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 35
Stran xvii
... notice a pattern in their others . References [ 6 , 19 ) are work that can be expressed as an identity . For example , students often come up just two of the many books with the fact that the sum of the entries in any row of Pascal's ...
... notice a pattern in their others . References [ 6 , 19 ) are work that can be expressed as an identity . For example , students often come up just two of the many books with the fact that the sum of the entries in any row of Pascal's ...
Stran 1
... notice that the outputs “ go up by 5 each time . ” It turns out that , if the differences go up by the same amount , there's a linear function ( in this case , f ( x ) = 5x + 3 ) that fits the table . We'll see why in the next section ...
... notice that the outputs “ go up by 5 each time . ” It turns out that , if the differences go up by the same amount , there's a linear function ( in this case , f ( x ) = 5x + 3 ) that fits the table . We'll see why in the next section ...
Stran 5
... Notice that the next difference column ( the A3 column ) will be constant , too ; it will be all Os . 6 2 9 6 3 15 6 4 21 6 To get the entry in the A column for an input of n , start with - 3 and add n 6s . 5 27 We might be able to make ...
... Notice that the next difference column ( the A3 column ) will be constant , too ; it will be all Os . 6 2 9 6 3 15 6 4 21 6 To get the entry in the A column for an input of n , start with - 3 and add n 6s . 5 27 We might be able to make ...
Stran 10
... Notice that , by the way we built difference tables , every entry in the interior of the table is the sum of its “ up and over . ” 49 11 + 38 , 62 50 + 12 , 262 = 188 + 74 , ... . So , we can take any entry in the f ( n ) column ...
... Notice that , by the way we built difference tables , every entry in the interior of the table is the sum of its “ up and over . ” 49 11 + 38 , 62 50 + 12 , 262 = 188 + 74 , ... . So , we can take any entry in the f ( n ) column ...
Stran 12
Dosegli ste zgornjo mejo števila strani te knjige, ki je na voljo.
Dosegli ste zgornjo mejo števila strani te knjige, ki je na voljo.
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 |
Pogosti izrazi in povedi
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