Handbook of Mathematical Induction : Theory and Applications.

By:

Gunderson, David S

Material type: Text

text

Media type:

computer

Carrier type:

online resource

ISBN:

9781420093650

Subject(s):

Logic, Symbolic and mathematical

Genre/Form:

Electronic books.

Additional physical formats: Print version:: Handbook of Mathematical InductionDDC classification:

LOC classification:

QA9.54 .G86 2011

Online resources:

Click to View

Contents:

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 -- Chapter 14: Logic and language -- Chapter 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 -- Chapter 28: Solutions: Inequalities -- Chapter 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 -- Appendix B: Inducing you to laugh?.

Appendix C: The Greek alphabet -- References.

Summary: This comprehensive handbook presents hundreds of classical theorems and proofs that span many areas, including basic equalities and inequalities, combinatorics, linear algebra, calculus, trigonometry, geometry, set theory, game theory, recursion, and algorithms. It derives many forms of mathematical induction, such as infinite descent and the axiom of choice, from basic principles. Requiring only a modest amount of mathematical maturity to understand most results and proofs, the book contains more than 750 exercises-with complete solutions to at least 500. It also includes nearly 600 bibliographic references, numerous cross references, and an extensive index of over 3,000 entries.

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Appendix C: The Greek alphabet -- References.

This comprehensive handbook presents hundreds of classical theorems and proofs that span many areas, including basic equalities and inequalities, combinatorics, linear algebra, calculus, trigonometry, geometry, set theory, game theory, recursion, and algorithms. It derives many forms of mathematical induction, such as infinite descent and the axiom of choice, from basic principles. Requiring only a modest amount of mathematical maturity to understand most results and proofs, the book contains more than 750 exercises-with complete solutions to at least 500. It also includes nearly 600 bibliographic references, numerous cross references, and an extensive index of over 3,000 entries.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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