Handbook of Mathematical Induction : Theory and Applications

Format:

Book

Author/Creator:

Gunderson, David S., author.

Series:

CRC Press series on discrete mathematics and its applications.

Discrete mathematics and its applications

Language:

English

Subjects (All):

Proof theory.

Induction (Mathematics).

Logic, Symbolic and mathematical.

Probabilities.

Physical Description:

1 online resource (xxv, 893 pages) : illustrations.

Edition:

First edition.

Place of Publication:

Boca Raton, FL : CRC Press, 2014.

Summary:

"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, Zorns 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."--Provided by publisher.

Contents:

What is mathematical induction?

Foundations

Variants of finite mathematical induction

Inductive techniques applied to the infinite

Paradoxes and sophisms from induction

Empirical induction

How to prove by induction

The written MI proof

Identities

Inequalities

Number theory

Sequences

Sets

Logic and language

Graphs

Recursion and algorithms

Games and recreations

Relations and functions

Linear and abstract algebra

Geometry

Ramsey theory

Probability and statistics.

Notes:

Includes bibliographical references and indexes.

Description based on print version record.

ISBN:

9781040069165

1040069169

9780429147937

0429147937

9781420093650

1420093657

OCLC:

1035519175