratio
Description:
This reproducible activity sheet, from an Illuminations lesson, features a series of questions pertaining to exact ratios and geometric sequences. In the lesson, students measure lengths on stringed musical instruments and discuss how the placement of frets on a fretted instrument is determined by a geometric sequence.
Standard(s): [MA2013] AL1 (9-12) 2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. [N-RN Mathematics Title: Exact Ratio Description: This reproducible activity sheet, from an Illuminations lesson, features a series of questions pertaining to exact ratios and geometric sequences. In the lesson, students measure lengths on stringed musical instruments and discuss how the placement of frets on a fretted instrument is determined by a geometric sequence. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Web Resources
Lesson Plans
Title: Hanging Chains
Description:Hanging Chains Title: Algebra vs. Cockroaches
Description:
In this game the student has to find the y-intercept to kill the roachesLearning Activities
Title: Egg Launch Contest
Description:Egg Launch Contest
Thinkfinity Interactive Games
Title: Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body: Modeling the Situation
Description:
This Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body: Modeling the Situation Description: This 9,10,11,12
Thinkfinity Learning Activities
Title: Tube Viewer Simulation
Description:
This student interactive, from Illuminations, simulates the effect of viewing an image through a tube. As students move the location of the person or change the length of the tube, the image and measurements also change Tube Viewer Simulation Description: This student interactive, from Illuminations, simulates the effect of viewing an image through a tube. As students move the location of the person or change the length of the tube, the image and measurements also change. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Flowing Through Mathematics
Description:
This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time GEO (9-12) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [G-GMD3 Flowing Through Mathematics Description: This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 |
Essential Understanding
Move beyond the mathematics you expect your students to learn. Students who fail to get a solid grounding in pivotal concepts struggle in subsequent work in mathematics and related disciplines. By bringing deeper understanding to your teaching, you can help students who don't get it the first time by presenting mathematics in multiple ways.
The Essential Understanding series addresses topics crucial to student development but often difficult to teach. Each book in the series (sixteen titles planned) gives an overview of the topic, highlights the differences between what teachers and students need to know, examines the big ideas and related essential understandings, reconsiders the ideas presented in light of connections with other mathematical ideas, and includes questions for readers' reflection.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research. |
Further Maths VCE Examination 2 Units 3 and 4 by null. Further Mathematics Exam 2 is a comprehensive practice exam book for VCE Further Mathematics Units 3 4. Features include: No teacher preparation ...
Common Core Eureka Math for Grade 4, Module 5 Created by teachers, for teachers, the research-based curriculum in this series presents a comprehensive, coherent sequence of thematic units for teaching...
StudyOn VCE Further Mathematics Units 3&4&Booklet studyON ; the next generation in online study, revision and exam practice! studyON is an interactive and highly visual online tool designed to help ma... |
Journal of Online Mathematics and its Applications offers articles, learning modules, "mathlets" (single-purpose learning tools), reviews of online resources, and a developers' area. Search contents of the journal by type of resource (e.g., article), by subject (e.g., number concepts, data presentation, plane geometry), or both. The journal makes extensive use of graphics, animations, video clips, and other media. Articles and other materials are peer reviewed.
Classroom Capsules is on-line version of part of The College Mathematics Journal. The purpose of the capsules is to make easily available, by web search, short mathematical articles, which can give a student new mathematical insights, and instructors effective teaching strategies. The articles might represent a nice application, an unusual point of view or example, or they might give the instructor a non-standard way of presenting the topic in class.
MathDL Mathematical Communication is a collection of instructional strategies, materials, and references for having students write and speak about mathematics, whether for the purpose of learning mathematics or learning to communicate as mathematicians.
Course Communities in Undergraduate Mathematics (or Course Communities for short) contains a new collection of online resource recommendations. So far we have listed over 340 resources: PDF files, applets, videos, and other formats.
The following types of materials will appear in Loci:
Articles
Modules: innovative, class-tested, web-based learning materials that can be used for guided explorations of particular topics in mathematics
Should math educations be separated into the two tracks? Math education is either practical or abstract. One is useful in everyday life and the other is essential for science, engineering or math investigation.
Discussion Question(s)
1.
How can we communicate about math to reduce math anxiety?
2.
How do we learn to communicate math effectively, in writing or orally? |
Jun 27, 2008
The National Institute of Standards and Technology (NIST) has released a five-chapter preview of the much-anticipated online Digital Library of Mathematical Functions (DLMF). In development for over a decade, the DLMF is designed to be a modern successor to the 1964 "Handbook of Mathematical Functions," a reference work that is the most widely distributed NIST publication (with over a million copies in print) and one of the most cited works in the mathematical literature (still receiving over 1,600 yearly citations in the research literature). The preview of the new DLMF is a fully functional beta-level release of five of the 36 chapters.
The DLMF is designed to be the definitive reference work on the special functions of applied mathematics. Special functions are "special" because they occur very frequently in mathematical modeling of physical phenomena, from atomic physics to optics and water waves. These functions have also found applications in many other areas; for example, cryptography and signal analysis. The DLMF provides basic information needed to use these functions in practice, such as their precise definitions, alternate ways to represent them mathematically, illustrations of how the functions behave with extreme values and relationships between functions.
The DLMF provides various visual aids to provide qualitative information on the behavior of mathematical functions, including interactive Web-based tools for rotating and zooming in on three-dimensional representations. These 3-D visualizations can be explored with free browsers and plugins designed to work in virtual reality markup language (VRML). Mouse over any mathematical function, and the DLMF provides a description of what it is; click on it, and the DLMF goes to an entire page on the function. The DLMF adheres to a high standard for handbooks by providing references to or hints for the proofs of all mathematical statements. It also provides advice on methods for computing mathematical functions, as well as pointers to available software.
The complete DLMF, with 31 additional chapters providing information on mathematical functions from Airy to Zeta, is expected to be released in early 2009. With over 9,000 equations and more than 500 figures, it will have about twice the amount of technical material of the 1964 Handbook. An approximately 1,000-page print edition that covers all of the mathematical information available online also will be published. The DLMF, which is being compiled and extensively edited at NIST, received initial seed money from the National Science Foundation and resulted from contributions of more than 50 subject-area experts worldwide. The NIST editors for the DLMF are Frank W. J. Olver, Daniel W. Lozier, Ronald F. Boisvert and Charles W. Clark.
Related Stories
The National Institute of Standards and Technology has released the Digital Library of Mathematical Functions (DLMF) and its printed companion, the NIST Handbook of Mathematical Functions, the much-anticipated successors |
Algebra and Trigonometry - 3rd edition
Summary: These authors have created a book to really help students visualize mathematics for better comprehension. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition, the authors have added a variety of new tools to help students better use the book for maximum effectiveness to not only pass the course, but truly 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 set45 +$3.99 s/h
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text book recycle ny malone, NY
2007-02-08 Hardcover |
Staten Island Statistics took a mathematical methods course in the physics department which included substantial material on ordinary differential equations. Additionally, I was exposed to a lot of partial differential equations material in several other physics classes (such as Electricity and Magnetism and Thermal P... |
site contains reference material in Matrix Algebra. Topics covered include matrix operations, linear equations,...
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This site contains reference material in Matrix Algebra. Topics covered include matrix operations, linear equations, determinants, eigenvectors and eigenvalues. S.O.S. Mathematics--Matrix Algebra is a part of an independent, commercial site that offers straightforward technical assistance primarily to high school and college students.
This video from the Harvard Business collection on YouTube is an interview with Cisco CEO John Chambers. In the video he...
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This video from the Harvard Business collection on YouTube is an interview with Cisco CEO John Chambers. In the video he explains how abandoning command-and-control leadership has enabled the company to innovate more quickly, using collaboration and teamwork. The video lasts about 6 1/2 minutes. This would be good for generating a class discussion about leadership, collaboration or teamwork.
This is a TED video that lasts less than 15 minutes. 'Why do teenagers seem so much more impulsive, so much less self-aware...
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This is a TED video that lasts less than 15 minutes. 'Why do teenagers seem so much more impulsive, so much less self-aware than grown-ups? Cognitive neuroscientist Sarah-Jayne Blakemore compares the prefrontal cortex in adolescents to that of adults, to show us how typically "teenage" behavior is caused by the growing and developing brain.'Rocked internally with hormones, outwardly with social pressures, you sometimes wondered what was going on in your head. So does Sarah-Jayne Blakemore. And what she and others in her field are finding is: The adolescent brain really is different.New brain imaging research and clever experiments are revealing how the cortex develops -- the executive part of the brain that handles things like planning, self-awareness, analysis of consequences and behavioral choices. It turns out that these regions develop more slowly during adolescence, and in fascinating ways that relate to risk-taking, peer pressure and learning.Which leads to a bigger question: How can we better target education to speak to teenagers' growing, changing brains?' |
Archive for the 'AlgebraWhen I was in the classroom, I used to tell students that if two students had exactly the same answers to a GCSE paper, some right, some wrong, then the one who showed their working out would get the better marks. I used to ban correction fluid, not because they would sniff it, but because [...]
A question asked by pupils all the time is "Why do we learn Algebra, where is it used in everyday life?" or "Why do we use x in Algebra as the unknown?" As educators we all have our own responses and it would be great to collect together examples all in one place so they [...] |
Featured Research
from universities, journals, and other organizations
The aftermath of calculator use in college classrooms
Date:
November 12, 2012
Source:
University of Pittsburgh
Summary:
Math instructors promoting calculator usage in college classrooms may want to rethink their teaching strategies, experts say. They have proposed the need for further research regarding calculators' role in the classroom after conducting a limited study with undergraduate engineering students.
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Math instructors promoting calculator usage in college classrooms may want to rethink their teaching strategies, says Samuel King, postdoctoral student in the University of Pittsburgh's Learning Research & Development Center. King has proposed the need for further research regarding calculators' role in the classroom after conducting a limited study with undergraduate engineering students published in the British Journal of Educational Technology.
"We really can't assume that calculators are helping students," said King. "The goal is to understand the core concepts during the lecture. What we found is that use of calculators isn't necessarily helping in that regard."
Together with Carol Robinson, coauthor and director of the Mathematics Education Centre at Loughborough University in England, King examined whether the inherent characteristics of the mathematics questions presented to students facilitated a deep or surface approach to learning. Using a limited sample size, they interviewed 10 second-year undergraduate students enrolled in a competitive engineering program. The students were given a number of mathematical questions related to sine waves -- a mathematical function that describes a smooth repetitive oscillation -- and were allowed to use calculators to answer them. More than half of the students adopted the option of using the calculators to solve the problem.
"Instead of being able to accurately represent or visualize a sine wave, these students adopted a trial-and-error method by entering values into a calculator to determine which of the four answers provided was correct," said King. "It was apparent that the students who adopted this approach had limited understanding of the concept, as none of them attempted to sketch the sine wave after they worked out one or two values."
After completing the problems, the students were interviewed about their process. A student who had used a calculator noted that she struggled with the answer because she couldn't remember the "rules" regarding sine and it was "easier" to use a calculator. In contrast, a student who did not use a calculator was asked why someone might have a problem answering this question. The student said he didn't see a reason for a problem. However, he noted that one may have trouble visualizing a sine wave if he/she is told not to use a calculator.
"The limited evidence we collected about the largely procedural use of calculators as a substitute for the mathematical thinking presented indicates that there might be a need to rethink how and when calculators may be used in classes -- especially at the undergraduate level," said King. "Are these tools really helping to prepare students or are the students using the tools as a way to bypass information that is difficult to understand? Our evidence suggests the latter, and we encourage more research be done in this area."
King also suggests that relevant research should be done investigating the correlation between how and why students use calculators to evaluate the types of learning approaches that students adopt toward problem solving 5, 2013 — Researchers have developed a classroom design that gives instructors increased flexibility in how to teach their courses and improves accessibility for students, while slashing administrative ... full story
May 21, 2012 — Discipline-based education research has generated insights that could help improve undergraduate education in science and engineering, but these findings have not yet prompted widespread changes inScienceDaily features breaking news and videos about the latest discoveries in health, technology, the environment, and more -- from major news services and leading universities, scientific journals, and research organizations. |
Conic Sections: Draw It, Write It, Do It Barbara Leapard, Joanne Caniglia A challenging activity for integrating mathematics and art using conic sections. Students create a drawing that is formed by the graphs of linear equations and conic sections and record the equations with domain and range for each. The art work incorporates graphing calculators and pencil and pencil and paper graphs.
Helping Students Connect Functions and Their Representations Deborah Moore-Russo, John Golzy A teaching method to help promote deeper understanding of both the graphical and algebraic representations of linear and quadratic functions. The authors ask students to find the graphical representation of the sum and product of given functions Various representations lead to a deeper understanding of the connections between the equation and its graph. Graphing calculators are utilized to enhance student understanding.
Interactive Geometry Software in the B.C. (Before Computers) Era Heather Whittaker, Iris Johnson The use of 3x5 cards to explore geometric relationships through the first three van Hiele levels of geometric reasoning. Students engage in reasoning and proof as they explore concepts related to parallel lines and quadrilaterals.
Sharing Teaching Ideas: Say What You Mean and Mean What You Say Julianna Csongor, Carolyn Craig A fun, proven classroom activity, designed to improve students' communication skills. Students write descriptions of geometric sketches and classmates use these directions to create the given image. Writing and listening skills are enhanced.
Tapping into Trapezoids Jeffrey Wanko The use of trapezoids to explore a number of mathematical concepts, including similarity, representation, and the Pythagorean theorem. Preservice teachers develop hypotheses about isosceles trapezoids which are investigated. Tiling with pattern blocks and the development of the formula for area are also examined.
Good Will Hunting Meets Graphing Calculators and CAS William O'Donnell, Richard Gibbs A solution, using CAS, to a graph theory problem that was presented in the movie Good Will Hunting. The author employs matrices, matrix multiplication and basic graph theory to solve the four part problem.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research. |
Exponents are everywhere in Algebra. You just can't get very far without understanding what they are and how they work. When you watch this video you will learn exactly that.
Exponents are wonderful shortcuts and they speak a language of their own. Always begin at the beginning, at the most basic level. You will have a good foundation that way and you will build your confidence in mathematics.
Download the Guide and along with me as you watch the video. Pat yourself on the back every time you are correct. I know that will be most of the time. :) If it isn't, ask me to slow down or repeat something for you by stopping the video and replaying what you need to hear and see again.
About this Author
Welcome! I'm so glad you are here! Math help is here for you when you need it.
I believe that using these Algebra and Geometry videos will help you understand the basics of Algebra and Geometry.
Some students try very hard and still struggle to pass math. They start off strong but things quickly begin to fall apart. That happens as soon as the student becomes lost. Teenagers who find themselves in this position often let it "get away from them" before they seek help. Because Math is always a class of stepping stones, it rarely gets better without help.
I urge you to seek help from your child's teacher first. Always. These Algebra and Geometry videos can help too. You can watch... |
For Teachers
Bootstrap is aligned to state and Common-Core standards for algebra, allowing teachers to integrate 20-30 hours of material within existing class time. Math teachers across the country have used Bootstrap as an algebra introduction (grades 6-8), enrichment (grades 9-10), or remediaton (grades 11-12).
When used as a precursor to the Program By Design curriculum, Bootstrap makes for an excellent "first-unit" to a high school or college level programming course. Students in Bootstrap learn fundamentals like unit-testing and data-modeling, which they can apply to any language you'd like to teach — it's even being used to build up to the AP CS Exam! |
About This Book:
Title: Algebra and Trigonometry
Publisher Notes
This best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, providing students with a solid foundation in the principles of mathematical thinking. Comprehensive and evenly paced, the book provides complete coverage of the function concept, and integrates a significant amount of graphing calculator material to help students develop insight into mathematical ideas. The authors' attention to detail and clarity, the same as found in James Stewart's market-leading Calculus book, is what makes this book the market leader.
Book Details Summary: The title of this book is Algebra and Trigonometry and it was written by James Stewart, Saleem Watson, Lothar Redlin. This particular 3rd edition is in a Hardcover format. This books publish date is February 18, 2011 and it has a suggested retail price of $284.95. It was published by Brooks/Cole Pub Co and has a total of 919 pages in the book. The 10 digit ISBN is 0840068131 and the 13 digit ISBN is 9780840068132. To buy this book at the lowest price, Click Here. |
After taking the Praxis and many other standardized tests, I have learned how I learn and test, and pass and achieve my goal of being an effective teacher. Algebra 2 is the continuum of Algebra 1. That is, Algebra 2 uses the same operations on advanced algebraic operations, introduce square roots and simplifying and perform the same operations as equations |
0471849022
9780471849025
Discrete Mathematics With Algorithms:This first-year course in discrete mathematics requires no calculus or computer programming experience. The approach stresses finding efficient algorithms, rather than existential results. Provides an introduction to constructing proofs (especially by induction), and an introduction to algorithmic problem-solving. All algorithms are presented in English, in a format compatible with the Pascal programming language. Contains many exercises, with answers at the back of the book (detailed solutions being supplied for difficult problems).
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Rent Discrete Mathematics With Algorithms 1st edition today, or search our site for Michael O. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Wiley. |
Mathematics
Materials on mathematics may be found in the QA call number range or by searching
the library catalog. Specific divisions are listed below.
QA1-43
General Works
QA71-90
Instruments and Machines
QA150-172
Algebra
QA299-433
Analysis
QA440-699
Geometry
REFERENCE WORKS
The Penguin Dictionary of Mathematics
Electronic Book
The Biographical Dictionary of Scientists
Ref Q141.B526
CRC Handbook of Mathematical Sciences
Ref QA47.H324
CRC Standard Mathematical Tables
Ref QA45.M315
Handbook of Mathematical Functions with Formulas, Graphs,
and Mathematical Tables
Ref QA3.U5
Machinery's Mathematical Tables
Ref QA47.M17
McGraw Hill Encyclopedia of Science & Technology
Ref Q121.M3
DATABASES
You may access the following databases from any computer workstation on campus. For off-campus access, please follow the instructions found on the library's homepage under "Off-Campus Access Instructions" or click here for an online tutorial.
Science in Context features authoritative information for assignments and projects in the sciences including technology
and mathematics.
S.O.S. Math - Mathematical Tables and Formulasis a free resource for math review from Algebra to Differential Equations for college students and adult learners. One can browse more that 2,500 math pages of short and easy-to-understand explanations.
If you have questions regarding any of these resources or need assistance finding
additional information, please Ask a Librarian. |
Algebra 2
Description
Help your student discover the logic, order, beauty, and practicality of algebra. Throughout the course, students are encouraged to use their reasoning ability as they work with the axioms, rules, and principles of algebra. Concepts are developed and mastered through an abundance of worked examples and exercises, with an emphasis on word problems that relate to the physical world. Reviews at the end of each unit measure progress, and special sections challenge the mathematically talented student. This text calls for a scientific calculator that has the trigonometric functions, statistics, powers, and roots. Designed to be used in grade 10 and is 362 |
Survey of Mathematics with Applications, A: Expanded Edition
edition: 7th
Author(s): Angel, Allen R.; Abbott, Christine D.; Runde, Dennis C.
ISBN: 9780321205650 |
Understand the concept of functions
verbally, numerically, graphically and symbolically.
Relate and apply algebraic
relationships to career applications.
Interpret and analyze data from
mathematical models in real world applications.
Use appropriate technology to
enhance mathematical thinking and judge the reasonableness of their
results.
Employ theories of functions and
tools of mathematics to obtain a solution.
Although slightly modified,
developmental mathematics course outcomes were originally taken from Dona
Ana Community College's state level competencies, and credit bearing course
outcomes were based on AMATYC standards, found in "Crossroads in
Mathematics," from the AMATYC website. |
17644849 / ISBN-13: 9780817644840
A Beginner's Guide to Graph Theory
This beginner's textbook is intended for a first course in graph theory. It strikes a balance between a theoretical and practical approach, ...Show synopsisThis beginner's textbook is intended for a first course in graph theory. It strikes a balance between a theoretical and practical approach, consisting of carefully chosen topics to develop graph-theoretic reasoning for a mixed audience.Hide synopsis |
AS Level Use of Maths
AS Level Use of Maths is designed for students who are NOT doing A Level Maths but are doing other A Level courses that have a mathematical element. These courses are principally Physics, Chemistry, Computing, Geography, Psychology, Business Studies and Economics. |
Geometry, Perspective Drawing, and Mechanisms
Description: The aim of this book is to examine the geometry of our world and, by blending theory with a variety of every-day examples, to stimulate the imagination of the readers and develop their geometric intuition. It tries to recapture the excitement thatMore...
The aim of this book is to examine the geometry of our world and, by blending theory with a variety of every-day examples, to stimulate the imagination of the readers and develop their geometric intuition. It tries to recapture the excitement that surrounded geometry during the Renaissance as the development of perspective drawing gathered pace, or more recently as engineers sought to show that all the world was a machine. The same excitement is here still, as enquiring minds today puzzle over a random-dot stereogram or the interpretation of an image painstakingly transmitted from Jupiter.The book will give a solid foundation for a variety of undergraduate courses, to provide a basis for a geometric component of graduate teacher training, and to provide background for those who work in computer graphics and scene analysis. It begins with a self-contained development of the geometry of extended Euclidean space. This framework is then used to systematically clarify and develop the art of perspective drawing and its converse discipline of scene analysis and to analyze the behavior of bar-and-joint mechanisms and hinged-panel mechanisms. Spherical polyhedra are introduced and scene analysis is applied to drawings of these and associated objects. The book concludes by showing how a natural relaxation of the axioms developed in the early chapters leads to the concept of a matroid and briefly examines some of the attractive properties of these natural structures |
Marvin L. Bittinger
Biography
KEY MESSAGE: This all new edition of Trigonometry, derived from the author's popular Algebra & Trigonometry, Third Edition, helps students visualize mathematics for better comprehension. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition, a variety of new tools help students better use the book for maximum effectiveness to not only pass the course, but truly understand the material. Trigonometry, Second Edition can be used for a brief Trigonometry course, or can be bundled with any Pearson Mathematics title. KEY TOPICS: The Trigonometric Functions; Trigonometric Identities, Inverse Functions, and Equations; Applications of Trigonometry MARKET: for all readers interested in Trigonometry. |
"Mathematics
– the unshaken Foundation of Sciences, and the plentiful Fountain of
advantage to human affairs."–
Isaac Barrow
Seeking
excellent teaching and learning practices in the study of mathematics
at Cuyamaca College, the members of the Mathematics Department have created
a philosophy to guide us in developing curriculum and implementing
effective teaching and learning methodologies. The Mathematics Department
Philosophy is an infusion of our individual values and beliefs about our
students and the nature and purpose of mathematics education.
We
understand that our students are multifaceted and approach the study of
mathematics from a broad spectrum of emotions, attitudes, backgrounds,
experience and needs. However, we believe that sound mathematics
curriculum coupled with consistent and effective teaching and learning
methodologies will enable every student to: apply critical thinking skills
in solving problems of everyday life; participate intelligently in civic
affairs; compete in the high-performance workplace; develop connections
among topics both within mathematics and between disciplines; and acquire
an appreciation for the beauty and intrinsic order of mathematics.
Specifically we believe that each student can be successful in learning
to: value mathematics; become confident in his or her own ability; become
a mathematical problem solver; communicate mathematically; and reason
mathematically. By offering a broad range and consistent continuum of
courses from basic mathematics to differential equations, we believe that
students are afforded better opportunities to experience success in
learning mathematics.
The
emphasis of the Mathematics program is to prepare students for transfer to
a four-year institution and/or for career preparation in a vocational or
professional field. In order to provide the best program for our students
and to meet the needs of our rapidly changing technological society, we
believe it is important to continually evaluate and if necessary revise
our curriculum and teaching methodologies. Additionally, we recognize that
mathematics provides fundamental problem solving skills applicable to
liberal arts, the sciences, engineering, and vocational programs, and we
believe that incorporating technology into the mathematics curriculum
allows students to study useful and relevant applications of mathematics
from a broad range of disciplines.
As
mathematics teachers, we understand the importance and relevance of our
responsibilities regarding student success and recognize that those
responsibilities extend beyond the classroom. We believe that our
excitement and passion for mathematics and mathematics education should be
imparted to our students in the classroom as well as the one-on-one
learning environment during office hours. Furthermore, we believe that we
have the added responsibility of inspiring all students to continue their
mathematics education and to seriously consider choosing a career
involving math, science, or engineering.Finally, we believe that excellent pedagogical practice
acknowledges the math anxiety that creates barriers to students success in
concept attainment and skill mastery.By creating a positive learning environment, building good rapport
with students, exercising patience when teaching, and employing multiple
teaching strategies, we believe we can alleviate our students' fear of
mathematics and promote student success. |
The History of the Calculus
The purpose of this essay is to trace the development of the concepts of the calculus from their first known appearance, through the formal invention of the method of the calculus in the second half of the seventeenth century, to our own day.
The purpose of this essay is to trace the development of the concepts of the calculus from their first known appearance, through the formal invention of the method of the calculus in the second half of the seventeenth century, to our own day. |
More About
This Textbook
Overview
This classic text presents problems of learning and teaching mathematics from both a psychological and mathematical perspective. The Psychology of Learning Mathematics, already translated into six languages (including Chinese and Japanese), has been revised for this American Edition to include the author's most recent findings on the formation of mathematical concepts, different kinds of imagery, interpersonal and emotional factors, and a new model of intelligence. The author contends that progress in the areas of learning and teaching mathematics can only be made when such factors as the abstract and hierarchical nature of mathematics, the relation to mathematical symbolism and the distinction between intelligent learning and rote memorization are taken into account and instituted in the classroom.
Related Subjects
Table of Contents
Contents: Part A:Introduction and Overview.The Formation of Mathematical Concepts. The Idea of a Schema. Intuitive and Reflective Intelligence. Symbols. Different Kinds of Imagery. Interpersonal and Emotional Factors. Part B:A New Model of Intelligence.From Theory into Action: Knowledge, Plans, and Skills. Type 1 Theories and Type 2 Theories: From Behaviorism to Constructivism. Mathematics as an Activity of Our Intelligence. Relational Understanding and Instrumental Understanding. Goals of Learning and Qualities of Understanding. Communicating Mathematics: Symbolic Understanding. Emotions and Survival in the Classroom. The Silent Music of Mathematics |
Real World Algebra
Book Description: Algebra is often taught abstractly with little or no emphasis on what algebra is or how it can be used to solve real problems. Just as English can be translated into other languages, word problems can be "translated" into the math language of algebra and easily solved. Real World Algebra explains this process in an easy to understand format using cartoons and drawings. This makes self-learning easy for both the student and any teacher who never did quite understand algebra. Includes chapters on algebra and money, algebra and geometry, algebra and physics, algebra and levers and many more. Designed for children in grades 4-9 with higher math ability and interest but could be used by older students and adults as well. Contains 22 chapters with instruction and problems at three levels of difficulty |
Mathematical biology is
a fascinating and fast growing area of
mathematics. It is an active research area of great potential using the
power of mathematics to study challenging biological problems. Students
can find many applications of mathematics in biology accessible even
with familiarity only with calculus. The workshop provides great
opportunities for the participants to learn more about mathematical
biology. A boat trip to the Louisiana swamps will allow participants
learn about plant and animal invasive species and experience the beauty
and adventure of mathematical biology.
The workshop is designed to intrigue and introduce college mathematics
teachers to the world of mathematical biology. There is no technical
background needed. However, a familiarity with difference and
differential equations will make your workshop experience more
productive and memorable. The primary goal of the workshop is to allow
the participants to engage in academic activities in the area of
mathematical biology, including teaching an undergraduate course and
pursuing and directing student research. Each day of the workshop
consists of a morning and an afternoon session. Lecturers will be given
primarily on the first and the third day of the workshop. The
second day is comprised of a problem session in the morning and an
exciting outdoor activity in the afternoon. During the last day, the
participants will explore interesting research projects with the aid of
computers. For more information, please visit the workshop webpage at |
Linear Systems and Optimization | Convex Optimization II
Course Content:
Resources
This page contains links to various interesting and useful sites that relate in
some way to convex optimization. It goes without saying that you'll
be periodically checking things using google and wikipedia. The wikipedia
entry on convex optimization (and related topics) could be improved
or extended.
1. Stephen
Boyd's research page. There's a lot of material there, and you
don't have to know every detail in every paper, but you should certainly
take an hour or more to browse through these papers. |
This site provides an extremely large encyclopedia-style collection of material related to mathematics at the college level...
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demonstrates real-world applications of math to all those students who say, "How will I ever use this?" You don't get much...
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demonstrates real-world applications of math to all those students who say, "How will I ever use this?" You don't get much more real world than solving the problems of dividing estates fairly, apportioning legislative seats, or cutting a cake in even pieces. Each activity includes printable worksheet materials as you incorporate this standards-based subject--discrete mathematics--in your math classes (grade 9 and up). award-winning site is billed as a resource for educators and students of game theory. It contains online lecture notes,...
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This award-winning site is billed as a resource for educators and students of game theory. It contains online lecture notes, book reviews, a large number of interactive materials in various categories, quizzes, and more.
Web-based resources on Numerical Methods are presented for engineering undergraduates. It is dedicated to reaching a large...
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Web-based resources on Numerical Methods are presented for engineering undergraduates. It is dedicated to reaching a large audience of undergraduate students through its holistic but customized approach. Holistically, the resources review background information; present numerical methods through youtube videos, notes, presentations, simulations and assessments; show how what they learned is applied in real life; tell stories to illustrate special topics and pitfalls; and give historical perspectives. From a customized perspective, the user can choose a major of choice - Chemical, Civil, Computer, Electrical, General, Industrial or Mechanical Engineering, and a language of choice - Maple, Mathcad, Matlab, Mathematica to illustrate algorithms, convergence and pitfalls of the numerical methods.
Quoted from site: "This site is dedicated to mathematical, historical and algorithmic aspects of some classical mathematical...
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Quoted from site: "This site is dedicated to mathematical, historical and algorithmic aspects of some classical mathematical constants (like pi, e, the Euler constant, ... ). A few results on prime numbers are added. Easy and fast programs are also included and can be downloaded." |
Find a Bull Valley, IL GeometryIntegral calculus is the branch of calculus focusing on accumulations; for example, areas under curves and volumes enclosed by surfaces. The two branches are connected by the Fundamental Theorem of Calculus discovered independently by Isaac Newton and Gottfried Leibnitz. My first exposure to calculus was in high school |
A logical introduction to proof Daniel W. Cunningham. "A Logical Introduction to Proof is a unique textbook that uses a logic-first approach to train and guide undergraduates through a transition or "bridge" course between calculus and advanced mathematics courses. The author's approach prepares the student for the rigors required in future mathematics courses and is appropriate for majors in mathematics, computer science, engineering, as well as other applied mathematical sciences. It may also be beneficial as a supplement for students at the graduate level who need guidance or reference for writing proofs. Core topics covered are logic, sets, relations, functions, and induction, where logic is the instrument for analyzing the structure of mathematical assertions and is a tool for composing mathematical proofs. Exercises are given at the end of each section within a chapter. Chapter 1 focuses on propositional logic while Chapter 2 is devoted to the logic of quantifiers. Chapter 3 methodically presents the key strategies that are used in mathematical proofs; each presented as a proof diagram. Every proof strategy is carefully illustrated by a variety of mathematical theorems concerning the natural, rational, and real numbers. Chapter 4 focuses on mathematical induction and concludes with a proof of the fundamental theorem of arithmetic. Chapters 5 through 7 introduce students to the essential concepts that appear in all branches of mathematics. Chapter 8 introduces the basic structures of abstract algebra: groups, rings, quotient groups, and quotient rings. Finally, Chapter 9 presents proof strategies that explicitly show students how to deal with the fundamental definitions that they will encounter in real analysis, followed by numerous examples of proofs that use these strategies. The appendix provides a useful summary of strategies for dealing with proofs." -- Publisher's description. View details » Place a hold »
Infinitesimal : how a dangerous mathematical theory shaped the modern world Amir Alexander. Explores "the"-- Provided by publisher. View details » Place a hold »
The sixth extinction : an unnatural history Elizabeth Kolbert. Over the last half billion years , there have been five major mass extinctions, when the diversity of life on Earth suddenly and dramatically contracted. Scientists are currently monitoring the sixth extinction, predicted to be the most devastating since the asteroid impact that wiped out the dinosaurs. This time around the cataclysm is us. In this book the author tells us why and how human beings have altered life on the planet in a way no species has before. She provides a moving account of the disappearances of various species occurring all around us and traces the evolution of extinction as concept, from its first articulation by Georges Cuvier in revolutionary Paris up to Lyell and Darwin, and through the present day. The sixth extinction is likely to be mankind's most lasting legacy, compelling us to rethink the fundamental question of what it means to be human. View details » Place a hold »
The pocket guide to wild mushrooms : helpful tips for mushrooming in the field Pelle Holmberg, Hans Marklund Depicts fifty-two edible mushrooms as well as the mushrooms with which they are often confused, edible or toxic. Uses symbol system, distribution maps and 175 photographs to help with identification. The reader will also become familiar with a wide variety of wild mushrooms, including morels, black trumpets, chanterelles, sheep polypore, porcini, a variety of boletes, and many more. View details » Place a hold »
Animals of the Masai Mara Adam Scott Kennedy, Vicki Kennedy. One of the greatest attractions of a trip to Kenya is the chance to see animals such as lions, cheetah, leopards, zebra, and giraffe up close and in their natural habitats. View details » Place a hold »
The homing instinct : meaning & mystery in animal migration Bernd Heinrich. Acclaimed scientist and author Bernd Heinrich has returned every year since boyhood to a beloved patch of western Maine woods. What is the biology in humans of this deep in the bones pull toward a particular place, and how is it related to animal homing? Heinrich explores the fascinating science chipping away at the mysteries of animal migration: how geese imprint true visual landscape memory; how scent trails are used by many creatures, from fish to insects to amphibians, to pinpoint their home if they are displaced from it; and how the tiniest of songbirds are equipped for solar and magnetic orienteering over vast distances. Most movingly, Heinrich chronicles the spring return of a pair of sandhill cranes to their home pond in the Alaska tundra. With his trademark "marvelous, mind altering" prose (Los Angeles Times), he portrays the unmistakable signs of deep psychological emotion in the newly arrived birds, and reminds us that to discount our own emotions toward home is to ignore biology itself. View details » Place a hold » |
This assignment will get the solutions to the many problems you do in an elementary algebra course. The procuder is not...
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This assignment will get the solutions to the many problems you do in an elementary algebra course. The procuder is not given, but the site provides the answers to many of the questions. Specially topics as multiplying, factoring and solving equations.
This homework is done online using Dr. Oakley Gordon's Homework, Quiz & Exam Applet. The Applet presents story problems and...
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This homework is done online using Dr. Oakley Gordon's Homework, Quiz & Exam Applet. The Applet presents story problems and questions to students, gives them immediate feedback and records their grades on a database. You must go to to find and access the Homework, Quiz & Exam Applet.
This is a Adobe Acrobat pdf file which contains the text of a homework with three questions, each of which has multiple...
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This is a Adobe Acrobat pdf file which contains the text of a homework with three questions, each of which has multiple parts. At the end of the pdf file is a handwritten answer key. The pdf file is accessed at |
text explores the translation of geometric concepts into the language of numbers in order to define the position of a point in space (the orbit of a satellite, for example). The two-part treatment begins with discussions of the coordinates of points on a line, coordinates of points in a plane, and the coordinates of points in space. Part 2 examines geometry as an aid to calculation and the necessity and peculiarities of four-dimensional space. Written for systematic study, it features a helpful series of "road signs" in the margins, alerting students to passages requiring particular attention, and an abundance of ingenious problems — with solutions, answers, and hints — promote habits of independent work |
Description
MATS 1300 This course develops a student's ability to analyze and work with functions and graphs, as part of the preparation for a rigorous calculus sequence (taking this course together with MATS1320 is equivalent to precalculus). Topics include tests for symmetry, finding intercepts and asymptotes, constructing piece wise-defined functions, transformations, polynomial and rational functions, composite and inverse functiions, and exponential and logarithmic functions. Techniques for solving linear, quadratic, rational, radical, exponential and logarithmic equations (with applications) are emphasized throughout the course. Systems of linear equations and matrix algebra are introduced, after wich sequences and series are also briefly introduced.
Meets MnTC Goal 4
Description
MATS 1350 A college level course designed to build a student's appreciation of both the beauty and utility of mathematics as it is used in society. Topics include voting and apportionment, fair division, scheduling and route planning, patterns of growth, and basic probability and statistics concepts including the bell curve. NOTE that this course does not serve as a prerequisite for any other math course.
Meets MnTC Goal 4
Description
MATS 1500 This course is designed for students who wish to explore the foundations of calculus in a more mathematically rigorous way than in MATS1480. The course begins with college trigonometry topics, including the six trigonometric functions and their inverses, the law of sines/law of cosines, radian measure and the unit circle, trigonometric identities and solving trigonometric equations. Fundamental concepts of calculus are then developed, including limits and continuity, differentiation of polynomial, trigonometric, exponential, and logarithmic functions with applications, and integration by numerical and exact methods with applications. Mathematical modeling with differential equations is also introduced.
Description
PHIL 1250 Students will learn to identify, analyze, and evaluate arguments derived from real-world problems using skills in formal logic. Concepts in informal logic will not be covered.
Prerequisites: Accuplacer score of 78 or higher in Reading Comprehension OR College Reading I, AND Accuplacer score of 51 or higher in Elementary Algebra OR MATS0305 Introduction to Algebra. Meets MnTC Goal 4. |
Elementary Algebra : Concepts: The Bittinger Concepts and Applications Series brings proven pedagogy to a new generation of students, with updates throughout to help today's students learn. Bittinger transitions students from skills-based math to the concepts-oriented math required for college courses, and supports students with quality applications and exercises to help them apply and retain their knowledge. New features such as Translating for Success and Visualizing for Success unlock the way students think, making math accessible to them. |
MIDTERMS
HOMEWORK
In addition to your WebWork problems, which are due every Friday 8 a.m., you have to hand in written homework every Friday in class (except when there is a midterm). The first written homework is due on Sept. 13.
OFFICE HOURS
You are most welcome to come to my office hours
to discuss
any questions about the course. You are also welcome to express
criticism or suggest any improvements to the course. The office hours
take place
Office hours start the second week of term, i.e. the first
one
takes place on Sept. 9. If you have a valid conflict that hinders you
to come to my office hours at the dates announced, please write an
e-mail to emil(at)math.ubc.ca
for alternative arrangements. |
In most of your mathematics courses to date,
you've learned to use powerful mathematical tools to solve problems,
and hopefully had lots of experience explaining and justifying your
reasoning. This is a good beginning; and in this course we will
formalize notions of mathematical reasoning and work on
proof-discovering and proof-writing skills.
The famous Hungarian mathematician Paul
Erdös had a favorite command for
mathematicians: "Conjecture and Prove!" summarizes the
two most important activities of mathematicians: Coming up with
plausible statements (making conjectures), and proving them true or
false. We'll work mostly on the second stage in this class, but we'll
work some on the first as well.
Formal mathematics begins with definitions,
axioms, and rules of logic; and from these we establish other
statements. The language we will learn is that of rigorous logic and
of set theory, which underlies much of what you will do in
upper-division math courses.
The only way to become good at understanding
and creating proofs is to do it – lots!
Resources
M*A*T*H
Colloquium – You should make this
a regular part of your week. Especially relevant to you this semester
are the talks on September 29, October 13, and November 17.
Other books:
I have put on reserve (3-day loan) in the
library several titles which you might find useful. Go to
and click on "Math 220" to see what's available. I might
add more during the semester. |
YEAR-AT-A-GLANCE AND UNIT OUTLINES
MAP4C: FOUNDATIONS FOR COLLEGE MATHEMATICS
Integrated
Unit 1 Unit 2 Unit 3 Unit 5 Unit 6 Unit 4
throughout
Working with Working with Exponential Measurement Trigonometry Renting, Culminating
One-Variable Two-Variable Computations, and Geometry Solve Owning, and Project
Data Data Solving Perform unit problems using Designing Gather,
Contexts Activate prior Exponential conversions in primary trig Budgets interpret, and
include: student knowledge of Equations, and context ratios of acute Interpret and describe
interests and/or linear, and Annuities Explore and obtuse compare costs information
learning styles, quadratic Connect points significance of triangles involved in about
possible careers, relationships on exponential optimal Use the sine owning and mathematics
and associated Explore cause graphs to dimensions in law and cosine renting concepts learned
educational and effect coordinates in its real 2D and 3D law to solve Solve problems and explore
pathways Recognize table of values contexts problems arising involving fixed occupations, and
Use large mis- and to solutions from real-world and variable college programs
amounts of data interpretations of of equations, and applications costs that use these
when working data express these in concepts
with percentiles, exponential form Prepare and
Use real data
interpretations of Investigate and present the
19 out of 20 use exponent results
Numerical and
mis- Graphical
laws
interpretations Models Investigate and
evaluate powers
Use clean data of rational
Working with
Two-Variable Activate prior exponents
Data knowledge from Demonstrate
Grades 9, 10, 11
Effective an understanding
surveys Select and of concepts of
justify choice of Personal Finance
Census at model
School (Stat Include
Can) Use a "rates of surveys
change" lens to Use
Compare and compare and
distinguish exponential
contrast types of computations
between relations using:
situations here
requiring one- finite
variable and differences
two-variable rate of change
analysis triangles on
graphs…"grow
ing faster" or
"growing
slower"
DRAFT: Grade 12 Foundations for College Mathematics – Year At A Glance (May 2007) 1
Unit 1 Foundations for College Mathematics
Working with Data
Lesson Outline
BIG PICTURE
Students will:
Personalize the course, and capitalize on their interests, post-secondary and career pathways
Collect, analyze, and summarize one Analyze a variety of surveys/questionnaires (e.g. Teen DM1.2
Magazine, Match Making Valentine Questionnaire, Census
at Schools, etc.) in order to describe the characteristics of an
effective survey/questionnaire
2 Design and critique questionnaires to collect data about the DM1.2
class (e.g. college destination, career interests, personal
interests, mathematics background, etc.)
Create a class questionnaire in order to conduct a survey
about the class (consider incorporating questions from the
Census at School questionnaire for later comparisons in
Day 6)
Assessment of class interests
3 Use examples from the media that include common DM2.1
statistical terms (e.g. percentile, quartile, standard
deviation) and expressions in order to review and interpret
them.
Analyze the class data using the statistical terms and
expressions for use by the media
4-5 Interpret statistics presented in the media. DM2.3, 2.4
Explain how the media misuses statistics.
Create a media advertisement from the class data that would
promote a certain point of view in order to lobby for a
school interest
Assess the validity of the conclusions presented by the class
media advertisements
Assess the validity of the conclusions presented in the
media
6-7 Analyze data from a secondary source (e.g. Census at DM2.1, 2.3, 2.4.
School) with technology (e.g. Fathom, spreadsheet, 1.1, 1.3
graphing calculator)
Validate class analysis of common attributes using the
secondary source (e.g. sample size, demographic bias)
Look for mathematical relationships in the data
Distinguish situations requiring one-variable and two-
variable data analysis
8 Summative Assessment (e.g. collection of case studies with
individual report, data project with report)
DRAFT: Grade 12 Foundations for College Mathematics – Year At A Glance (May 2007) 2
Unit 2 Foundations for College Mathematics
Two-variable data analysis
Lesson Outline
BIG PICTURE
Students will:
Personalize the course, and capitalize on their interests, post-secondary and career pathways
Collect, analyze, and summarize two Use a scatter plot from Unit 1, Days 6-7 in order to DM1.3, 1.5, 1.7
summarize properties (e.g. dependent and independent MM2.1, 2.2
variables, line of best fit, correlation, etc.)
Create a graphical summary of two-variable data using a
scatter plot without technology
Describe possible interpretations of the line of best fit of a
scatter plot and reasons for misinterpretations
2-3 Determine whether the line of best fit for a scatter plot is an DM1.8, 1.7, 1.6,
appropriate summary of a set of two-variable data 1.9,
MM2.1, 2.2
Determine an algebraic summary of the relationship
between two variables
Describe possible interpretations of the line of best fit of a
scatter plot and reasons for misinterpretations
Make and justify conclusions from the analysis of two-
variable data
4 Given a scatter plot for which the line of best fit is not an DM2.1
appropriate model of a set of two-variable data, introduce
the need to apply other models
5
6-7
8
DRAFT: Grade 12 Foundations for College Mathematics – Year At A Glance (May 2007) 3
Unit 3 Exponentials Foundations for College Mathematics
Lesson Outline
BIG PICTURE
Students will:
Solve exponential equations
Investigate the effects of changing parameters when investing in an annuity or a mortgage
Day Lesson Title Math Learning Goals Expectations
1 Graph exponential functions to look at key features of the graph MM 2.1, MM1.6,
including rate of change MM2.3, MM2.4,
MM3.3
Compare exponential functions with linear and quadratic
functions in real-world context
Explore rates of change using finite differences
2 Determine, through investigation, the exponents laws for MM1.1
multiplying, dividing and power of a power MM1.2
Simplify and evaluate algebraic expressions containing integer
exponents
3 Determine through investigation using a variety of tools and MM1.3, MM1.4
strategies the value of a power with a rational exponent
Evaluate numerical expressions involving rational exponents
and rational bases
Play a game involving powers
4 Solve exponential equations, graphically and numerically MM1.5, MM1.7,
Solve problems involving exponential equations MM1.6
5 Solve equations of the form xn = a using rational exponents MM3.1, MM3.2,
using inverse operations MM2.6, MM1.6,
MM3.4
Using a real world formula, determine the value of a variable of
degree no higher than three by substituting known values and
then solving for the unknown variable
Solve problems involving exponential equations
6 Summative task on solving exponential equations and exponent
laws and real world applications
7 Gather and interpret possible investments involving annuities PF1.1, PF1.5
Gather and interpret information about mortgages
8 Solve problems that involve amount, the present value, and the regular PF1.3, PF1.4
payment of an ordinary annuity in situations where the compounding
period and the payment period are the same
Demonstrate through investigation using technology the
advantage of investing early on
9-10 Determine through investigation using technology the effect of PF1.2, MM2.5
changing the conditions (payment, frequency, interest rate,
compounding period) keeping the compound period and
payment period the same
11 Read and interpret an amortization table for a mortgage PF1.6, PF1.7
Generate and amortization schedule
12 Determine, through investigation using technology the effects of PF1.8
varying payment periods, regular payments and interest rates on the
length of time needed to pay off a mortgage.
13 Summative Task
Establish the criteria for level 3 of the rubric for the personal
finance expectation as a class
DRAFT: Grade 12 Foundations for College Mathematics – Year At A Glance (May 2007) 4
Unit 4 Personal Finance
Foundations for College Mathematics
Lesson Outline
BIG PICTURE
Students will:
Gather, interpret, and compare information about owning or renting accommodation
Prepare budgets based on possible wages connected to career choice and case studies
Collect data regarding career choice in a portfolio for use with culminating project
Day Lesson Title Math Learning Goals Expectations
1 Gather, interpret, and describe information about living PF3.1
costs, and estimate the living costs of different
households in the local community
Connect career choice with estimated wages and living
expenses for a certain time period (this may include a
scenario of marital status and number of dependents)
2 Establish residence criteria PF2.1
- e.g. Cost, location, pets, laundry facility,
parking, public transit, shopping, fitness facilities,
school, furnishings, etc
Establish wants versus needs
Research in newspapers, Internet
Understand advertisement language and intent
3 Gather information about different rental PF2.1
accommodations in the local community (eg.
Apartment, condominium, townhouse, detached home,
room in a house, mobile home) such as availability,
conditions for renting.
Establish pros and cons for each of the various options
4 Identify and describe the factors to be considered in PF3.4
determining the affordability of accommodation in the
local community, and consider the affordability of
accommodation based on circumstances
5,6 Research rental costs PF2.1,PF2.3,PF3.4
- e.g. First and last rent, parking fee, laundry, heat and
hydro, internet, cable, appliances, hot water tank, water
Survey rental properties and select five possible
properties to meet given needs
Interpret the information from the five properties to
make an informed decision in selecting a rental
property that would suit given needs
- include cost analysis (rental and other associated costs
like transportation), convenience factors
7 Gather and interpret information about procedures and PF2.1
costs involved in buying and owning accommodation in
the local community
- e.g. home inspection, survey, approval of mortgage,
lawyer's fees, taxes, location, size of home,…
DRAFT: Grade 12 Foundations for College Mathematics – Year At A Glance (May 2007) 5
8 Survey possible accommodations to purchase PF2.1,PF2.3
- e.g. detached, semi-detached, condominium, town
house
and select five possible properties to meet their needs
Interpret the information from the five properties to
make an informed decision in selecting a property to
purchase that would suit given needs
- include cost analysis (purchase price and other
associated costs like transportation), convenience
factors
9 Compare renting accommodation with owning PF2.2
accommodation by describing the advantages and
disadvantages of each
Justify selection of accommodation between the rental
choice and the purchase choice for given needs
10 Design and present a savings plan to facilitate the PF3.2
achievement of a long-term goal
11 Design, explain, and justify a monthly budget suitable for PF3.3
their scenario
12, Summative Task PF3.5
13 Make adjustments to a budget to accommodate changes in
circumstances
Unit 5 Geometry Foundations for College Mathematics
Lesson Outline
BIG PICTURE
Students will:
Understand the relationships between imperial and metric units
Consolidate understanding of perimeter, area, surface area, and volume through real-life problems
Explore optimization of two-dimensional and three-dimensional figures
Day Lesson Title Math Learning Goals Expectations
1 Explore relationships that exist between inches and centimeters GT1.1
(measuring tools: string, both types of rulers, or tapes)
Reading ruler, measuring tape (fraction)
Create a scatter plot from the student's data
Perform a linear regression and get the equation
Connect to the actual conversion (inches <->
centimetres)
2 Trundle wheel activity for perimeter GT1.1
Converting mixed imperial measurements <-> metric
Example convert 5 1/8" to cm
3 Finding the area of rectangles, triangles, and circles, and of GT1.2
related composite shapes, in situations arising from real-
world applications
Using imperial, metric and conversions when necessary
DRAFT: Grade 12 Foundations for College Mathematics – Year At A Glance (May 2007) 6
4 Maximum area for a given perimeter GT2.2,GT2.1
Problem: Cagey Problem, Why are copper wires round?
5 Minimum perimeter for a given area GT2.2,GT2.1
Problem: Fencing
6 Jazz Day
7 Volume problems involving rectangular prisms, GT1.3
triangular prisms, cylinders, and composite figures
Using imperial, metric and conversions when necessary
Example: Volume of Concrete Pad in cubic meters with
initial measurements in feet and inches. Example 8' x
24' x 4"
8 Surface area problems involving rectangular prisms, GT1.3
triangular prisms, cylinders, and composite figures
Using imperial, metric and conversions when necessary
9 Maximum volume for a given surface area GT2.3,GT2.1
Using imperial, metric and conversions when necessary
10 Minimum surface area for a given volume GT2.3,GT2.1
Using imperial, metric and conversions when necessary
11-13 Summative Task
Packaging Project
Unit 6 Trigonometry Foundations for College Mathematics
Lesson Outline
BIG PICTURE
Students will:
Consolidate understanding of primary trigonometric ratios, sine and cosine laws for acute triangles, using
imperial and/ or metric measure as appropriate
Extend understanding of primary trigonometric ratios to include obtuse angles
Solve problems using the sine or cosine laws for oblique triangles (non-ambiguous cases only)
Day Lesson Title Math Learning Goals Expectations
1 Activate prior knowledge through a graffiti exercise GT3.1
- Pythagorean Theorem, sine ratio, cosine ratio,
tangent ratio, sine law and cosine law (acute
angles)
Solve problems requiring use of the primary
trigonometric ratios and involving imperial
measurements
2 Explore applications imperial measurements using a GT3.1
Clinometer's activity
3 Solve problems using the sine law for acute triangles GT3.1
using imperial measurements
4 Solve problems using the cosine law for acute triangles GT3.1
using imperial measurements
DRAFT: Grade 12 Foundations for College Mathematics – Year At A Glance (May 2007) 7
5 Solve problems using the primary trigonometric ratios, GT3.1
sine law or cosine law of acute triangles using metric or
imperial measurements
6 Investigate connections between primary trigonometric GT3.2, GT3.3
ratios of acute angles and obtuse angles
Determine the values of the sine ratio, cosine ratio, and
tangent ratio for obtuse angles
7 Solve problems involving oblique triangles, including GT3.4
those that arise from real-world applications, using the
sine law (non-ambiguous cases only)
8 Solve problems involving oblique triangles, including GT3.4
those that arise from real-world applications, using the
cosine law
9 Solve problems involving oblique triangles, including GT3.4
those that arise from real-world applications, using the
sine law or cosine law (non-ambiguous cases only)
10-11 Measure the area of a polygon shaped figure requiring GT1.2,
use of trigonometry to determine missing sides. GT3.4,GT3.1
Example: (landscaping, construction)
12 Summative Assessment
DRAFT: Grade 12 Foundations for College Mathematics – Year At A Glance (May 2007) 8 |
Mathematical analysis This is a module framework. It can be viewed online or downloaded as a zip file. As taught in 2007-2008 and 2009-2010. This module introduces mathematical analysis building upon the experience of limits of sequences and properties of real numbers and on calculus. It includes limits and continuity of functions between Euclidean spaces, differentiation and integration. A variety of very important new concepts are introduced by investigating the properties of numerous examples, and developing the a Author(s): Feinstein Joel F. Dr |
This site is designed to answer many important questions regarding carrers and professional placement of math majors. It...
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This site is designed to answer many important questions regarding carrers and professional placement of math majors. It contains very useful statistical data on the subject as well as information on different connections between mathematics and real life. The site can be very useful for all kinds of professional orientation sessions for math majors.
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This site is the mathematics area of the larger Wolfram Alpha project – described as a computational knowledge engine to make the world's knowledge computable. In response to natural language questions it provides direct answers, explanations, related information and comparisons. In addition to mathematics the main site offers, for example, chemistry, engineering, places and geography, money and finance. Mathematica is used as the underlying software engine.From the point of view of mathematics education it poses advantages and disadvantages in the way of most technology – but the free availability of a powerful mathematical tool opens up vast new possibilities for students and teachers to explore. For the professional mathematician it's not clear if it solves anything that their stand alone version of Mathematica could not.
TeXnicCenter is a front end for TeX implementations that supports editing in an environment looking similar to Microsoft...
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TeXnicCenter is a front end for TeX implementations that supports editing in an environment looking similar to Microsoft Visual C++. The program is available as a free download under the GNU public license.
This is a sub-page of the large and comprehensive Eric Weisstein's World of Mathematics site which is separately reviewed...
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This is a sub-page of the large and comprehensive Eric Weisstein's World of Mathematics site which is separately reviewed elsewhere on MERLOT. At the time of review this recreational mathematics area listed ten subtopics including: cryptograms, dissection, illusions, magic squares, and puzzles. A total of approximately 140 separate recreational mathematics items were included.
This site contains lots of helpful hints about how to easily type different mathematical expressions in e-mail messages (or...
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This
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The Beamer package is a LaTeX class for creating presentations that are held using a projector, but it can also be used to create transparency slides. The Beamer is perfect for creating a presentation with a large amount of mathematical formulas. It is freely available for download. |
This online course includes elements from an undergraduate seminar on mathematical problem solving. The material will help students develop their mathematical and problem solving skills. A few topics that are covered...
This learning object from Wisc-Online covers the trapezoid, examining the properties and components of the shape. The lesson uses the geometric formulas for finding the perimeter and area of the shape. Practice...
This learning object from Wisc-Online covers the triangle, examining the properties and components of the shape. The lesson uses the geometric formulas for finding the perimeter and area of the shape. Practice questions...
Gilbert Strang, of the Massachusetts Institute of Technology, highlights calculus in a series of short videos that introduces the basic ideas of calculus ? how it works and why it is important. The intended audience i... |
SECTION MAY BE USED BY STUDENTS TO SATISFY RESEARCH WRITING
PREREQUISITE: MATH-M 216 |
This three-volume set addresses the interplay between topology, functions, geometry, and algebra. Bringing the beauty and fun of mathematics to the classroom, the authors offer serious mathematics in a lively, reader-friendly style. Included are exercises and many figures illustrating the main concepts. It is suitable for advanced high-school students, graduate students, and researchers. |
linearity
(mathematics) A relationship between several quantities which can be considered as proportional and expressed in terms of linear algebra, or any mathematical property of a relationship, operation or function that is analogous to such proportionality, satisfying additivity and homogeneity. |
More About
This Textbook
Overview
Recognizing the enormous need for well-trained Pharmacy Technicians as well as the serious need to decrease medication errors, Math for Pharmacy Technicians: Concepts and Calculations was developed. This textbook is organized from simple to complex and walks the student through the necessary information to pass the math portion of the PTCB exam. The text includes Pharmacy Technician-specific information that is non-threatening and helps the student learn to safely practice as a Pharmacy Technician. This text is organized into 11 chapters, along with a pretest and a comprehensive evaluation or posttestMath for the Pharmacy Technician
The author of this book took me under her wing to teach me the mathematical intricacies that the Pharmacy Technician must accomplish.
After being out of school for 25 years and not being sure that I would understand the 'new math' I achieved what I thought would be impossible, a GPA of 4.0.
This book takes the complicated mathematical formulas needed in the Pharmacy and makes them understandable; it breaks down advanced math to make it easy for anyone to understand.
This book should be the baseline for future generations of Pharmacy Technicians to learn from.
By the end of my classes with Mrs Egler she had explained to me that I would have to count to ten before answering any questions in her class to give the other students a chance
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. |
This student-friendly textbook for the Statistics 1 Module of A-Level Maths comprehensively covers the Edexcel exam specification. It contains straightforward, accessible notes explaining all the theory, backed up with useful step-by-step examples. There are practice questions throughout the book to test understanding, with recap and exam-style questions at the end of each section (detailed answers to all the questions are included at the back). Finally, there's a CD-ROM containing two complete Statistics 1 practice exam papers - ideal to print out for realistic practice before the final tests |
More About
This Textbook
Overview
Known for its clear, no-nonsense explanations as well as for mathematical accuracy and rigor, Gustafson and Frisk has long been counted among the tried-and-true algebra texts. The Sixth Edition features an early introduction to functions. Long-time Gustafson/Frisk users will appreciate the updates the authors have made while non-users now have plenty of reasons to take a closer look.
Related Subjects
Meet the Author
R. David Gustafson is Professor Emeritus of Mathematics at Rock Valley College in Illinois and has also taught extensively at Rockford College and Beloit College. He is coauthor of several best-selling mathematics textbooks, including Gustafson/Frisk/Hughes' COLLEGE ALGEBRA, Gustafson/Karr/Massey's BEGINNING ALGEBRA, INTERMEDIATE ALGEBRA, BEGINNING AND INTERMEDIATE ALGEBRA, BEGINNING AND INTERMEDIATE ALGEBRA: A COMBINED APPROACH, and the Tussy/Gustafson and Tussy/Gustafson/Koenig developmental mathematics series. His numerous professional honors include Rock Valley Teacher of the Year and Rockford's Outstanding Educator of the Year. He has been very active in AMATYC as a Midwest Vice-president and has been President of IMACC, AMATYC's Illinois affiliate. He earned a Master of Arts from Rockford College in Illinois, as well as a Master of Science from Northern Illinois University.
Rosemary Karr graduated from Eastern Kentucky University (EKU) in 1976 with a B.S. in Mathematics, attained her M.A. at EKU in Mathematics Education in 1981, and earned her Ph.D. from the University of North Texas in 1996. After two years teaching high school mathematics, she joined the faculty at Eastern Kentucky University, where she earned tenure as Assistant Professor of Mathematics. A professor of mathematics at Collin College in Plano Texas since 1990, Prof. Karr has written more than ten solutions manuals, presented numerous papers, and been an active member in several educational associations (including President of the National Association for Developmental Education). She has been honored several times by Collin College, and has received such national recognitions as U.S. Professor of the Year (2007), Minnie Stevens Piper Professor (2008), and CLADEA fellow (2012).
Marilyn Massey teaches mathematics at Collin College in McKinney, Texas. She has been President of the Texas Association for Developmental Education, featured on the list of Who's Who among America's Teachers and received an Excellence in Teaching Award from the National Conference for College Teaching and Learning. Professor Massey has presented at numerous state and national conferences; her article "Service-Learning Projects in Data Interpretation" was one of two included from community college instructors for the Mathematical Association of America's publication, Mathematics in Service to the Community. She earned her Bachelor's degree in Secondary Education from the University of North Texas and Master's Degree in the Art of Teaching Mathematics from the University of Texas at Dallas |
Math - From Classroom to Career
Freshman Year
Academic Advising Use your academic advisor, your favorite professor, and the peer advising program to explore mathematics and other potential majors, minors, programs and courses, given your interest.
Dream Job
What is your "dream job" after graduation? What are you passionate about? Talk to your faculty advisor and other mentors. As a mathematics major, how can you use your time at Fairfield to prepare for it through class work, internships, volunteer activities, summer jobs, leadership positionswith clubs and organizations, and other relevant out of class experiences?
The skills of mathematicians are crucial to many business, nonprofit, and government operations. Graduates who have majored in mathematics are employed in a wide range of professional fields. Many have made their careers in the insurance industry, beginning as actuaries. Teaching is a popular option, with a number of students seeking secondary school opportunities. Mathematicians are, of course, much in demand for computer-related work where their analytic skills are highly prized.
Sigma XI Attend the annual Sigma Xi poster session, held in the Campus Center every spring. See the work of other majors, and imagine how your work will be displayed in future years.
Sigma Xi, The Scientific Research Society, was founded in 1886 as an honor society for scientists and engineers. Headquartered in Research Triangle Park, N.C., it is an international research society whose programs and activities promote the health of the scientific enterprise and honor scientific achievement. There are more than 80,000 Sigma Xi members in about 500 chapters at colleges and universities, industrial research centers, and government laboratories.
Tutoring Appointments The Mathematics Center, located in the Bannow Science Center (BNW129A), is a place where students can get free tutoring for first year statistics and calculus courses. In order to make the most of your tutoring session, please read through your class notes beforehand, bring your textbook and come prepared with specific questions. This will help you and your tutor identify what to focus on most.
Colloquium Series
The department runs a very successful colloquium series, offering about three talks each semester. Most of these talks are geared toward sophomore majors, but often a talk will be targeted at a more general audience. These can be very entertaining and, more importantly, very informative, offering a glimpse into the world of mathematics.
Get Honored! Pi Mu Epsilon is the national mathematics honor society. The Fairfield University Connecticut Beta chapter was chartered in 1986. The purpose of PME is the promotion of scholarly activity in mathematics. Students are invited to membership based upon their outstanding academic achievements in mathematics. PME sponsors several mathematical activities throughout the year. Contact: Dr. Joan Weiss at (203) 254-4000 ext. 2223 or weiss@fairfield.edu.
That's just the start. Take a look at this career information from other University offices that we think is also valuable to majors. |
Calculus. For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. In Everyday Calculus , Oscar Fernandez shows us how to see the math in our coffee, on the highway, and even in the night sky. Fernandez usesCalculus Made Easy has long been the most popular calculus primer, and this major revision of the classic math text makes the subject at hand still more comprehensible to readers of all levels. With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems,... more...... more...
Real quaternion analysis is a multi-faceted subject. Created to describe phenomena in special relativity, electrodynamics, spin etc., it has developed into a body of material that interacts with many branches of mathematics, such as complex analysis, harmonic analysis, differential geometry, and differential equations. It is also a ubiquitous factor... more...
The study of linear positive operators is an area of mathematical studies with significant relevance to studies of computer-aided geometric design, numerical analysis, and differential equations. This book focuses on the convergence of linear positive operators in real and complex domains. The theoretical aspects of these operators have been an active... more... |
$114 advent of powerful desktop computers has revolutionized scientific analysis and engineering design in fields as disparate as particle physics and telecommunications. This up-to-date volume provides the essential mathematical and computational education for students, researchers, and practicing engineers. The author begins with a review of computation, and then deals with a range of key concepts including sets, fields, matrix theory, and vector spaces. He then goes on to cover more advanced subjects such as linear mappings, group theory, and special functions. He concentrates exclusively on the most important topics for the working physical scientist or engineer with the aim of helping them to make intelligent use of the latest computational and analytical methods. The book contains well over 400 homework problems and covers many topics not dealt with in other textbooks. It will be ideal for senior undergraduate and graduate students in the physical sciences and engineering, as well as a valuable reference for working engineers.
Covers many topics not dealt with in other textbooks on mathematical methods
Distinguished author: Fellow of APS, IEEE, and OSA
Uses a few simple but powerful concepts to enable the reader to organize and comprehend many topics that are important in applications |
Description
An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students.
Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists--who include mathematicians and scientists--examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery.
Classroom-tested activities and problem solving
Accessible problems that move beyond regular art school curriculum
Multiple solutions of varying difficulty and applicability
Appropriate for students of all mathematics and art levels
Original and exclusive essays by contemporary artists
Forthcoming: Instructor's manual (available only to teachersSpaceyAcey
LibraryThing Review Uses more words than necessary to explain his ideas. I kind of understand what he's trying to say but not really. I'm sure there is a more eloquent way to convey his ideas.
FPdC
LibraryThing Review Here we have one of those important books we should approach with some care and about which I am somewhat divided (or, should I say, ambiguous...). The main argument of the book, as the subtitle
fpaganUser reviews
SpaceyAcey SpaceyAcey
LibraryThing
LibraryThing Review Uses more words than necessary to explain his ideas. I kind of understand what he's trying to say but not really. I'm sure there is a more eloquent way to convey his ideas.
LibraryThing Review Here we have one of those important books we should approach with some care and about which I am somewhat divided (or, should I say, ambiguous...). The main argument of the book, as the subtitleAbout the authors
Marc Frantz holds a BFA in painting from the Herron School of Art and an MS in mathematics from Purdue University. He teaches mathematics at Indiana University, Bloomington where he is a research associate. Annalisa Crannell is professor of mathematics at Franklin & Marshall College. She is the coauthor of "Writing Projects for Mathematics Courses".
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From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines this with an in-depth look at their aesthetics, history, and structure. Whether using trigonometry and vectors to explain why Gothic arches are structurally superior to Roman arches, or showing how simple ruler and compass constructions can produce sophisticated architectural details, Alexander Hahn describes the points at which elementary mathematics and architecture intersect.
Beginning in prehistoric times, Hahn proceeds to guide readers through the Greek, Roman, Islamic, Romanesque, Gothic, Renaissance, and modern styles. He explores the unique features of the Pantheon, the Hagia Sophia, the Great Mosque of Cordoba, the Duomo in Florence, Palladio's villas, and Saint Peter's Basilica, as well as the U.S. Capitol Building. Hahn celebrates the forms and structures of architecture made possible by mathematical achievements from Greek geometry, the Hindu-Arabic number system, two- and three-dimensional coordinate geometry, and calculus. Along the way, Hahn introduces groundbreaking architects, including Brunelleschi, Alberti, da Vinci, Bramante, Michelangelo, della Porta, Wren, Gaudí, Saarinen, Utzon, and Gehry.
Rich in detail, this book takes readers on an expedition around the globe, providing a deeper understanding of the mathematical forces at play in the world's most elegant buildings.This third and final volume of Strategic Activities on fractal geometry and chaos theory focuses upon the images that for many people have provided a compelling lure into an investigation of the intricate properties embedded within them. By themselves the figures posses fascinating features, but the mechanisms by which they are formed also highlight significant approaches to modeling natural processes and phenomena. The general pattern and specific steps used to construct a fractal image illustrated throughout this volume, comprise an iterated function system. The objective of this volume is to investigate the processes and often surprising results of applying such systems. These strategic activities have been developed from a sound instructional base, stressing the connections to the contemporary curriculum as recommended in the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards for School Mathematics. Where appropriate, the activities take advantage of the technological power of the graphics calculator. The contents of this volume joined with the details contained in the prior two books. Together they provide a comprehensive survey of fractal geometry and chaos theory. The dynamic nature of the research and the experimental characteristics of related applications provides an engaging paradigm for classroom activity.Awesome aliens, warriors, martial artists, monsters, robots and more are waiting for you to bring them to life on the pages of your sketchbook!
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Optimization problems are relevant in many areas of technical, industrial, and economic applications. At the same time, they pose challenging mathematical research problems in numerical analysis and optimization. Harald Held considers an elastic body subjected to uncertain internal and external forces. Since simply averaging the possible loadings will result in a structure that might not be robust for the individual loadings, he uses techniques from level set based shape optimization and two-stage stochastic programming. Taking advantage of the PDE's linearity, he is able to compute solutions for an arbitrary number of scenarios without significantly increasing the computational effort. The author applies a gradient method using the shape derivative and the topological gradient to minimize, e.g., the compliance . and shows that the obtained solutions strongly depend on the initial guess, in particular its topology. The stochastic programming perspective also allows incorporating risk measures into the model which might be a more appropriate objective in many practical applications.
This book is a survey of current topics in the mathematical theory of knots. For a mathematician, a knot is a closed loop in 3-dimensional space: imagine knotting an extension cord and then closing it up by inserting its plug into its outlet. Knot theory is of central importance in pure and applied mathematics, as it stands at a crossroads of topology, combinatorics, algebra, mathematical physics and biochemistry.
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Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B. H. Neumann introduced this system in the 1950s, and J. Moser popularized it as a toy model for celestial mechanics. All along, the so-called Moser-Neumann question has been one of the central problems in the field. This question asks whether or not one can have an outer billiards system with an unbounded orbit. The Moser-Neumann question is an idealized version of the question of whether, because of small disturbances in its orbit, the Earth can break out of its orbit and fly away from the Sun. In Outer Billiards on Kites, Richard Schwartz presents his affirmative solution to the Moser-Neumann problem. He shows that an outer billiards system can have an unbounded orbit when defined relative to any irrational kite. A kite is a quadrilateral having a diagonal that is a line of bilateral symmetry. The kite is irrational if the other diagonal divides the quadrilateral into two triangles whose areas are not rationally related. In addition to solving the basic problem, Schwartz relates outer billiards on kites to such topics as Diophantine approximation, the modular group, self-similar sets, polytope exchange maps, profinite completions of the integers, and solenoids--connections that together allow for a fairly complete analysis of the dynamical |
Basic College Mathematics with Early Integers
9780321726438
ISBN:
032172643X
Edition: 2 Pub Date: 2011 Publisher: Pearson Education
Summary: Martin-Gay, Elayn is the author of Basic College Mathematics with Early Integers, published 2011 under ISBN 9780321726438 and 032172643X. Seven hundred thirty nine Basic College Mathematics with Early Integers textbooks are available for sale on ValoreBooks.com, one hundred seventy nine used from the cheapest price of $34.75, or buy new starting at $124.97 shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions.[less]
All the information used inside the book was helpful for my desire to re-learn math from the bottom up.
Developmental math appreciation, I simply took the course so I could re-learn math from the bottom due to not having had a math class in over 10 yrs as well as I don't remember ever having a math teacher that really cared if I learned and understood. |
Find a Houston PrecalThey are mostly used for solving a system of equations in order to determine the answers. I have studied many areas of LA, not only the theoretical part but also the application's part. My major application area has been in engineering and related math and science areas |
Todays Developmental Math students enter college needing more than just the math, and this has directly impacted the instructors role in the ...Show synopsisTodays Developmental Math students enter college needing more than just the math, and this has directly impacted the instructors role in the classroom. Instructors have to teach to different learning styles, within multiple teaching environments, and to a student population that is mostly unfamiliar with how to be a successful college student. Authors Andrea Hendricks and Pauline Chow have noticed this growing trend in their combined 30+ years of teaching at their respective community colleges, both in their face-to-face and online courses. As a result, they set out to create course materials that help todays students not only learn the mathematical concepts but also build life skills for future success. Understanding the time constraints for instructors, these authors have worked to integrate success strategies into both the print and digital materials, so that there is no sacrifice of time spent on the math. Furthermore, Andrea and Pauline have taken the time to write purposeful examples and exercises that are student-centered, relevant to todays students, and guide students to practice critical thinking skills. Intermediate Algebra and its supplemental materials, coupled with ALEKS or Connect Math Hosted by ALEKS, allow for both full-time and part-time instructors to teach more than just the math in any teaching environment without an overwhelming amount of preparation time or even classroom time.Hide synopsis
Description:Hardcover. Instructor Edition: Same as student edition with...Hardcover. Instructor Edition: Same as student edition with additional notes or answers. New Condition. SKU: 9780073360973-1-0-1 Orders ship the same or next business day. Expedited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions. ISBN: 9780073384269.
Description:New. PLEASE READ: INSTRUCTOR'S EDITION WITH NO ONLINE ACCESS...New. PLEASE READ: INSTRUCTOR'S EDITION WITH NO ONLINE ACCESS CODES. Same as student edition but with teaching tips and answers. Ships same or next day. Order expedited for 2-4 day delivery |
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About the Course & AP Exam Strategies
Transcript
[0:00:00] My name is John Postovit and this is advanced placement calculus AB. In this course we're going to cover a ton of stuff. We're going to do the problems involving the basics of calculus. And we're also going to do problems involving those strange theoretical things that you'll definitely see on AP test. You can use this of course in a couple of different ways. You could use it all year long as a supplement to your regular calculus course. I have a lot of episodes where I do lots of problems involving things like the chain rule, things like finding areas between curves, finding volumes, all sorts of the essentials that you need. Or, maybe using this course at the very end of the year in that last month or two while you were leaving for the AP test. Either way, I first recommend that you go to the bonus materials, down with the follow alongs.
The reason I want you to do that is because, I often do a lot of writing and you have more coordinated, organised notes if you're writing them down and can look at the tips and the hints and the problem itself, without having to madly scribble that down. You can just concentrate on taking good notes for yourself. Of course you can always stop the video to give yourself a second to catch up.
After you watch every episode, I'd also say that you ought to try the extra practise problems. I've written up a bunch of practise problems along the lines of what I show you during this course, so that you can try two or three of them on your own.
[0:02:00] These practise problems also involve the solution including every step, it's probably first it'll do that sometimes that the calculus text book will say, "Well okay, here's a problem. Do this problem and there is one example, and by the way we left out a bunch of steps because you're just too smart to need all the steps." Well I'm assuming that you're like me and when you were taking calculus, sometimes I didn't see those steps that were left off. And I had to think how did they get from there to there. In my extra practices, I've tried to show you everything. Well settle in, relax a little bit, and I hope you enjoy the course.
Before you walk into the room on that fateful day where you're going to be a total success on the calculus test, you need to know how it's organised, so that you're prepared and ready to go. Sections, questions and time. Tests are broken up into two large sections. The first large section is multiple choice. The second one is free response. Each of these two sections is weighted the same. So you get an equal amount of credit for multiple choice and free response on the whole.
When they score it, they'll score this part, they'll score this part, add up the results and then compare that to their standards for what's considered a one, two, three, four or five on the test. Depending what college you go to, you'll need a three or a four, or sometimes even a five in order to get credit for moving on to the next level of calculus. The whole test takes 3 hour and 15 minutes and that doesn't include the fiddling around time for passing out the test, reading the rules, collecting the tests and all of that.
Now within each part of multiple choice and free response, there is two subsections. So when you get the test, the first thing they'll tell you is, "Put your calculator away." And they give you part A. They say, "Do this part A and when your done stop. Put our head on down and just sit soundly."
[0:04:00] Then on part B they'll allow you to get your calculator out to do just part B. Well, look at the timing on the number of questions. Part A, 28 questions in 55 minutes, that's about two minutes a question. Part B, 17 questions, 50 minutes, that's about three minutes a question. That should tell you something right there. They're allowing you more time because they think you'll need it.
Part B is more likely to have some unusual theoretical problems that might have to pause and think about just to organise your thoughts. And part A will tend to have the more straight forward ones that don't require a lot of calculations, or they're fairly direct derivative, chain rules, that kind of thing.
A little bit of strategy, you might have felt, go through the test first and decide which problems to do. I wouldn't recommend that because of the amount it takes. But I'd recommend something very similar. Look at question number one, and if you immediately think you know, "I think that's more than a two minute question." Circle it and then go on to the next one. Then you can go back later to those harder questions that you circled. The reason I recommend that is because hard and easy, on multiple choice they're all worth the same. So you don't want to spend a time on a hard question when you could be knocking out some of those thirty second questions.
Go back later to finish the harder ones, same thing for part B of the multiple choice.
Free response, you're allowed a total of 90 minutes and that's broken up into two sections. The first part takes a calculator. So after you finish this they'll let you keep your calculator. The second part doesn't and there is only three questions for each part. What that tells you is that, each of those three questions has a lot of subsections. So there may be four or five things you need to find for each of those questions. But still, I would recommend the strategy of looking it over first.
[0:06:00] Now this, since they are only three questions probably is worth reading each question and deciding which one to do first. You want to do the one first that you immediately know how to do. Then say you're going through one of those questions and you get to the second or last part and you think, "I don't know how to do that." Think about it for just a little while, but not too long. And if you can't do the last part, that's okay. It's free response and you get credit for each sub-section that you do of each question. And actually within each sub section there is different things they are looking for. They'll be looking for having the integral written up properly, looking for some of the details, the solution etcetera. So remember you can get partial credit, don't panic and give up. If you can write something down that you think can makes sense, do it. 15 minutes a question so that's a lot of steps.
Now after you've done this 45 minutes they'll say, "Stop," to have you put away your calculator. Then for the next 45 minutes, you'll have part B. Three questions again, tend to be questions that don't allow a calculator. Which means that they tend to be more theoretical questions where you'll have charts to work from or with the calculations are very simple. Whereas part A, with the calculator, will often have integrals that you can't do by hand, and where you'll have to approximate the solutions by using some of the functions on your graphing calculator.
If you finish the three questions on part B and still have some time left, they're going to let you go back to part A, on the free response section only. They won't let you have your calculator back because no one else in the room will have one. But at least you can go in and maybe fill in some more of the theoretical parts and almost finish some of the problems that you're asked to do in the calculator section.
Now that I've shown you how the test is organised, I'm going go to show you some general strategies for preparing for the test and for actually taking the test.
[0:08:0] I'm going to begin by covering some basic strategies that can really help you earn high score on AP test. First strategy, go back and review. That's kind of vague isn't it? So I want to give you some specific hints on how you could do that.
First thing I would recommend doing, is going and finding all your old tests. Find the problems that you got wrong the first time, that's what you should concentrate on. Look at the problems you got wrong in the first time, and then stop and think, "Do I know how to do this now?" If you do, then don't spend a lot of time on it. Just enough time to remember how it works. Go back and review.
The reason I'm saying this is because in order to score well on the AP test, you really have to know the calculus. You have to be able to do the basic operations like differentiation and integration, and even things like chain rule, which is fairly basic. You have to be able to them instinctively. So you don't have to concentrate on how you do that when you're trying to figure out what the problem is asking for. There are a lot of problems where it's not entirely clear what they want. There are a lot of problems where it'll say do such and such, find the rate of change of an integral. It won't just always say, "Here is something integrated." Sure you have some of those problems where you just do an operation, but knowing how to do those isn't enough.
Next, do the official AP practise test. Of course before you do that, this course is designed to get you through that stuff. What I've done is, I've gone through the officially released course description which includes, multiple choice questions and free response questions. And I've modelled a lot of what I'm teaching you on what they are asking you there. And sometimes I've taken it a step beyond.
[0:10:00] Once you've done that, then you'll want to do the practise problems that I give you, so that you get these down a little bit better. And then go do the official test, which is going to have a lot of similarities. Take that official test, try to figure out which technique you are using. You might even want to go back and say, "Hey! What episode was this on?" And go through it. It's really important to do the AP practise test.
Next thing you need to do, is be really strategic on the free response section. First off, the problems are weird. They are seriously weird problems because, the AP people want to find out if you really know calculus, or whether not you're just parroting a bunch of operations. So they've put in questions where you have to know the theory behind calculus, and you know how to be calm and collected. To read a problem and realise, "Well are they asking me to integrate it, or to eliminate some or do the derivative. Just what are they asking for?" You have to be strategic on it.
Also, while you're doing the free response section, you have to make sure that the scorer can read what you're doing. That's actually humans that grade these. The way it's set up is, the AP people hire calculus teachers to come in during the summer and grade your test. Now, they are given really strict guidelines on how it should be graded, how many points you get for each part. Do you notice I said each part? yeah. Because you get points for everything that you do right. But there is a lot of particularities that they look for.
For example, if you're not using correct notation, you're probably going to loose some points. If you skip a detail at the end of an integral like putting the constant integration, that's right.
[0:12:00] One of the points that you can get is actually for just writing plus C at the end of the integral. Make your writing clear. Again these are humans that are grading this. If they can't read what you did, guess how many points you get? Zero. That's right.
Also since you're under time constraints, you want yo page through the entire section, that entire section that you're allowed to do at that point and see which problems you can do first, most quickly. Otherwise there's chance that you might just sit there looking at a problem and then your head gets filled up and starts buzzing and you start thinking, "How do I do this one?" You panic, and that actually makes it harder for you to do the easier problems.
Last thing, if you're doing the test and you suddenly realised, "You know what I made a big mistake." Don't spend time erasing. Cross it off, it's faster to cross it off, and the AP scores are told if something is crossed off, they just ignore it. So be sure as you're going through the course, to follow along with how I model the ways to write out problems.
Guess, guessing is evil. I think so but also, one of your goals of course is to pass the AP test, and there's no way you're going to get every question right. There is no way. Some of the multiple choice questions will have often 70-80-90% of the students who take the test will get those right. There are other questions where only 20-30% of the students taking the test that year, get that one right. And that doesn't mean that they qualified the question, not at all. It's still included.
So be prepared, there is going to be some that you just can't do, and that's okay.
[0:14:00] Because they don't really compare you against you know, "Did you get 90% on the test? Did you get 90% right and you can't pass unless you get 70% right." That's not how it's done at all. It's a normed test. What they do is research on students actually taking the test, and they look to see how an overall very large group of students does on the test. And then they figure out what the passing score is and 70% probably isn't a passing score, it's probably lower than that. That being said, guessing in the multiple choice, you don't want just to randomly guess. Sorry they see it coming on that one.
If they didn't correct for guessing, you would score a little bit higher than you should. Because there is five possible choices and if you guessed on every one, you would probably get a 20% on the test and they don't want that to happen. So what they do is they give you one point for every question you get right on multiple choice. They give you nothing for something you leave blank, notice I said leave blank. It's okay to leave questions blank. If you put an answer down and it's wrong, they take away a quarter of a point.
On the average by doing that, the statistics show that if you take a quarter point off for everything that is wrong, it balances out the results of guessing. But still it doesn't mean that you can't guess sometimes. If you can narrow down a little bit and you know that say, two of the possible choices are obviously bogus, and you know it's one of three. Make an educated guess on those one or three, because the odds are a little bit in you're favour at that point.
If you're an old school guy like me, you've got to be told this one, use a calculator when possible. I grew up in the dark ages of slide rules. So I don't instinctively think of calculators.
[0:16:00] Or maybe you're a mathematical tough guy, you can do algebra all day long and you're right every time and yo just hate using that calculator. I'd still recommend you do it, when you're allowed to do it. The AP test has basically four sections. There is multiple choice with the calculator, multiple choice without. There is free response with the calculator, free response without.
Especially on the free response part, that involves the calculator, if you don't have a calculator you can't do it because you will be given crazy integrals that you can't integrate by hand. And you don't even want to do that many steps on it by hand, you want to do as little as possible by hand.
For example, later on the course you'll see some problems where I set up an integral and then I don't even try to integrate the thing. What I do is I type it in undistributed, I type it into the calculator and let the calculator find the area underneath that curve. Notice I said undistributed. I know it's instinct because you've done it for years, you always simplify. But you don't want to on this, because the calculator doesn't care if you simplified, as long as you use the correct number of parentheses to make the calculator understand the order of operations. Simplifying just increases the chances that you make some kind of an error.
Finally, when you are using the calculator on the free response section, you have to be careful on how you write down your answer. Part of the required answer is going to be set up for the problem. In other words a correctly written derivative or a correctly written integral or a graph, something like that. You have to write that down, even though you get final answer with your calculator, you have to. If you just write down, "I pressed this button on the calculator and then I pressed graph then I pressed second calculate integrate and got this answer."
[0:18:00] Sorry, they're not going to give you any credit for that. They don't care what brand of calculator you use. There is lots of good brands are out there. What they care about is that, you know how to write it out in technical form, write out the calculus with all the correct symbols and then get the answer using whatever calculator you have, and they don't care about those steps.
The functions you should really know on your calculator are finding zeros, usually by using a graph. Finding approximations for intersections between lines, that's a very important one, especially for finding limits of integrals. And finding the area underneath curves. Usually as you use that one, you have to find an integral but find the area underneath a curve for some formula that you can't integrate.
So what you've seen as some strategies for both reviewing for the exam and actually taking the AP exam.
Our introductory episode began with giving you some strategies that you can use to get ready for the test, to really solidify your knowledge for the calculus. Along with some hints that you can use during the test to increase your score, to format your answers in a way that you're going to get maximum credit on it. |
I will take great pride in helping you reach your personal goals.This subject introduces the concepts of variables and functions. These new concepts allow students to solve a range of problems involving unknown quantities in areas such as geometry, probability and statistics, and various real-world scenarios.
1. Identify and define Algebra terms.
2. |
A no-nonsense, practical guide to help you improve your algebra II skills with solid instruction and plenty of practice, practice, practice
Practice Makes Perfect: Algebra II presents thorough coverage of skills, such as handling decimals and fractions, functions, and linear and quadratic equations, as well as an introducing you to probability... more...
This book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals. Providing a useful and quick introduction to areas of research spanning these fields, Monomial Ideals is split into three parts. Part I offers a quick introduction to the modern theory... more...
This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features... more... |
Middle School Mathematics (0069)
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Topics Covered
In each of the content categories, the test will assess an examinee's ability to use appropriate mathematical language
and representations of mathematical concepts, to connect mathematical concepts to one another and to real-world situations,
and to integrate mathematical concepts to solve problems. Because the assessments were designed to measure the ability
to integrate knowledge of mathematics, answering any question may involve more than one competency and may involve competencies
from more than one content category. Representative descriptions of topics covered in each category are provided below.
I. Arithmetic and Basic Algebra
Add, subtract, multiply, and divide rational numbers expressed in various forms; apply the order of operations; identify
the properties of the basic operations on the standard number systems (e.g., closure, commutativity, associativity, distributivity);
identify an inverse and the additive and multiplicative inverses of a number; use numbers in a way that is most appropriate
in the context of a problem
Order any finite set of real numbers and recognize equivalent forms of a number; classify a number as rational, irrational,
real, or complex; estimate values of expressions involving decimals, exponents, and radicals; find powers and roots
Given newly defined operations on a number system, determine whether the closure, commutative, associative, or distributive
properties hold
Demonstrate an understanding of concepts associated with counting numbers (e.g., prime or composite, even or odd, factors,
multiples, divisibility)
Interpret and apply the concepts of ratio, proportion, and percent in appropriate situations
Recognize the reasonableness of results within the context of a given problem; using estimation, test the reasonableness of
results
Determine the equations of lines, given sufficient information; recognize and use the basic forms of the equation for a straight line
Solve and graph linear equations and inequalities in one or two variables; solve and graph systems of linear equations and
inequalities in two variables; solve and graph nonlinear algebraic equations; solve equations and inequalities involving absolute
values |
Introductory Linear Algebra An Applied First Course
9780131437401
ISBN:
0131437402
Edition: 8 Pub Date: 2004 Publisher: Prentice Hall
Summary: This book presents an introduction to linear algebra and to some of its significant applications. It covers the essentials of linear algebra (including Eigenvalues and Eigenvectors) and shows how the computer is used for applications.Emphasizing the computational and geometrical aspects of the subject, this popular book covers the following topics comprehensively but not exhaustively: linear equations and matrices an...d their applications; determinants; vectors and linear transformations; real vector spaces; eigenvalues, eigenvectors, and diagonalization; linear programming; and MATLAB for linear algebra.Its useful and comprehensive appendices make this an excellent desk reference for anyone involved in mathematics and computer applications.
Kolman, Bernard is the author of Introductory Linear Algebra An Applied First Course, published 2004 under ISBN 9780131437401 and 0131437402. One hundred ninety nine Introductory Linear Algebra An Applied First Course textbooks are available for sale on ValoreBooks.com, thirty two used from the cheapest price of $14.27, or buy new starting at $13337401-4-0-3 Orders ship the same or next business day. Expedited shipping within U.S. [more]
May include moderately worn cover, writing, markings or slight discoloration. SKU:9780131437401 |
Matrices as a rectangular array of real
numbers, equality of matrices, addition,
multiplication by a scalar and product of
matrices, transpose of a matrix, determinant of
a square matrix of order up to three, inverse of
a square matrix of order up to three, properties
of these matrix operations, diagonal, symmetric
and skew-symmetric matrices and their
properties, solutions of simultaneous linear
equations in two or three variables.
Addition and multiplication rules of probability,
conditional probability, Bayes Theorem,
independence of events, computation of
probability of events using permutations and
combinations.
Trigonometry: Trigonometric functions, their
periodicity and graphs, addition and subtraction
formulae, formulae involving multiple and submultiple angles, general solution of
trigonometric equations.
Relations between sides and angles of a
triangle, sine rule, cosine rule, half-angle
formula and the area of a triangle, inverse
trigonometric functions (principal value only).
Analytical geometry (2 dimensions):
Cartesian coordinates, distance between two
points, section formulae, shift of origin.
Equation of a straight line in various forms,
angle between two lines, distance of a point
from a line; Lines through the point of
intersection of two given lines, equation of the
bisector of the angle between two lines,
concurrency of lines; Centroid, orthocentre,
incentre and circumcentre of a triangle.
Equation of a circle in various forms, equations
of tangent, normal and chord.
Parametric equations of a circle, intersection of
a circle with a straight line or a circle, equation
of a circle through the points of intersection of
two circles and those of a circle and a straight
line.
Equations of a parabola, ellipse and hyperbola
in standard form, their foci, directrices and
eccentricity, parametric equations, equations of
tangent and normal.
Locus Problems.
Analytical geometry (3 dimensions):
Direction cosines and direction ratios, equation
of a straight line in space, equation of a plane,
distance of a point from a plane.
Limit and continuity of a function, limit and
continuity of the sum, difference, product and
quotient of two functions, L'Hospital rule of
evaluation of limits of functions.
Even and odd functions, inverse of a function,
continuity of composite functions, intermediate
value property of continuous functions.
Derivative of a function, derivative of the sum,
difference, product and quotient of two
functions, chain rule, derivatives of polynomial,
rational, trigonometric, inverse trigonometric,
exponential and logarithmic functions.
Derivatives of implicit functions, derivatives up
to order two, geometrical interpretation of the
derivative, tangents and normals, increasing
and decreasing functions, maximum and
minimum values of a function, Rolle's Theorem
and Lagrange's Mean Value Theorem
Using Logarithmic Tables
Authors
Express the given number "n" in the form of m * 10pwhere 1≤m<10 and p is an integer(positive or negative whole number).
For example number 2 is expressed as 2*100
log n become equal to p + log m
log 2 becomes equal to 0 + log 2
p is called the characeristic and log m is called the mantissa. Mantissa is read from the logarithmic tables.
Logarithmic tables are show three sets of columns
i) the first set of column on the extreme left contains numbers from 10 to 99.
ii) in the seocnd set there 10 columns headed by 0,1,2,...,9
iii) after this, in the third set there 9 more columns headed by 1,2,3...9. These are known as mean differences.
As 1≤m<10, the mantissa is for a number between 1 and 10. Hence the interpretation of the first set of column in the table is 1.0 to 9.9, If you add the digit in the second set one more digit is added to the number. Which mean 1.0 becomes 1.01. If we add a digit in the third column on more digit is added to the number. Which means 1.01 becomes 1.011.
Hence log 2 = 0 + 0.3010 = 0.3010
How to see its antilogarithm.
Antilogaritm tables are written from .00. If mantissa of a logarithm is .00, then antilogarithm is 1.000
Antilogarithm of .3010 is equal to 2.000
As the characteristic of the number is 0 the number is 2.0*100. Which is equal to 2.
Suppose the problem is to find 2^(1/6). It is 2 to the power (1/6).
When we take logarithms, it becomes (1/6)* log 2 which is equal to (1/6)*(0.3010) = 0.0617 (rounded) |
Today at Central Library Cooperative of Knowledge
Upon entering high school students should have completed all the necessary math courses available at the junior high level. Students should know basic math such as addition, subtraction, multiplications and division. They should also have an understanding of algebra, geometry, percentages, decimals, data analysis and probability, along with other junior...
An online Bible study course can be useful in helping an individual to learn and understand the teachings of the Bible, and how to apply them practically in daily life. This is particularly ideal for those who have no time to spare because of other commitments. Online Bible study courses...
For some reason many college students are anxious about taking algebra. Many college students have been out of high school for many years. In fact, a moderate percentage of college students are men and women in their mid to late 30s, and a smaller percentage of students entering...
This is a course that teaches the integration between mathematics and physics. It will demonstrate and help students to understand the application of math to the various problems in physics. Under the umbrella of mathematics this form of calculations often falls under the titles of partial differential equations and algebraic...
Political science, the study of government and politics, public issues and the processes through which conflict over such issues are resolved, is fascinating, surprising, and affects everyone, every day, in many ways. And an education in political science involves much more than merely learning about politics and history.
As the world... |
McConnell, Brue, and Flynn is the #1 principles of economics textbook in the world. It has long set the standard for providing high-quality economic content to instructors and students alike. The 19th edition continues to be innovative while building upon the traditions of helping the student understand and apply the economic perspective, reason accurately and objectively about economic matters, and develop a lasting interest in economics and the economy Each graph in Connect for McConnell maintains the "look and feel" of the graphs in the printed text to ensure consistency for the student and support the learning process.
End of Chapter and Testbank Content
Instructors can create automatically graded assignments using extensive material directly from McConnell/Brue/Flynn's 19th edition. End of chapter problems appear in both static and algorithmic format to provide practice with multiple versions of problem types. End of chapter essay questions can be assigned in their original, manually-graded form, or in autogradable format. Select problems feature narrated, step-by-step explanations. Thousands more autogradable questions can be found in McConnell's two comprehensive test banksMath Preparedness Modules
Provide review of basic algebra, slope, percentages, and graphing to help students acquire the appropriate background in mathematics necessary for success in economics.
Self-Quiz and Study
Connect's Self-Quiz and Study takes students through a practice test, then recommends readings, study tools, and additional practice. |
Find a San Anselmo ACTAlgebra 2 introduces independent and dependent variables and how their solution can be determined by for linear relationships for two or three variables. Algebra 2 also gives an overview of more complex mathematical functions like basic trigonometric functions, power functions, logarithms, and |
Ready to learn the fundamentals of complexvariables but can't seem to get your brain to function on the right level? No problem! Add ComplexVariables Demystified to the equation and you'll exponentially increase your chances of understanding this fascinating subject. Written in an easy-to-follow format, this book begins by covering complex numbers, functions, limits, and continuity, and the Cauchy-Riemann equations. You'll delve into sequences, Laurent series, complex integration, and residue theory. Then it's on to conformal mapping, transformations, and boundary value problems. Hundreds of examples and worked equations make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning.
The book may serve as a text for an undergraduate course in complexvariables designed for scientists and engineers or for mathematics majors interested in further pursuing the general theory of complex analysis. The only prerequistite is a basic knowledge of advanced calculus. The presentation is also ideally suited for self-study.
Working as an effective professional Java developer requires you to know Java APIs, tools, and techniques to solve a wide variety of Java problems. Building upon Ivor Hortons Beginning Java 2, this resource shows you how to use the core features of the latest JDK as well as powerful open source tools such as Ant, JUnit, and Hibernate. It will arm you with a well rounded understanding of the professional Java development landscape.
Susanna Epp's DISCRETE MATHEMATICS, THIRD EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof.
There's plenty of documentation on installing and configuring the Apache web server, but where do you find help for the day-to-day stuff, like adding common modules or fine-tuning your activity logging? That's easy. The new edition of the Apache Cookbook offers you updated solutions to the problems you're likely to encounter with the new versions of Apache.
Acclaimed economists Hall and Lieberman have made the latest edition of MICROECONOMICS: PRINCIPLES AND APPLICATIONS as current as the headlines. Since real-world policy issues, decisions, and applications impact you on an everyday basis, Hall and Lieberman use these true, cutting-edge examples to illustrate core economic theory and application. Straightforward and easy-to-understand, this comprehensive text will equip you with a solid foundation in economics that you can build upon wherever your career path may lead. Hall and Lieberman's careful focus on important economic theories and applications, and how they relate to practical questions, effectively communicates that economics is an integrated, powerful body of knowledge that can address complex domestic and global issues. A wealth of interactive online exercises, graphing applications, and research resources will help reinforce your understanding of economic principles. |
Algebra I—Semester B
Double the equations, double the fun.
Course Description
It doesn't matter whether you love it or hate it. The fact remains that Algebra is around and by golly, it's here to stay.
What's not to love about it, though? We'll admit that it might get a bit irrational from time to time, and there's no denying a few of its radical tendencies, but it can simplify your life in more ways than the square root of one. Besides, its graphing skills are off the charts. Why not give it a chance? Take it from us: there's a high probability of it working out.
Semester B is chock-full of stuff that we haven't come across in other math classes. In this course, we'll
start out in familiar territory with systems of equations.
move quickly onto radicals and quadratics, lines' curvy cousins.
open the gate to polynomials and rational expressions, which are all about factoring. (And plaid! They're pretty stylish.)
finish up with probability and statistics. (Well, maybe. There's a 99% chance we'll get there.)
Get ready for interactive readings, activities, and problem sets galore.
P.S. Algebra I is a two-semester course. You're looking at Semester B, but you can check out Semester A hereRequired Skills
Knowledge of pre-algebra concepts and the material from Semester A of this course
Course Breakdown
Unit 7. Systems of Equations
After having graphed linear equations and learned the bare bones of functions, we'll solve and graph systems of linear equations. Whether they're given as equations or word problems, we'll be able to tackle these problems in their many forms. Wear a helmet, though. The last thing you want is a concussion.
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Unit 8. Radicals and Quadratic Equations
We'll start by performing major arithmetic operations on square roots and by the time this unit's over, we'll be able to wrangle radicals just about anywhere. That'll lead us into quadratic equations, which are like linear equations with more twists and turns. (We're not kidding. Have you seen them behind the wheel?)
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Unit 9. Polynomials
Polynomials are all about factoring. They also have a fondness for Bocce ball, but that's not as relevant. Once we learn a thing or five about factoring, we'll be able to understand polynomials on the equation level. And if you really want to connect with polynomials, consider joining in a round of Bocce ball.
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Unit 10. Division of Polynomials
Right when you thought you knew all there was to know about polynomials, we go and start dividing them. Luckily, all our old factoring tricks will still apply and they'll be even more useful as we start dealing with rational expressions. Too bad they aren't nearly as rational as their name suggests!
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Unit 11. Probability and Statistics
We'll start out with the beautification of data, because data alone is just boring. Get ready for stem and leaf plots, bar graphs, histograms, pie charts, box and whisker plots, and finally scatter plots. Then, we'll move on to probability, which is probably going to be fun. Actually, scratch that. It's definitely going to be fun. |
Synopses & Reviews
Publisher Comments:
An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture. 1975 edition. References. List of Symbols. Index.
Book News Annotation:
A brief introduction for undergraduate students and teachers, presenting detailed proofs and explanations of the elementary components of classical algebraic number theory. Begins with divisibility and Gaussian primes, and proceeds to ideal classes and class numbers and the Fermat conjecture. A slightly revised and totally unexpurgated edition of the 1975 publication by the Mathematical Association of America. Annotation c. by Book News, Inc., Portland, OR (booknews@booknews.com)
Synopsis:
Excellent intro to basics of algebraic number theory. Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral bases; uses of arithmetic in algebraic number fields; more. 1975 |
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more |
The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confocal ellipses.
The book demonstrates the advantage of purely geometric methods of studying conics. It contains over 50 exercises and problems aimed at advancing geometric intuition of the reader. The book also contains more than 100 carefully prepared figures, which will help the reader to better understand the material presented.
Readership
Undergraduate and graduate students interested in geometry.
Reviews
"The book is well written and contains a lot of figures illustrating the theorems and their proofs." |
More About
This Textbook
Overview
This book is a short, focused introduction to Mathematica, the comprehensive software system for doing mathematics. Written for the novice, this engaging book contains an explanation of essential Mathematica commands, as well as the rich Mathematica interface for preparing polished technical documents. Mathematica can be used to graph functions, solve equations, perform statistics tests, and much more. In addition, it incorporates word processing and desktop publishing features for combining mathematical computations with text and graphics, and producing polished, integrated, interactive documents. You can even use it to create documents and graphics for the Web. This book explains everything you need to know to begin using Mathematica to do all these things and more. Written for Mathematica version 3, this book can also be used with earlier versions of the software. Intermediate and advanced users may even find useful information here, especially if they are making the switch to version 3 from an earlier version.
Editorial Reviews
From the Publisher
"Coombes and colleagues offer a 'short, focused introduction to Mathematica,' designed to be useful to beginners as well as more experienced Mathematica users. The text is well written; graphics are used effectively." Choice |
Beginning Algebra With Applications
9780618803590
ISBN:
0618803599
Pub Date: 2007 Publisher: Houghton Mifflin
Summary: Intended for developmental math courses in beginning imm...ediate feedback, reinforcing the concept, identifying problem areas, and, overall, promoting student success."New!" "Interactive Exercises" appear at the beginning of an objective's exercise set (when appropriate), and provide students with guided practice on some of the objective's underlying principles."New!" "Think About It" Ex."New!" "Important Points" have been highlighted to capture students' attention. With these signposts, students are able to recognize what is most important and to study more efficiently."New!" A Concepts of Geometry section has been added to Chapter 1."New!" Coverage of operations on fractions has been changed in Section 1.3 so that multiplication and division of rational numbers are presented first, followed by addition and subtraction"New!" A Complex Numbers section has been added to Chapter 11, "Quadratic Equations.""New Media!" Two key components have been added to the technology package: HM Testing (powered by Diploma) and, as part of the Eduspace course management tool, HM Assess, an online diagnostic assessment tool.
Aufmann, Richard N. is the author of Beginning Algebra With Applications, published 2007 under ISBN 9780618803590 and 0618803599. Two hundred seventy seven Beginning Algebra With Applications textbooks are available for sale on ValoreBooks.com, one hundred twenty nine used from the cheapest price of $3.00, or buy new starting at $51 [more(never been opened).Might contain minor shelf ware or remainder marks.100% satisfaction guaranteed or your money back.Thank you for your support.WE SHIP NEXT BUSINESS DAY IN BUBBLE MAILER WITH TRACKING NUMBER.i1[less]
BRAND NEW BOOK(never been opened). Might contain minor shelf ware or remainder marks.100% satisfaction guaranteed or your money back. Thank you for your support. WE SHIP NEXT BUSINESS DAY IN BUBBLE MAILER WITH TRACKING NUMBER. i1. [less] |
Linear, simultaneous algebraic equations, ordinary differential equations, partial differential equations; and difference equations are the four most common types of equations encountered in engineering. This book provides methods for solving general equations of all four types and draws examples from the major branches of engineering. Problems illustrating electric circuit theory, linear systems, electromagnetic field theory, mechanics, bending of beams, buckling of columns, twisting of shafts, vibration, fluid flow, heat transfer, and mass transfer are included. Essential Engineering Equations is an excellent book for engineering students and professional engineers. |
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SJSU Catalog
MATH 106
Intuitive Geometry
Description
Introductory geometry, measurement, inductive and deductive reasoning, introduction to transformations, and problem-solving techniques; technology integrated throughout the course.
Prerequisite: MATH 012 and MATH 105 (with grades of "C-" or better); two years of high school algebra; one year of high school geometry. |
textbook introduces several major numerical methods for solving various partial differential equations (PDEs) in science and engineering, including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques that include the classic finite difference method and the finite element method as well as state-of-the-art numerical methods, such as the high-order compact difference method and the radial basis function meshless method.
Helps Students Better Understand Numerical Methods through Use of MATLAB® The authors uniquely emphasize both theoretical numerical analysis and practical implementation of the algorithms in MATLAB, making the book useful for students in computational science and engineering. They provide students with simple, clear implementations instead of sophisticated usages of MATLAB functions.
All the Material Needed for a Numerical Analysis Course Based on the authors' own courses, the text only requires some knowledge of computer programming, advanced calculus, and difference equations. It includes practical examples, exercises, references, and problems, along with a solutions manual for qualifying instructors. Students can download MATLAB code from enabling them to easily modify or improve the codes to solve their own problems.
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The book not only cover classic finite difference methods, but also finite element methods, and meshless methods. The book also include some advanced topics such as high-order compact difference methods, radial basis meshless methods and Maxwell's equaations in dispersive media.
I found those codes are very helpful for me to learn the algorithms (many books just talk the algorithms in the air), and I can even extend some codes in the book immediately for my research, since the authors kindly released their most recent work (such as compact scheme and meshless methods, which are currently quite active research areas) in the book.
I bought this book from Amazon.com for a graduate course in numerical solution of PDE. It comes with a CD that contain all MATLAB codes. This book is kind of middle of engineer and mathematician's perspective on numerical analysis. MATLAB codes runs great, exercise problems are also good to understand many difficult relevant concepts. Overall, I think, this book is one the best numerical analysis book. Amazon did a little delay to deliver this book to me. |
Econometrics
Introduction to Econometrics provides students with clear and simple mathematics notation and step-by step explanations of mathematical proofs to ...Show synopsisIntroduction to Econometrics provides students with clear and simple mathematics notation and step-by step explanations of mathematical proofs to give them a thorough understanding of the subject. Extensive exercises are incorporated throughout to encourage students to apply the techniques and build confidence. This new edition has been thoroughly revised in line with market feedback. Retaining its student-friendly approach, Introduction to Econometrics has a comprehensive revision guide to all the essential statistical concepts needed to study econometrics, more Monte Carlo simulations than before and new summaries and non-technical introductions to more advanced topics at the end of chapters. Online Resource Centre For lecturers: - Instructor manuals for the text and data sets, detailing the exercises and their solutions - PowerPoint slides For students: - Data sets - Study guide - Software manual - PowerPoint slides with explanations - Contact the author |
Formula Reference is a simple application that helps you access a vast collection of math formulas, with thousands of mathematical equations. This app can help you as a quick reference (cheat sheet) so you can access math formulas whenever and wherever you want. This math formulary app is one of the most comprehensive of its kind includes |
This book, meant for the undergraduate students of all disciplines, is written with the intention of developing the basic concepts in the minds of students. With the right blend of theory in the right depth and a wide variety of problems the book is a perfect offering on the subject.
Key features
Emphasis on the basic concepts: Detailed coverage on the topics related to Projection like Orthographic Projections, Projection of Points, Projection of Straight lines, Projection of Planes and Solids, etc.( the basic topics which builds up the fundamentals in Graphics) enables the students to gain a firm knowledge on the subject.
(Refer chapters 7,8,9,10 and 11of our book.). The same comprehension is missing in the competition books.
Clarity in concepts: Good clarity in concepts with step-by-step explanations in a simplified manner. (Refer Chapter 7 on Orthographic Projections) |
Description
Almost everyoneis acquainted with plane Euclidean geometry as it is usually taught in high school. This book introduces the reader
to a completely different way of looking at familiar geometrical facts.
It is concerned with transformations of the plane that do not alter the
shapes and sizes of geometric figures. Such transformations play a
fundamental role in the group theoretic approach to geometry. The
treatment is direct and simple. The reader is introduced to new ideas
and then is urged to solve problems using these ideas. The problems form
an essential part of this book and the solutions are given in detail in
the second half of the Yaglom - Geometric Transformations I |
Now in its eighth edition, this text masterfully integrates skills, concepts, and activities to motivate learning. It emphasises the relevance of mathematics to help students learn the importance of the information being covered. This approach ensures that they develop a sold mathematics foundation and discover how to apply the content in the real |
Mathematical problem solving has been the subject of substantial and often controversial research for several decades. We use the term, problem solving, here in a broad sense to cover a range of activities that challenge and extend one's thinking. In this chapter, we initially present a sketch of past decades of research on mathematical problem solving and its impact on the mathematics curriculum. We then consider some of the factors that have limited previous research on problem solving. In the remainder of the chapter we address some ways in which we might advance the fields of problem-solving research and curriculum development. |
MATH 222 – MATHEMATICS FOR ELEMENTARY EDUCATION
Theory and application of arithmetic, algebra, geometry, and probability at the primary school level. This course is exclusively for students pursuing a certification in elementary school education; it is a co-requisite of EDUC 322 (3 credits).
MATH 261 –SYMBOLIC COMPUTING - Elective Concepts and practical use of a Computer Algebra System such as Maple: Data types and control structures. Two- and three dimensional plotting. Symbolic computing of solutions to selected problems in algebra and analysis. Contrasting exact and numerical solutions (3 credits).
MATH 341 –ABSTRACT ALGEBRA I
The first part of a two semester sequence. An introduction to algebraic structures with an emphasis on groups, normal subgroups, cosets, Lagrange's Theorem, and the fundamental homomorphism theorems (3 credits).
Pre-requisites: Linear Algebra I.
MATH 342 – ABSTRACT ALGEBRA II - Elective
The second part of a two semester sequence. Further study of algebraic structures, such as rings, integral domains, fields. The homomorphism theorem and its applications (3 credits).
Pre-requisites: Abstract Algebra I. |
realgebra
This book is designed to help a variety of readers bridge the gap between arithmetic and algebra. Slightly more rigorous than most arithmetic books - ...Show synopsisThis book is designed to help a variety of readers bridge the gap between arithmetic and algebra. Slightly more rigorous than most arithmetic books -- but not as difficult or comprehensive as elementary algebra books -- it uses an innovative, "integrated arithmetic/algebra approach" that develops algebraic skills using "small steps," spirals topics throughout, emphasizes that algebra rules are just an "extension" of arithmetic, and teaches readers the specific study skills necessary to accommodate their individual learning styles -- including skills for "translating" the language of mathematics into plain English. Covers: Addition and Subtraction of Whole Number Expressions. Multiplication and division of Whole Number Expressions. Signed Numbers. Fractions and Ratio and Proportion. Equations and Polynomials. Fractional Expressions. Decimals and Percents and Radical Expressions. Graphing and Statistics. Measurement and Geometric Figures. For those with math anxiety or frustration who need to make the transition from arithmetic to algebra.Hide synopsis17735481756 |
Mathematics - General (484 results)
The purpose of this book, as implied in the introduction, is as follows: to obtain a vital, modern scholarly course in introductory mathematics that may serve to give such careful training in quantitative thinking and expression as well-informed citizens of a democracy should possess. It is, of course, not asserted that this ideal has been attained. Our achievements are not the measure of our desires to improve the situation. There is still a very large "safety factor of dead wood" in this text. The material purposes to present such simple and significant principles of algebra, geometry, trigonometry, practical drawing, and statistics, along with a few elementary notions of other mathematical subjects, the whole involving numerous and rigorous applications of arithmetic, as the average man (more accurately the modal man) is likely to remember and to use. There is here an attempt to teach pupils things worth knowing and to discipline them rigorously in things worth doing.<br><br>The argument for a thorough reorganization need not be stated here in great detail. But it will be helpful to enumerate some of the major errors of secondary-mathematics instruction in current practice and to indicate briefly how this work attempts to improve the situation. The following serve to illustrate its purpose and program:<br><br>1. The conventional first-year algebra course is characterized by excessive formalism; and there is much drill work largely on nonessentials.
In issuing this new volume of my Mathematical Puzzles, of which some have appeared in the periodical press and others are given here for the first time, I must acknowledge the encouragement that I have received from many unknown correspondents, at home and abroad, who have expressed a desire to have the problems in a collected form, with some of the solutions given at greater length than is possible in magazines and newspapers. Though I have included a few old puzzles that have interested the world for generations, where I felt that there was something new to be said about them, the problems are in the main original. It is true that some of these have become widely known through the press, and it is possible that the reader may be glad to know their source.<br><br>On the question of Mathematical Puzzles in general there is, perhaps, little more to be said than I have written elsewhere. The history of the subject entails nothing short of the actual story of the beginnings and development of exact thinking in man. The historian must start from the time when man first succeeded in counting his ten fingers and in dividing an apple into two approximately equal parts. Every puzzle that is worthy of consideration can be referred to mathematics and logic. Every man, woman, and child who tries to "reason out" the answer to the simplest puzzle is working, though not of necessity consciously, on mathematical lines. Even those puzzles that we have no way of attacking except by haphazard attempts can be brought under a method of what has been called "glorified trial" - a system of shortening our labours by avoiding or eliminating what our reason tells us is useless. It is, in fact, not easy to say sometimes where the "empirical" begins and where it ends.<br><br>When a man says, "I have never solved a puzzle in my life," it is difficult to know exactly what he means, for every intelligent individual is doing it every day. The unfortunate inmates of our lunatic asylums are sent there expressly because they cannot solve puzzles - because they have lost their powers of reason. If there were no puzzles to solve, there would be no questions to ask; and if there were no questions to be asked, what a world it would be! We should all be equally omniscient, and conversation would be useless and idle.<br><br>It is possible that some few exceedingly sober-minded mathematicians, who are impatient of any terminology in their favourite science but the academic, and who object to the elusive x and y appearing under any other names, will have wished that various problems had been presented in a less popular dress and introduced with a less flippant phraseology.
Bringing to life the joys and difficulties of mathematics this book is a must read for anyone with a love of puzzles, a head for figures or who is considering further study of mathematics. On the Study and Difficulties of Mathematics is a book written by accomplished mathematician Augustus De Morgan. Now republished by Forgotten Books, De Morgan discusses many different branches of the subject in some detail. He doesn't shy away from complexity but is always entertaining. One purpose of De Morgan's book is to serve as a guide for students of mathematics in selecting the most appropriate course of study as well as to identify the most challenging mental concepts a devoted learner will face. "No person commences the study of mathematics without soon discovering that it is of a very different nature from those to which he has been accustomed," states De Morgan in his introduction. The book is divided into chapters, each of which is devoted to a different mathematical concept. From the elementary rules of arithmetic, to the study of algebra, to geometrical reasoning, De Morgan touches on all of the concepts a math learner must master in order to find success in the field. While a brilliant mathematician in his own right, De Morgan's greatest skill may have been as a teacher. On the Study and Difficulties of Mathematics is a well written treatise that is concise in its explanations but broad in its scope while remaining interesting even for the layman. On the Study and Difficulties of Mathematics is an exceptional book. Serious students of mathematics would be wise to read De Morgan's work and will certainly be better mathematicians for it.
eBook
Rapid ArithmeticQuick and Special Methods in Arithmetical Calculation Together With a Collections of Puzzles and Curiosities of Numbers
by T. O'Conor Sloane
Rapid Arithmetic: Quick and Special Methods in Arithmetical Calculation, authored by doctor and lawyer T. O'Conor Sloane, is a guidebook to improving your mental math skills. The book is a mixture of valuable and applicable strategies for solving problems of arithmetic, and simple and amusing mental diversions. It is a work that treats the subject of mathematics as something that can be enjoyed. Rapid Arithmetic opens with a brief section on notation and signs before delving more fully into the subject matter. Separate chapters are presented covering addition, subtraction, multiplication and division, as well as fractions, the decimal point, exponents, and several other topics. Each chapter consists of an overview of the topic, as well as a variety of different strategies for tackling different mathematical problems. The author presents short practice activities throughout the work, intended to both reinforce the lesson and serve as fun diversion for the reader. T. O'Conor Sloane has a gift for making a challenging subject entertaining. Rapid Arithmetic is not a book only for the math enthusiast, but for anybody that sees the value in honing their arithmetical skills. It is a well-written and clearly presented treatise on the topic. Rapid Arithmetic: Quick and Special Methods in Arithmetical Calculation is the rare text about mathematics that can appeal even to one not interested in the subject. Sloane's methods can actually improve the daily life of the reader by allowing one to more quickly work out common math problems, and for this reason his work is highly recommended.
In this book, all the principles of Arithmetic are fully developed, and sufficient examples are given to fix them on the mind.<br><br>When a student is very apt and thoroughly understands the Primary Lessons, he may omit the Elementary, and immediately take up this book, which is complete in itself.<br><br>I have discarded puzzles of every kind, which only perplex the student without advancing him a step in science.<br><br>A few simple principles of algebra are introduced, in order to elucidate more clearly, the different functions of interest, the series of equal ratios, and the square and cube root.<br><br>Problems in mensuration are also given, the principles of which are derived from Geometry.<br><br>Arithmetic is a pure mathematical science, and if its principles are systematically developed, the student will progress with easy and rapid steps, and when he has finished this book, he will discover that he has already so far ascended the hill of science that a retrospect will present to him many beauties which are greatly enhanced when seen in their harmonious relation to each other.
There are many men and women who, from lack of opportunity or some other reason, have grown up in ignorance of the elementary laws of science. They feel themselves continually handicapped by this ignorance. Their critical faculty is eager to submit, alike old established beliefs and revolutionary doctrines, to the test of science. But they lack the necessary knowledge.<br><br>Equally serious is the fact that another generation is at this moment growing up to a similar ignorance. The child, between the ages of six and twelve, lives in a wonderland of discovery; he is for ever asking questions, seeking explanations of natural phenomena. It is because many parents have resorted to sentimental evasion in their replies to these questionings, and because children are often allowed either to blunder on natural truths for themselves or to remain unenlightened, that there exists the body of men and women already described. On all sides intelligent people are demanding something more concrete than theory; on all sides they are turning to science for proof and guidance.<br><br>To meet this double need - the need of the man who would teach himself the elements of science, and the need of the child who shows himself every day eager to have them taught him - is the aim of the "Thresholds of Science" series.<br><br>This series consists of short, simply written monographs by competent authorities, dealing with every branch of science - mathematics, zoology, chemistry and the like. They are well illustrated, and issued at the cheapest possible price.
William Timothy Call was a mathematician and an individual interested in using mathematics to improve daily life. In A New Method in Multiplication and Division, Call presents a method he personally devised to solve multiplication and division problems. In his introduction the author acknowledges that the method presented in this book is of no great significance, rather it is a curious way of attacking a problem that likely differs from what the reader has been taught. It is clear from the beginning that this is a book aimed at those with a keen interest in math. The book opens with Call's method for solving simple multiplication problems, before progressing to his method for problems of division. A New Method in Multiplication and Division is a brief work and one that will appeal to those for whom mathematics is a hobby. The subject matter is largely trivial, and while the methods detailed are effective, they are presented largely as a novelty. Those who are passionate about mathematics will likely enjoy the casual approach of the author and the general tone of the book. For readers passionate about mathematics and problem solving, William Timothy Call's A New Method in Multiplication and Division is recommended. This is not a textbook or a resource guide, but rather a lighthearted presentation of a simple but alternative mathematical approach, intended to entertain and inform the reader.
Joseph Ray's Ray's New Practical Arithmetic is a textbook intended for use by teachers instructing mathematics. The book guides the reader through the most important principals of arithmetic while presenting questions and solutions. The text opens with several brief chapters on notation, outlining both the Arabic and the Roman methods. From there, Ray proceeds to tackle a host of arithmetical subjects, including addition, subtraction, multiplication, division, factoring, fractions, percentages, calculating interest, taxes, ratios, and more. Each section consists of a core lesson accompanied by a series of study questions that can be posed to students. Ray's New Practical Arithmetic accomplishes its goal of plainly and concisely presenting its subject matter. As an instructor's guide, the book is a success, and one that could still be used as effectively more than one hundred years after its initial publication as in it's original time. The text covers all of the material one would expect, and does so in a fashion that makes the life of a teacher easier. Readers seeking a guidebook for teaching arithmetic should consider Ray's New Practical Arithmetic. The book can be used by either the independent learner or the classroom instructor, and the fundamental math skills covered remain essential to this day solvingThis work outlines for students of the third and fourth high-school years a more advanced and more thorough course in applied business mathematics than the ordinary first-year course in elementary commercial arithmetic. The attempt has been made to construct a practical course which will contain all the essential mathematical knowledge required in a business career, either as employee, manager, or employer.<br><br>The fact that the field has been covered in this text both more intensively and more comprehensively than it has yet been covered in other texts, and the added fact that the material gathered together has stood the test of six years experience in the teaching of large and varied classes of the fourth year in a city high school, seem sufficient warrant for its publication.<br><br>The work is adapted not only for use in the classroom but also as a reference manual for those actively engaged in business life. Thus it will be found a practical guide for, young employees who wish through private study to master the fundamental mathematics involved in "running a business." The tabulations, forms, illustrative examples, charts, logarithmic applications, and simple rules, are all applicable to the financial and other mathematical problems which business presents. Lack of knowledge of this side of a business, or inability to work out its mathematics, often results in haphazard guessing where accurate and careful calculations are required.
This extensive collection of Mathematical Tables comprehends the most important of those required in Trigonometry, Mensuration, Land-surveying, Navigation, Astronomy, Geodetic Surveying, and the other practical branches of the Mathematical Sciences. This new and greatly enlarged Edition is well adapted for general use, and will be found to be more convenient, in size and arrangement, than any other compilation of the kind. The Tables of Logarithms of Numbers, of Logarithmic Sines, Tangents, and Secants; also those of Natural Sines, Cosines, Versed Sines and Chords, Tangents and Cotangents, Secants and Cosecants, and of Circular Arcs, are carried to seven decimal places, and are so arranged that the functions required in any calculation may all be foundy so far as possible, at the same opening of the book. As accuracy is the most important element in such tables, the greatest care has been bestowed in collating the whole with the best editions of the tables of Taylor, Button, Callet, Kohler, Schron, and Shortrede; and wherever any difference has been found, the logarithms so differing have been calculated anew, so that it is confidently hoped these Tables will be found at least as accurate as any set hitherto published.
Until recently upper elementary and high school work in mathematics was planned for the pupil who was expected to continue it in the university. Although logical, its arrangement was neither psychological nor pedagocal. Some progress, however, has been made recently in adapting the study to the needs and abilities of pupils. In the junior high and intermediate school, work in mathematics in the seventh, eighth, and ninth grad should be complete in itself and at the same time preparatory to senior high school work. No effort should be made to fihish arithmetic in the eighth grade and abra in the ninth, while denying the child the interest and beauty that lie in geometry and trigonometry until his taste for mathematics has been destroyed. Nor will alternate bits of formal abra, geometry, and trigonometry solve the problem. The result is a mastery of none and a confusion in all. Experience has proved that the necessary elements of arithmetic can be taught and certain definite skill developed in the first six grades. In the seventh grade business appheations of arithmetic with the simplest elements of bookkeeping should be given.
The New Primary Arithmetic is designed for the use of pupils of the second, third, and fourth school years, the first chapter covering the ground to be completed by the end of the second year, and each of the remaining chapters furnishing a half-year swork. In the distribution of the subject-matter, care has been taken to combine the best features of the spiral and the topical arrangement, and to adapt the work at every stage to the growing powers of the pupil. A large quantity of material for drill is provided under each subdivision before a new one is taken up, while carefully graded reviews are continued throughout. Especial attention has been given to the grading and the character of the problems. They deal with numbers smaller than those used in the corresponding abstract work; the conditions are limited to such as are within the experience or the comprehension of the average pupil; and the solution of those in the earlier chapters involves but a single operation.
Counting a series of things and keeping tally of the tens on the fingers were processes used by primitive peoples. From the ten fingers arose ultimately the decimal system of numeration. Recording the results of counting was done by the Egyptians and other ancient nations by means of strokes and hooks; for one thing a single stroke | was made, for two things two strokes || were used, and so on up to ten which was represented by Π. Then eleven was written |Π, twelve ||Π, and so on up to twenty, or two tens, which was represented by ΠΠ. In this way the numeration proceeded up to a hundred, for which another symbol was employed.<br><br>Names for ||, |||, ||||, ΠΠ, etc., appear in the Egyptian hieroglyphics, but a special symbol for each name is not used. Probably the Hindoos first invented such symbols, and passed them on to the Arabs, through whom they were introduced into Europe.<br><br>2<br><br>Greek Notation<br><br>The Greeks used an awkward notation for recording the results of counting.
This text differs widely from that marked out by custom and tradition. It treats the various branches of mathematics more with reference to their unities and less as isolated entities (sciences). It seeks to give pupils usable knowledge of the principles underlying mathematics and ready control of them. These texts are not an experiment; they were thoroughly tried out in mimeograph form on hundreds of high school pupils before being put into book form. The scope of Books I and II does not vary greatly from that covered in algebras and geometries of the usual type. However, Book I is different in that arithmetic, algebra, and geometry are treated side by side. The effect of this arrangement is increased interest and power of analysis on the part of the learner, and greater accuracy in results. Some pupils like arithmetic, others like algebra, still others like geometry; the change is helpful in keeping up interest. The study of geometry forces analysis at every step and stage; consequently written problems and problems to be stated have no terrors for those who are taught in this way. For several years mathematical associations have urged that all work should be based upon the equation. In accordance with this view we have made the demonstrations in this book largely algebraic, thus making the demonstration essentially a study in simultaneous equations. In this method of treatment, we have found it advantageous not to hurry the work. Pupils gain power, not in solving many problems, but in analyzing and tio?oxt 3 xaAwafcaxs.- ing the principles of a few.
Mathematical Tables: Contrived After a Most Comprehensive Method; Viz, A Table of Logarithms was written by Henry Briggs in 1706. This is a 419 page book, containing 83506 words and 153 pictures. Search Inside is enabled for this title.
Volume of this work bciqg clofed, as it were, with the beginniag of a new fubjefk; the reader might readil conjefture, that it was defighed xo profccute it in a fubfequent volume but the author, at that time, was dubious whether it could be donfy conGftent with the reftrion, which he had laid himfelf under, of introducing no procefs that could not be underftobd by thofe, whofe knowledge extended only to common algebra: he faw, that the dodlrine of fluxions had been ufed, by authors of the greatciit reputation, in the folution of fome of the moft fimple of the queftions, which remained to be conHdered -, and was not fanguine enough to conceive, that he fliould fucceed, not only in them, but ai! in the more cpmplex, upon fimpler principles: he faw, neverthelefs, the great advantage, that would reiult from the folution of thofe quefVions, by a procefs purely arithmetical, and therefore determined to attempt it; the attempt has fucceeded, even beyond his hopes, and he now fubmits to the approbation or cenfure of the public, a third volume, every q.
The former gives to the student a mastery of figures, vhich will be serviceable in commercial and scientihc pursi it: the latter tends to concentrate his attention to in luce lhits of patient abstraction and accurate tl ougl t;to familiarize him with the laws of reasoning and to lead im examine carefully the grounds of every inference he draws. The diiiicu yl: herto let with in text-books on Arithmetic is that the theoretical lf as nmam subordinate to the practica. But if the theory is imperiectl understood, and tl1e principles are not comprel ended, tlllen questions can only he solved mechanicallv. Hncc the necessity of first making the rules intellirfihlp 4 ii, impressing them on the mind by copious an lnra ti With this object in view, two mportait princip have been kept in mind: (I) That the exercises shall bf so constructed as to require the pupil to think, and) Phat they shall consist largely of examples selected with especial to the pursuits of an agricultural and commercial A comparison fthe present work with those which are specially valued on account of the character and number of the problems they contain will, it is believed, show that it comprehends everything that is usually regarded as of practical importanee in Arithmetic.
The Constructive Development of Group-Theory: With a Bibliography was written by Burton Scott Easton in 1902. This is a 100 page book, containing 28215 words and 4 pictures. Search Inside is enabled for this title.
eBook
Discoveries in MathematicsIntroducing New Principles, Formulæ,& Double Equations, Which Abridge All the Operations of Algebra & Arithmetic
by Heyer M. Nexsen
Discoveries in Mathematics by Heyer M. Nexsen is a handbook that would help every student of mathematics in deconstructing complex formulae, equations and principles underlying algebra and arithmetic. Nexsen understands the general impediments to students of the subject in terms of memorising theorems, special cases as well as hypotheses and therefore provides a pointed discussion on abridging them for quick recall and application. Nexsen opens with an introductory note on algebraic formulae including logs, differentiation, powers and roots among various other concepts. He provides an innovative method for calculating the root of numbers which is much faster and simpler than the existing methodology. He then discusses specific operations like multiplication in double equations, squaring and square roots, cubes as well as formulae for many coefficients. Discoveries in Mathematics is brief which makes it even more appealing for students as referencing is quick and easy and Nexsen makes sure that concepts are explained in the most simplistic manner possible with multiple examples and sample equations. Of the various topics covered, the notes on algebra are perhaps explained the best. In the end, the use of this book would ensure that students of mathematics will be able to reduce calculation times substantially as it holds within its pages some excellent tips and tricks for various mathematical principles.
This Elementary not been neglected. An abundance of oral and written problems within the limits of the comprehension of pupils furnishes material for concrete work. Technical explanations of processes, necessarily con fusing to immature minds, are purposely omitted. A minimum of theory and a maximum of practice are generally conceded to be the wisest method of teaching the principles of arithmetic to young pupils. Experience proves that an elementary arithmetic should be simple, progressive, and teachable, and in a direct and practical way aim to develop arithmetical power.
This Primary ngt been neglected. An abundance of oral and written problems within the limits of the comprehension of pupils furnishes material for concrete work. Technical explanations of processes, necessarily confusing to immature minds, are purposely omitted. A minimum of theory and a maximum of practice are generally conceded to be the wisest method of teaching the principles of arithmetic to young pupils. Experience proves that a primary arithmetic should be simple, progressive, and teachable, and in a direct and practical way aim to develop arithmetical power.
In offering the present edition of Perkins Elementary Arithmetic to the public, the Publishers desire to call atten-tion to what they deem the peculiar merits of the work. I. They regard as a prominent feature of the book, the presence throughout of the distinguished mathematical mind of the Author. Its not everything labelled an explanation, in an Arithmetic, that brings recLSons to view; nor every operation marked an analysis that reveals princfylea or essential relations. There is still a lower deep where the groundmatter lies; and tiiis we think Professor Perkins has ploughed up. The examiner may select, at random, proofs of this radical excellence. We, therefore, believe that the Arithmetic which we submit; is peculiarly adapted to discipline the minds of those who study it, in the science of Numbers, and to advance Ihem to a higher level of intellectual capability; in short, to train them JUly for advanced departments in Mathematics. We are confident that the present work will maintain a longer than usual hold on the interest of both teachers and pupils; for it is not, like a cistern, to be exhausted by a few drawings, but like natures reservoins, it has the fountain within itself. IL The Pubfishers would present as another excellence of the book, its freedom from minute jepetitional details which cumber a page, and obstruct a pupiPs progress. It is believed that no principle is left unelucidated; and that new light is thrown upon many, heretofore imperfectly illustrated. It is regarded aano toall merit of the worVilikBX .a -wcX %si dilate.
The theonof equations is not only a necessity in the subsequent mathematical courses and their apphcations, but furnishes an illuminating sequel to geometry-, algebra and analytic geometn. Moreover, it develops anew and in greater detail various fundamental ideas of calculus for the simple, but important, case of poh-nomials. The theon, of equations therefore affords a useful supplement to differential calculus whether taken subsequentlj or simultaneoush. It was to meet the numerous needs of the student in regard to his earUer and future mathematical courses that the present book was planned with great care and after wide consultation. It differs essentially from the authors Elementary Theory of Equations, both in regard to omissions and additions, and since it is addressed to younger students and Tna.y be used parallel with a course in differential calculus. Simpler and more detailed proofs are now emplo ed. The exercises are simpler, more numerous, of greater variety, and involve more practical apphcations. This book throws important Ught on various elementarjtopics. For example, an alert student of geometrj who has learned how to bisect any angle is apt to ask if everjangle can be trisected with ruler and compasses and if not, whj not. After learning how to construct regular polygons of 3, 4, 5, 6, 8 and 10 sides, he wi Ube inquisitive about the missing ones of 7 and 9 sides. The teacher will be in a comfortable position if he knows the facts and what is involved in the simplest discussion to date of these questions, as given in Chapter III. Other chapters throw needed hght on various topics of algebra. In particular, the theory of graphs is presented in Chapter Vin a more scientific and practical manner than was possible in algebra and anah tic geometry. There is developed a method of computing a real root of an equation with minimum labor and with certainty as to the accuracy of all the decimals obtained. |
Show your students that numbers don't have to be difficult---in fact, they can be enjoyable! More than just another textbook, this supplement to your curriculum traces the history of mathematics principles and theory; features simple algebra, geometry, and scientific computations; and offers practical tips for everyday math use. Includes biblical examples, fun activities, chapter tests, and lots of illustrations and diagrams. 160 pages, softcover from New Leaf. |
Crafting new instructional aids for math courses can be difficult, but this helpful new article from Markus Hohenwarter and Judith Preiner will bring much joy to the hearts of mathematics teachers everywhere. This...
Michigan State University has a well-known geography department, and an equally fine map library. On the map library's website, visitors will find a very nice selection of digital exhibits and maps. By clicking on the...
Written by J.A. Bondy and U.S.R. Murty of the Pierre and Marie Curie University in Paris, this online 270-page textbook presents graph theory and its applications. The topics covered here include connectivity,...
From the Graduate Texts in Mathematics series comes this textbook on graph theory by Reinhard Diestel from the University of Hamburg. Topics covered include flows, planar graphs, infinite graphs, and Hamilton cycles. ...
This lesson presents a comparison of the outlook for energy independence between the United States and France. Topics include the average per capita energy usage between the two countries, differences in types of energy... |
This is the eBook version of the printed book. If the book includes supplemental materials, the supplemental materials are not included within the eBook version. The Holt McDougal Larson Secondary Mathematics series is designed for students studying pre-algebra, algebra, geometry, and advanced algebra. It supports students working at the regular level, and also provides significant challenge and support for advanced and Pre-AP students.Larson Mathematics is Built for the Common Core State StandardsThe new tables of contents for the Holt McDougal Larson Secondary Mathematics series reflect comprehensive alignment to the new Common Core State Standards. Correlations are placed at the front of the texts, and on every lesson. Larson Pre-Algebra addresses both accelerated 7th grade standards and all 8th grade standards, and is appropriate for students preparing to study algebra. Algebra 1, Geometry, and Algebra 2 cover the course-level standards, including the plus standards.Larson Mathematics Takes Students to the Next Level of ComprehensionThe program is designed to emphasize conceptual understanding, to focus on critical thinking and reasoning, and to develop strong skills through mathematical modeling and problem solving. The Activity Generator provides full Investigations for all Standards. The investigations are leveled for universal access and include a section of "Drawing Conclusions" to foster discourse and develop reasoning. Lessons open with "Essential Questions" in the Teacher's Editions to foster discourse about the topic. Teachers also have "Key Questions" for Examples as they are working through lessons. Performance Tasks are available for formative and summative assessments.Larson Mathematics Paves the Way to Higher MathematicsThe Holt McDougal Larson Secondary Mathematics series provides a superior foundation for the study of advanced level mathematics. Lead author, Dr. Ron Larson, is nationally recognized for his award-winning precalculus and calculus level textbooks, and he has written this series so that students will be "college and career ready".Larson Mathematics Utilizes Technology to Enhances LearningWith the interactive Online Editions, students have access to their book, Lesson Tutorial Videos, additional practice with immediate feedback, and intervention resources. eText Student Editions come to life on a variety of devices. The Teacher One Stop CD-ROM with Test and Practice Generator supplies teachers with everything they need to plan and manage lessons. The Activity Generator provides additional tasks, investigations and activities correlated to the Common Core State Standards. Interactive Whiteboard Lessons provide an interactive pathway to present the Explorations Lessons. The Interactive Answers and Solutions CD-ROM allows teachers to select questions, as well as customize answer keys with stepped-out solutions. Assessment resources provide diagnosis tools as well as remediation opportunities.Strengths of the Holt McDougal Larson Secondary Mathematics SeriesLaser Focus on Developing the Standards for Mathematical PracticeThe Standards for Mathematical Practice are embedded in every lesson through the exercise sets, and correlated in the Teacher's Editions. The Explorations in Core Math component presents lessons through guided-discovery activities that encourage development of the Practices. The Activity Generator includes a bank of activities written specifically to develop the Practices.Attention to Problem Solving, Modeling, and Performance TasksMath modeling and the integration of relevant applications is paramount to the design of the Holt McDougal Larson Secondary Mathematics series. Every lesson begins with "Before, Now, and Why?" that connects to a real-world application problem that incorporates the math of the lesson. Real-World Situations are used in Examples as the lessons progress. Every homework set focuses on relevant, real-world Problem Solving. The Assessment Book includes authentic assessments for use in performance-based tasks. The Activity Generator includes a bank of Performance Tasks and authentic assessment tools.Comprehensive Interactive Whiteboard LessonsHolt McDougal Larson Secondary Mathematics includes full, comprehensive standards-based lessons for use on interactive whiteboards. Every lesson begins with an Essential Question, followed by Explore activities and Examples, and then closes with Standardized Test Prep a lesson Summary. These lessons integrate the use of interactive whiteboard tools, digital manipulatives, and student response systems.Opportunities for Challenging Students on the Pre-AP TrackThe Larson Secondary Mathematics series is known to provide rigorous coursework, and includes instruction on the "Plus" Standards. There are "C-level" exercises in both the Practice and Problem Solving exercise sets. There are "C-level" and "Challenge" practice pages in the Chapter Resources for every lesson. Several Extension Lessons are placed throughout each course so that teachers may extend content at appropriate points during instruction. The Pre-AP Resources book provides an alternate pacing and assignment guide to use the texts with advanced students. It also includes best practices and teaching strategies for extending content of the lessons appropriately. The Activity Generator provides C-level investigations for lessons, and there are additional Problem Solving Applications for lessons and extended Projects to culminate work through the chapters.Best Common Core Assessment PreparationIn addition to the course-specific test generator provided on the Teacher One Stop, the On Core 6-12 Deluxe ExamView Assessment Suite provides over 11,000 items correlated to the Common Core State Standards and written to DOK Levels 1-4 with which to prepare additional standards-based practice and assessment |
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