Excursions in Calculus: An Interplay of the Continuous and the Discrete, 第 13 卷

封面
Cambridge University Press, 1992 - 417 頁
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.
 

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內容

Proof by Induction
15
Applications
22
Infinite Descent
38
Function and Form
123
From Order to Chaos
170
On the Average
185
The Law of Errors
206
From Pi to the Prime Number Theorem
247
A Potpourri
309
The Congruence Notation
369
References
379
Sources for Solutions
397
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