Numbers And Proofs: NUA01ERS & PROOFS

Paperback

byReg AllenbyEditorReg Allenby

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Numbers and Proofspresents a gentle introduction to the notion of proof to give the reader an understanding of both 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). 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 authors entertaining and informal style and written to reflect the change profile of students entering universities 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.

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From the Publisher

Numbers and Proofspresents a gentle introduction to the notion of proof to give the reader an understanding of both 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). Each proof is pr...

Format:PaperbackDimensions:288 pages, 9.63 × 6.75 × 0.5 inPublisher:Butterworth (trade)

The following ISBNs are associated with this title:

ISBN - 10:0340676531

ISBN - 13:9780340676530

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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.