ABSTRACT

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 discuss

chapter 1|18 pages

What is mathematical induction?

chapter 2|16 pages

Foundations

chapter 3|16 pages

Variants of finite mathematical induction

chapter 5|8 pages

Paradoxes and sophisms from induction

chapter 6|12 pages

Empirical induction

chapter 7|20 pages

How to prove by induction

chapter 8|12 pages

The written MI proof

part |4 pages

Part II: Applications and exercises

chapter 9|28 pages

Identities

chapter 10|8 pages

Inequalities

chapter 11|26 pages

Number theory

chapter 12|30 pages

Sequences

chapter 13|16 pages

Sets

chapter 14|6 pages

Logic and language

chapter 15|22 pages

Graphs

chapter 16|28 pages

Recursion and algorithms

chapter 17|20 pages

Games and recreations

chapter 18|16 pages

Relations and functions

chapter 19|24 pages

Linear and abstract algebra

chapter 20|16 pages

Geometry

chapter 21|22 pages

Ramsey theory

chapter 22|14 pages

Probability and statistics

part |4 pages

Part III: Solutions and hints to exercises

chapter 23|8 pages

Solutions: Foundations

chapter 25|4 pages

Solutions: Paradoxes and sophisms

chapter 26|6 pages

Solutions: Empirical induction

chapter 27|90 pages

Solutions: Identities

chapter 28|38 pages

Solutions: Inequalities

chapter 29|54 pages

Solutions: Number theory

chapter 30|44 pages

Solutions: Sequences

chapter 31|18 pages

Solutions: Sets

chapter 32|4 pages

Solutions: Logic and language

chapter 33|28 pages

Solutions: Graphs

chapter 34|16 pages

Solutions: Recursion and algorithms

chapter 35|14 pages

Solutions: Games and recreation

chapter 36|14 pages

Solutions: Relations and functions

chapter 37|34 pages

Solutions: Linear and abstract algebra

chapter 38|16 pages

Solutions: Geometry

chapter 39|8 pages

Solutions: Ramsey theory

chapter 40|10 pages

Solutions: Probability and statistics