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Programming for mathematicians. (English)
Springer, Berlin (ISBN 3-540-66422-X). 444 p. (2000).
The aim of the book is to teach mathematics students how to program using their knowledge of mathematics. For this they require only to know how to construct a proof. The entire book$\rq$s emphasis is on "how to think" when programming. Three methods for constructing an algorithm or a program are used: a) manipulation and enrichment of existing code; b) use of recurrent sequences; c) deferral of code writing, in order to deal with one difficulty at a time. Many theorems are mathematically proved and programmed. The last chapter explains how a compiler works and shows how to compile "by hand" little (but not trivial - even recursive) programs. The book is intended for anyone who thinks mathematically and wants to program and play with mathematics. Contents: Programming proverbs; Review of arithmetic; An algorithm description language; How to create an algorithm; Algorithms and classical constructions; The Pascal language; How to write a program; The integers; The complex numbers; Polynomials; Matrices; Recursion; Elements of compiler theory.
Classification: P40
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