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Book
xiv, 319 pages : illustrations ; 23 cm
  • Foreword 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.
  • (source: Nielsen Book Data)9781118164020 20160613
Solow, "How to Read and Do Proofs, " provides a systematicapproach for teaching students how to read, think about, understand, and create proofs. It develops a method forcommunicating proofs, categorizing, identifying, and explaining (atthe student's level) the various techniques that are usedrepeatedly in virtually all proofs. These clear, conciseexplanations promote understanding of the theoretical mathematicsbehind abstract mathematics and give students a greater opportunityto succeed in advanced courses. Along with the addition of threenew chapters, a "Part 2" is added to the SixthEdition, which focuses on the mathematical thought processesassociated with proofs. The teaching of this foregoingthinking processes reduces the time needed for readers tolearn advanced mathematics courses while simultaneously increasingtheir depth of understanding so as to enable them to usemathematics more effectively as a problem-solving tool in theirpersonal and professional lives.
(source: Nielsen Book Data)9781118164020 20160613
Engineering Library (Terman), Science Library (Li and Ma)
CS-103-01
Book
xxii, 458 p. : ill ; 24 cm.
  • 1. Regular languages
  • 2. Context-free languages
  • 3. The Church-Turing thesis
  • 4. Decidability
  • 5. Reducibility
  • 6. Advanced topics in computability theory
  • 7. Time complexity
  • 8. Space complexity
  • 9. Interactibility
  • 10. Advanced topics in complexity theory.
Engineering Library (Terman)
CS-103-01, CS-154-01