{"product_id":"how-to-read-and-do-proofs-9781118164020","title":"How to Read and Do Proofs","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis 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. \u003ci\u003eHow to Read and Do Proofs\u003c\/i\u003ealso 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"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)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eForeword xi\u003c\/p\u003e \u003cp\u003ePreface to the Student xiii\u003c\/p\u003e \u003cp\u003ePreface to the Instructor xv\u003c\/p\u003e \u003cp\u003eAcknowledgments xviii\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Proofs\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1 Chapter 1: The Truth of It All 1\u003c\/p\u003e \u003cp\u003e2 The Forward-Backward Method 9\u003c\/p\u003e \u003cp\u003e3 On Definitions and Mathematical Terminology 25\u003c\/p\u003e \u003cp\u003e4 Quantifiers I: The Construction Method 41\u003c\/p\u003e \u003cp\u003e5 Quantifiers II: The Choose Method 53\u003c\/p\u003e \u003cp\u003e6 Quantifiers III: Specialization 69\u003c\/p\u003e \u003cp\u003e7 Quantifiers IV: Nested Quantifiers 81\u003c\/p\u003e \u003cp\u003e8 Nots of Nots Lead to Knots 93\u003c\/p\u003e \u003cp\u003e9 The Contradiction Method 101\u003c\/p\u003e \u003cp\u003e10 The Contrapositive Method 115\u003c\/p\u003e \u003cp\u003e11 The Uniqueness Methods 125\u003c\/p\u003e \u003cp\u003e12 Induction 133\u003c\/p\u003e \u003cp\u003e13 The Either\/Or Methods 145\u003c\/p\u003e \u003cp\u003e14 The Max\/Min Methods 155\u003c\/p\u003e \u003cp\u003e15 Summary 163\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Other Mathematical Thinking Processes\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16 Generalization 179\u003c\/p\u003e \u003cp\u003e17 Creating Mathematical Definitions 197\u003c\/p\u003e \u003cp\u003e18 Axiomatic Systems 219\u003c\/p\u003e \u003cp\u003eAppendix A Examples of Proofs from Discrete Mathematics 237\u003c\/p\u003e \u003cp\u003eAppendix B Examples of Proofs from Linear Algebra 251\u003c\/p\u003e \u003cp\u003eAppendix C Examples of Proofs from Modern Algebra 269\u003c\/p\u003e \u003cp\u003eAppendix D Examples of Proofs from Real Analysis 287\u003c\/p\u003e \u003cp\u003eSolutions to Selected Exercises 305\u003c\/p\u003e \u003cp\u003eGlossary 357\u003c\/p\u003e \u003cp\u003eReferences 367\u003c\/p\u003e \u003cp\u003eIndex 369 \u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406838112599,"sku":"9781118164020","price":72.15,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118164020.jpg?v=1730497291","url":"https:\/\/bookcurl.com\/products\/how-to-read-and-do-proofs-9781118164020","provider":"Book Curl","version":"1.0","type":"link"}