How to read and do proofs

Daniel Solow

270 pages, parution le 12/11/2004 (4^eme édition)

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Résumé

Daniel Solow's new Fourth Edition of How to Read and Do Proofs will help you master the basic techniques that are used in all proofs, regardless of the mathematical subject matter in which the proof arises. Once you have a firm grasp of the techniques, you'll be better equipped to read, understand and actually do proofs. You'll learn when each technique is likely to be successful, based on the form of the theorem.

This Fourth Edition features quick reference summaries of the proof techniques on the front and back covers, a new forward uniqueness method, a new section on counterexamples, and four new appendices in discrete mathematics, linear algebra, modern algebra, and real analysis that illustrate how the various proof techniques from the body of the text arise in doing actual mathematics.

Sommaire

Foreword
Preface to the Student
Preface to the Instructor
Acknowledgments
The Truth of It All
The Forward-Backward Method
On Definitions and Mathematical Terminology
Quantifiers I: The Construction Method
Quantifiers II: The Choose Method
Quantifiers III: Specialization
Quantifiers IV: Nested Quantifiers
Nots of Nots Lead to Knots
The Contradiction Method
The Contrapositive Method
Uniqueness Methods and Induction
Either/or and Max/Min Methods
Summary
Appendix A: Examples of Proofs from Discrete Mathematics
Appendix B: Examples of Proofs from Linear Algebra
Appendix C: Examples of Proofs from Modern Algebra
Appendix D: Examples of Proofs from Real Analysis
Solutions to Select Exercises
Glossary
References
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	Daniel Solow
Parution	12/11/2004
Édition	4^eme édition
Nb. de pages	270
Format	15,5 x 23,5
Couverture	Broché
Poids	371g
Intérieur	Noir et Blanc
EAN13	9780471680581
ISBN13	978-0-471-68058-1