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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. TOC:Programming Proverbs.- Review of Arithmetic.- An Algorithmic Description Language.- How to Create an Algorithm.- Algorithms and Classical Constructions.- The Pascal Language.- How to Write a Program.- The Integers.- The Comlex Numbers.- Polynomials.- Matrices.- Recursion.- Elements of Compiler Theory.