Excursions in Calculus: An Interplay of the Continuous and the Discrete, Band 13Cambridge University Press, 1992 - 417 Seiten The purpose of this book is to explore the rich and elegant interplay that exists between the two main currents of mathematics, the continuous and the discrete. Such fundamental notions in discrete mathematics as induction, recursion, combinatorics, number theory, discrete probability, and the algorithmic point of view as a unifying principle are continually explored as they interact with traditional calculus. The book is addressed primarily to well-trained calculus students and those who teach them, but it can also serve as a supplement in a traditional calculus course for anyone who wants to see more. The problems, taken for the most part from probability, analysis, and number theory, are an integral part of the text. There are over 400 problems presented in this book. |
Inhalt
Function and Form | 123 |
On the Average | 185 |
From Pi to the Prime Number Theorem | 247 |
A Potpourri | 309 |
The Congruence Notation | 369 |
| 379 | |
Sources for Solutions | 397 |
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Excursions in Calculus: An Interplay of the Continuous and the Discrete Robert M. Young Eingeschränkte Leseprobe - 1992 |
Häufige Begriffe und Wortgruppen
algorithm appear application approximation arithmetic asserts begin Book calculus called century chapter circle coefficients conjecture consider construction contains continuous converges curve defined denote derived determine digits discovered discovery divide divisible divisors elementary equal equation error Euler example exists expressed fact factor Fermat Fibonacci numbers FIGURE finite formula function geometric give given important induction infinite interval known least length limit mathematical mathematicians mean method multiple natural number Observe obtain once origin pattern polynomial positive integers possible prime prime number principle probability problem proof Prove rational reason recursive relation remains remarkable result sequence Show sides simple single solution square step successive Suppose theorem theory triangle true values volume writes zero
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