Numbers and Proofs - 1st Edition - ISBN: 9780340676530, 9780080928777

Numbers and Proofs

1st Edition

Authors: Reg Allenby
Paperback ISBN: 9780340676530
eBook ISBN: 9780080928777
Imprint: Butterworth-Heinemann
Published Date: 26th September 1997
Page Count: 288
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Table of Contents

The need for proof * Statements and connectives * True or false? * Sets, negations, notations and functions * Proofs....for all * There exists....proofs * The principle of mathematical induction * The integers and rational numbers * The rational numbers and the real numbers * Real numbers and complex numbers * Guessing, analogy and transformation * Generalisation and specialisation * Fallacies and paradoxes * A mixed bag * Solutions appendix * Answers to exercises * References.

Description

'Numbers and Proofs' presents a gentle introduction to the notion of proof to give the reader an understanding of how to decipher others' proofs as well as construct their own. Useful methods of proof are illustrated in the context of studying problems concerning mainly numbers (real, rational, complex and integers). An indispensable guide to all students of mathematics. Each proof is preceded by a discussion which is intended to show the reader the kind of thoughts they might have before any attempt proof is made. Established proofs which the student is in a better position to follow then follow.

Presented in the author's entertaining and informal style, and written to reflect the changing profile of students entering universities, this book will prove essential reading for all seeking an introduction to the notion of proof as well as giving a definitive guide to the more common forms. Stressing the importance of backing up "truths" found through experimentation, with logically sound and watertight arguments, it provides an ideal bridge to more complex undergraduate maths.

Readership

1st/2nd year mathematics undergraduates.


Details

No. of pages:
288
Language:
English
Copyright:
© Butterworth-Heinemann 1997
Published:
Imprint:
Butterworth-Heinemann
eBook ISBN:
9780080928777
Paperback ISBN:
9780340676530

Reviews

'Numbers and Proofs' presents a gentle introduction to the notion of proof to give the reader an understanding of how to decipher others' proofs as well as construct their own. Useful methods of proof are illustrated in the context of studying problems concerning mainly numbers (real, rational, complex and integers). An indispensable guide to all students of mathematics. Each proof is preceded by a discussion which is intended to show the reader the kind of thoughts they might have before any attempt proof is made. Established proofs which the student is in a better position to follow then follow. Presented in the author's entertaining and informal style, and written to reflect the changing profile of students entering universities, this book will prove essential reading for all seeking an introduction to the notion of proof as well as giving a definitive guide to the more common forms. Stressing the importance of backing up "truths" found through experimentation, with logically sound and watertight arguments, it provides an ideal bridge to more complex undergraduate maths.


About the Authors

Reg Allenby Author

Affiliations and Expertise

School of Mathematics, University of Leeds, UK