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|a 9781420093650
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|a (OCoLC)1035519175
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|a QA9.54.G86 2011
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|a HCDD
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|a Gunderson, David S.
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|a Handbook of Mathematical Induction.
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|a Boca Raton :
|b Chapman and Hall/CRC,
|c 2014.
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| 300 |
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|a 1 online resource (894 pages)
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| 336 |
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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|a Discrete Mathematics and Its Applications Ser.
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|a Print version record.
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|a Front Cover; Dedication; Contents; Foreword; Preface; About the author; Part I: Theory; Chapter 1: What is mathematical induction?; Chapter 2: Foundations; Chapter 3: Variants of finite mathematical induction; Chapter 4: Inductive techniques applied to the infinite; Chapter 5: Paradoxes and sophisms from induction; Chapter 6: Empirical induction; Chapter 7: How to prove by induction; Chapter 8: The written MI proof; Part II: Applications and exercises; Chapter 9: Identities; Chapter 10: Inequalities; Chapter 11: Number theory; Chapter 12: Sequences; Chapter 13: Sets.
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|a Chapter 14: Logic and languageChapter 15: Graphs; Chapter 16: Recursion and algorithms; Chapter 17: Games and recreations; Chapter 18: Relations and functions; Chapter 19: Linear and abstract algebra; Chapter 20: Geometry; Chapter 21: Ramsey theory; Chapter 22: Probability and statistics; Part III: Solutions and hints to exercises; Chapter 23: Solutions: Foundations; Chapter 24: Solutions: Inductive techniques applied to the infinite; Chapter 25: Solutions: Paradoxes and sophisms; Chapter 26: Solutions: Empirical induction; Chapter 27: Solutions: Identities.
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|a Chapter 28: Solutions: InequalitiesChapter 29: Solutions: Number theory; Chapter 30: Solutions: Sequences; Chapter 31: Solutions: Sets; Chapter 32: Solutions: Logic and language; Chapter 33: Solutions: Graphs; Chapter 34: Solutions: Recursion and algorithms; Chapter 35: Solutions: Games and recreation; Chapter 36: Solutions: Relations and functions; Chapter 37: Solutions: Linear and abstract algebra; Chapter 38: Solutions: Geometry; Chapter 39: Solutions: Ramsey theory; Chapter 40: Solutions: Probability and statistics; Part IV: Appendices; Appendix A: ZFC axiom system.
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|a Appendix B: Inducing you to laugh?Appendix C: The Greek alphabet; References.
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|a "Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics. In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces ordinals and cardinals, transfinite induction, the axiom of choice, Zorn's lemma, empirical induction, and fallacies and induction. He also explains how to write inductive proofs. The next part contains more than 750 exercises that highlight the levels of difficulty of an inductive proof, the variety of inductive techniques available, and the scope of results provable by mathematical induction. Each self-contained chapter in this section includes the necessary definitions, theory, and notation and covers a range of theorems and problems, from fundamental to very specialized. The final part presents either solutions or hints to the exercises. Slightly longer than what is found in most texts, these solutions provide complete details for every step of the problem-solving process."--Publisher's description.
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| 650 |
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|a Proof theory.
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| 650 |
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|a Induction (Mathematics)
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| 650 |
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|a Logic, Symbolic and mathematical.
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| 650 |
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|a Probabilities.
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| 650 |
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7 |
|a probability.
|2 aat
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| 650 |
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7 |
|a Induction (Mathematics)
|2 fast
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| 650 |
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7 |
|a Logic, Symbolic and mathematical
|2 fast
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| 650 |
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7 |
|a Probabilities
|2 fast
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| 650 |
|
7 |
|a Proof theory
|2 fast
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| 700 |
1 |
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|a Rosen, Kenneth H.
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| 758 |
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|i has work:
|a Handbook of Mathematical Induction (Text)
|1 https://id.oclc.org/worldcat/entity/E39PCYKmHwbvKD3pKxGcDPRPDC
|4 https://id.oclc.org/worldcat/ontology/hasWork
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| 776 |
0 |
8 |
|i Print version:
|a Gunderson, David S.
|t Handbook of Mathematical Induction.
|d Boca Raton : Chapman and Hall/CRC, ©2014
|z 9781420093643
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| 830 |
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0 |
|a Discrete Mathematics and Its Applications Ser.
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| 856 |
4 |
0 |
|u https://ebookcentral.proquest.com/lib/holycrosscollege-ebooks/detail.action?docID=5379135
|y Click for online access
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|a EBC-AC
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| 994 |
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|a 92
|b HCD
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