Mathematical Connections: A Companion for Teachers and OthersAmerican Mathematical Soc., 31. dec. 2005 - 239 strani Mathematical Connections 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. While the book will appeal to many audiences, one of the primary audiences is high school teachers, both practicing and prospective. It can be used as a text for undergraduate or professional courses, and the design lends itself to self study. Of course, good mathematics for teaching is also good for many other uses, so readers of all persuasions can enjoy exploring some of the beautiful ideas presented in the pages of this book. |
Iz vsebine knjige
Zadetki 1–5 od 89
Stran xi
... shows students some of the results . ways in which mathematicians work . In developing The CME Project , my colleagues and I consulted regularly About the sidenotes : Because with high school teachers . Almost all of them told us that ...
... shows students some of the results . ways in which mathematicians work . In developing The CME Project , my colleagues and I consulted regularly About the sidenotes : Because with high school teachers . Almost all of them told us that ...
Stran xvii
... shows up all over mathematics and science . This many beautiful patterns in the sequence brings coherence to trigonometry , and it connects trigonometry with sequence of Chebyshev arithmetic , algebra , and geometry . polynomials ...
... shows up all over mathematics and science . This many beautiful patterns in the sequence brings coherence to trigonometry , and it connects trigonometry with sequence of Chebyshev arithmetic , algebra , and geometry . polynomials ...
Stran xviii
... show that each side of the identity counts the same thing . In this case , the story involves picking subsets from a set of n things . How many ways are there to do this ? Well , for each element there are two choices ( in or out ) , so ...
... show that each side of the identity counts the same thing . In this case , the story involves picking subsets from a set of n things . How many ways are there to do this ? Well , for each element there are two choices ( in or out ) , so ...
Stran 2
... shows that many of the habits of mind underlying calculus are independent from notions of limit . 4. In sections 1.3–1.5 ... show all over mathematics . 6. This idea of subtracting successive numbers in a table , which seems to be up ...
... shows that many of the habits of mind underlying calculus are independent from notions of limit . 4. In sections 1.3–1.5 ... show all over mathematics . 6. This idea of subtracting successive numbers in a table , which seems to be up ...
Stran 3
... Show that , in an input - output table like the one below , every output is the We could say “ The outputs are sum of the output for 0 and the elements in the A column up to the number the running totals of the differences . " above the ...
... Show that , in an input - output table like the one below , every output is the We could say “ The outputs are sum of the output for 0 and the elements in the A column up to the number the running totals of the differences . " above the ...
Vsebina
1 | |
The Algebra of Polynomials | 53 |
Chapter 3 Complex Numbers Complex Maps and Trigonometry | 101 |
Chapter 4 Combinations and Locks | 161 |
Chapter 5 Sums of Powers | 199 |
Bibliography | 235 |
Index | 237 |
About the Author | 239 |
Back cover | 241 |
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agrees algebra am,k angle binomial buttons calculate called Chapter circle coefficients column combinations combinatorial complex numbers connected constant Corollary count course cubic defined definition derivative Describe develop difference difference table elements entries equal equation exactly example expanded expression f and g fact factor filled Julia set five formula give given graph high school ideas identity Input Output integer least length linear lock look mathematics means method multiply Notes for problem Notice obtained orbit origin Pascal's triangle pick picture plane points polynomial function polynomial of degree positive integer powers produce proof prove push quadratic replace result roots Show side Sm(x solve squares starting subsets Suppose teachers Theorem there's things true values we'll write zeros