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Handbook of Mathematical Induction: Theory and Applications

Authored by: David S. Gunderson

Print publication date:  September  2010
Online publication date:  January  2014

Print ISBN: 9781420093643
eBook ISBN: 9781420093650
Adobe ISBN:

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Book description

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.

Table of contents

Chapter  1:  What is mathematical induction? Download PDF
Chapter  2:  Foundations Download PDF
Chapter  3:  Variants of finite mathematical induction Download PDF
Chapter  4:  Inductive techniques applied to the infinite Download PDF
Chapter  5:  Paradoxes and sophisms from induction Download PDF
Chapter  6:  Empirical induction Download PDF
Chapter  7:  How to prove by induction Download PDF
Chapter  8:  The written MI proof Download PDF
Chapter  9:  Identities Download PDF
Chapter  10:  Inequalities Download PDF
Chapter  11:  Number theory Download PDF
Chapter  12:  Sequences Download PDF
Chapter  13:  Sets Download PDF
Chapter  14:  Logic and language Download PDF
Chapter  15:  Graphs Download PDF
Chapter  16:  Recursion and algorithms Download PDF
Chapter  17:  Games and recreations Download PDF
Chapter  18:  Relations and functions Download PDF
Chapter  19:  Linear and abstract algebra Download PDF
Chapter  20:  Geometry Download PDF
Chapter  21:  Ramsey theory Download PDF
Chapter  22:  Probability and statistics Download PDF
Chapter  23:  Solutions: Foundations Download PDF
Chapter  24:  Solutions: Inductive techniques applied to the infinite Download PDF
Chapter  25:  Solutions: Paradoxes and sophisms Download PDF
Chapter  26:  Solutions: Empirical induction Download PDF
Chapter  27:  Solutions: Identities Download PDF
Chapter  28:  Solutions: Inequalities Download PDF
Chapter  29:  Solutions: Number theory Download PDF
Chapter  30:  Solutions: Sequences Download PDF
Chapter  31:  Solutions: Sets Download PDF
Chapter  32:  Solutions: Logic and language Download PDF
Chapter  33:  Solutions: Graphs Download PDF
Chapter  34:  Solutions: Recursion and algorithms Download PDF
Chapter  35:  Solutions: Games and recreation Download PDF
Chapter  36:  Solutions: Relations and functions Download PDF
Chapter  37:  Solutions: Linear and abstract algebra Download PDF
Chapter  38:  Solutions: Geometry Download PDF
Chapter  39:  Solutions: Ramsey theory Download PDF
Chapter  40:  Solutions: Probability and statistics Download PDF
References Download PDF
AppendixA Download PDF
Name_Index Download PDF
AppendixC Download PDF
prelims Download PDF
Subject_Index Download PDF
AppendixB Download PDF
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