100 percent mathematical proof

Rowan Garnier, John Taylor0471961981, 9780471961987, 9780585302287

Proof has been and remains one of the concepts which characterises mathematics. Covering basic propositional and predicate logic as well as discussing axiom systems and formal proofs, the book seeks to explain what mathematicians understand by proofs and how they are communicated. The authors explore the principle techniques of direct and indirect proof including induction, existence and uniqueness proofs, proof by contradiction, constructive and non-constructive proofs, etc. Many examples from analysis and modern algebra are included. The exceptionally clear style and presentation ensures that the book will be useful and enjoyable to those studying and interested in the notion of mathematical proof.

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Table of contents :
Cover Page……Page 1
Title Page……Page 2
ISBN 0471961981……Page 3
3 Predicate Logic……Page 4
4 Axiom Systems and Formal Proof……Page 5
8 Further Proof Techniques……Page 6
Appendix, References, Hints and Solutions, Index……Page 7
Preface……Page 8
1 Proofs, Mathematical and Non-Mathematical……Page 10
2 Propositional Logic……Page 24
3 Predicate Logic……Page 72
4 Axiom Systems and Formal Proof……Page 98
5 Direct Proof……Page 130
6 Direct Proof: Variations……Page 176
7 Existence and Uniqueness Proofs……Page 194
8 Further Proof Techniques……Page 218
9 Mathematical Induction……Page 248
Appendix: Some Definitions and Terminology……Page 274
References and Further Reading……Page 282
Hints and Solutions to Selected Exercises……Page 284
B……Page 322
C……Page 323
E……Page 324
I……Page 325
M……Page 326
P……Page 327
S……Page 328
T……Page 329
Z……Page 330