Preface
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Part I: Mathematical statements and proofs
The language of mathematics
Implications
Proofs
Proof by contradiction
The induction principle
Problems I
Part II: Sets and functions
The language of set theory
Quantifiers
Functions
Injections, surjections and bijections
Problems II
Part III: Numbers and counting
Counting
Properties of finite sets
Counting functions and subsets
Number systems
Counting infinite sets
Problems III
Part IV: Arithmetic
The division theorem
The Euclidean algorithm
Consequences of the Euclidean algorithm
Linear diophantine equations
Problems IV
page ix
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Part V: Modular arithmetic
19 Congruence of integers
20 Linear congruences
21 Congruence classes and the arithmetic of remainders
22 Partitions and equivalence relations
Problems V
Part VI: Prime numbers
23 The sequence of prime numbers
24 Congruence modulo a prime
Problems VI
Solutions to exercises
Bibliography
List of symbols
Index
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