Contents

* Notations and summary definitions
* Preliminary considerations
* Mathematical induction
* Algebraic preliminaries
o Groups, rings, fields and ideals
o Domains
o Factorization in integral domains
o Greatest Common Divisor
o Unique Factorization Domains
o Ideals and principal ideal domains
* Computing in Z
o Ordinary Euclidean algorithm
o Relatively prime numbers
o Extended Euclidean algorithm
o Efficiency of the Euclidean algorithm
o Properties of the Fibonacci numbers

Computations are designed to solve problems. Programs are descriptions of computations written for execution on computers. The field of computer science is concerned with the development of methodologies for designing programs, and with the development of computers for executing programs. It is therefore of central importance for those involved in the field that the characteristics of programs, computers, problems, and computation be fully understood.

Contents
I Models of computation
1 Introduction
2 Mathematical preliminaries
201 Sets                                    
202 Relations and Functions                         
203 Principle of Mathematical Induction                  
3 A functional model of computation
31 The primitive expressions                            
32 Substitution of functions