Programming for Mathematicians (Universitext)

"The aim of this 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'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."--Jacket

Aimed at teaching mathematics students how to program using their knowledge of mathematics, the entire books emphasis is on how to think when programming. Three methods for constructing an algorithm or a program are used: manipulation and enrichment of existing code; use of recurrent sequences; deferral of code writing, in order to deal with one difficulty at a time. Many theorems are mathematically proved and programmed, and the text concludes with an explanation of how a compiler works and how to compile by hand little programs. Intended for anyone who thinks mathematically and wants to program and play with mathematics.

...this well known author is a must for anyone who thinks mathematically & wants to program & play with math...his last chapter explains how a compiler works & how to compile by hand short programs.

Preface......Page 4 Table of Contents ......Page 7 1. Programming Proverbs ......Page 14 2. Review of Arithmetic ......Page 18 3. An Algorithmic Description Language ......Page 42 4. How to Create an Algorithm ......Page 72 5. Algorithms and Classical Constructions ......Page 104 6. The Pascal Language ......Page 122 7. How to Write a Program ......Page 148 8. The Integers ......Page 172 9. The Complex Numbers ......Page 238 10. Polynomials ......Page 266 11. Matrices......Page 310 12. Recursion ......Page 350 13. Elements of compiler theory ......Page 372 References......Page 436 Index......Page 438 Programmers enjoy creating proverbs which reflect their professional experience.