Mathematical Connections: A Companion for Teachers and OthersCambridge University Press, 11. avg. 2005 - 239 strani 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. |
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A Companion for Teachers and Others Albert Cuoco. EDC ONAL SCIENCE OUNDATION Mathematical Connections was developed at Education Development Center , Inc. ( EDC ) within the Center for Mathematics Education ... Teachers and Others Al Cuoco.
A Companion for Teachers and Others Albert Cuoco. EDC ONAL SCIENCE OUNDATION Mathematical Connections was developed at Education Development Center , Inc. ( EDC ) within the Center for Mathematics Education ... Teachers and Others Al Cuoco.
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A Companion for Teachers and Others Albert Cuoco. Contents Introduction . Annotated Table of Contents 1 Difference Tables and Polynomial Fits 1.1 Doing It with Sums . . . 1.2 Doing It with Differences 1.3 Finding a Formula ...
A Companion for Teachers and Others Albert Cuoco. Contents Introduction . Annotated Table of Contents 1 Difference Tables and Polynomial Fits 1.1 Doing It with Sums . . . 1.2 Doing It with Differences 1.3 Finding a Formula ...
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A Companion for Teachers and Others Albert Cuoco. 3.3 The Geometry behind Multiplying 3.4 Trigonometric Identities 3.5 Complex Maps . . . 3.6 Julia Sets and the Mandelbrot Set • 4 Combinations and Locks . . . 4.1 Combinatorial Proofs and ...
A Companion for Teachers and Others Albert Cuoco. 3.3 The Geometry behind Multiplying 3.4 Trigonometric Identities 3.5 Complex Maps . . . 3.6 Julia Sets and the Mandelbrot Set • 4 Combinations and Locks . . . 4.1 Combinatorial Proofs and ...
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Difference Tables and Polynomial Fits | 1 |
The Algebra of Polynomials | 53 |
Complex Numbers Complex Maps and Trigonometry | 101 |
Combinations and Locks | 161 |
Sums of Powers | 204 |
Bibliography | 235 |
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algebra am,k angle Bernoulli numbers binomial coefficients binomial theorem bm,k calculate Chapter Chebyshev polynomials column combinatorial proof complex numbers conjecture constant Corollary cos² cubic defined derivative difference table example expression factor filled Julia set find a formula find a polynomial five buttons function that agrees ƒ and g Gaussian integers high school Hint Input Output iterate look Mandelbrot set mathematics method multiply n-element set nonnegative integers Notes for problem number of combinations orbit Pascal's triangle pick points polynomial function polynomial ƒ polynomial of degree polynomial that agrees positive integer produce push quadratic formula real numbers replace right-hand side Show Simplex lock sm(x solve subsets Suppose f(x Suppose ƒ symmetric functions there's trigonometric identities unit circle values write zeros