| Document Type
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BL
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| Record Number
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1047484
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| Doc. No
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b801854
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| Main Entry
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Cuoco, Albert.
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| Title & Author
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Mathematical connections : : a companion for teachers and others /\ Al Cuoco.
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| Publication Statement
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[Washington, DC] :: Mathematical Association of America,, ©2005.
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| Series Statement
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Classroom resource materials
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| Page. NO
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xix, 239 pages :: illustrations ;; 28 cm.
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| ISBN
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0883857391
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: 9780883857397
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| Notes
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"Developed at Education Development Center, Inc. (EDC) within the Center for Mathematics Education (CME)"--Page facing title page.
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| Bibliographies/Indexes
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Includes bibliographical references (pages 235-236) and index.
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| Contents
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1. Difference tables and polynomial fits. Doing it with sums -- Doing it with differences -- Finding a formula: combinatorial polynomials -- Making it formal: the [delta] operator -- Going the other way: polynomials to tables -- Conversions -- From Newton to Lagrange -- Agreeing to disagree. -- 2. Form and function: the algebra of polynomials. Polynomials -- The basic theorems -- Coefficients and values -- Up a level -- Transformations -- Coefficients and zeros. -- 3. Complex numbers, complex maps, and trigonometry. Complex numbers -- The complex plane -- The geometry behind multiplying -- Trigonometric identities -- Complex maps -- Julia sets and the Mandelbrot set. -- 4. Combinations and locks. Combinatorial proofs and identities -- The simplex lock -- Some approaches to the simplex lock problem -- Connections to the Mahler basis. -- 5. Sums of powers. Summatory polynomials -- Bernoulli's method.
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| Abstract
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Covers some topics that form the foundations of high school mathematics, such as polynomial functions.
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This book is about some of the topics that form the foundations for high school mathematics. It focuses on a closely-knit collection of ideas that are at the intersection of algebra, arithmetic, combinatorics, geometry, and calculus. Most of the ideas are classical: methods for fitting polynomial functions to data, for summing powers of integers, for visualizing the iterates of a function defined on the complex plane, or for obtaining identities among entries in Pascal's triangle. Some of these ideas, previously considered quite advanced, have become tractable because of advances in computational technology. Others are just beautiful classical mathematics, topics that have fallen out of fashion and that deserve to be resurrected. Most importantly, the book is about some mathematical ways of thinking the author found extremely useful, both in his roles as a mathematician and as a mentor of young people learning to do mathematics.--Publisher description.
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| Subject
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Mathematics-- Study and teaching (Secondary)
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| Subject
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Mathématiques-- Étude et enseignement (Secondaire)
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| Subject
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Mathematics-- Study and teaching (Secondary)
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| Subject
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Mathematics-- Study and teaching (Secondary)
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| Dewey Classification
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510
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| LC Classification
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QA11.2.C86 2005
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| Added Entry
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Education Development Center.
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Mathematical Association of America.
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