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How to Read and Do Proofs : An Introduction to Mathematical Thought Processes by Daniel Solow (2013, Trade Paperback)
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About this product
Product Identifiers
PublisherWiley & Sons, Incorporated, John
ISBN-101118164024
ISBN-139781118164020
eBay Product ID (ePID)170137204
Product Key Features
Number of Pages336 Pages
LanguageEnglish
Publication NameHow to Read and Do Proofs : an Introduction to Mathematical Thought Processes
SubjectLogic
Publication Year2013
TypeTextbook
Subject AreaMathematics
AuthorDaniel Solow
FormatTrade Paperback
Dimensions
Item Height0.7 in
Item Weight14.4 Oz
Item Length8.8 in
Item Width6 in
Additional Product Features
Edition Number6
Intended AudienceCollege Audience
LCCN2013-020037
Reviews"The instructional material is to the point, with well-considered examples and asides on common mistakes. Good examples of the author's thoughtfulness appear in the discourses on pp. 5-6 of identifying the hypothesis and conclusion when they are not obvious, on pp. 28-29 regarding overlapping notation, and on pp. 190-191 of the advantages and disadvantages of generalization." (Zentralblatt MATH 2016)
Dewey Edition22
IllustratedYes
Dewey Decimal511.3/6
Table Of ContentForeword xi Preface to the Student xiii Preface to the Instructor xv Acknowledgments xviii Part I Proofs 1 Chapter 1: The Truth of It All 1 2 The Forward-Backward Method 9 3 On Definitions and Mathematical Terminology 25 4 Quantifiers I: The Construction Method 41 5 Quantifiers II: The Choose Method 53 6 Quantifiers III: Specialization 69 7 Quantifiers IV: Nested Quantifiers 81 8 Nots of Nots Lead to Knots 93 9 The Contradiction Method 101 10 The Contrapositive Method 115 11 The Uniqueness Methods 125 12 Induction 133 13 The Either/Or Methods 145 14 The Max/Min Methods 155 15 Summary 163 Part II Other Mathematical Thinking Processes 16 Generalization 179 17 Creating Mathematical Definitions 197 18 Axiomatic Systems 219 Appendix A Examples of Proofs from Discrete Mathematics 237 Appendix B Examples of Proofs from Linear Algebra 251 Appendix C Examples of Proofs from Modern Algebra 269 Appendix D Examples of Proofs from Real Analysis 287 Solutions to Selected Exercises 305 Glossary 357 References 367 Index 369
SynopsisThis text makes a great supplement and provides a systematic approach for teaching undergraduate and graduate students how to read, understand, think about, and do proofs., This text makes a great supplement and provides a systematic approach for teaching undergraduate and graduate students how to read, understand, think about, and do proofs. The approach is to categorize, identify, and explain (at the student's level) the various techniques that are used repeatedly in all proofs, regardless of the subject in which the proofs arise. How to Read and Do Proofs also explains when each technique is likely to be used, based on certain key words that appear in the problem under consideration. Doing so enables students to choose a technique consciously, based on the form of the problem.
LC Classification NumberQA9.54.S65 2014
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