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Handbook of Mathematical Induction: Theory and Applications (Discrete Mathematics and Its Applications) - Softcover

Gunderson, David S.

 
9781138199019: Handbook of Mathematical Induction: Theory and Applications (Discrete Mathematics and Its Applications)
Softcover
ISBN 10: 113819901X ISBN 13: 9781138199019
Verlag: Chapman and Hall/CRC, 2016

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

David S. Gunderson is a professor and chair of the Department of Mathematics at the University of Manitoba in Winnipeg, Canada. He earned his Ph.D. in pure mathematics from Emory University. His research interests include Ramsey theory, extremal graph theory, combinatorial geometry, combinatorial number theory, and lattice theory.

Von der hinteren Coverseite

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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Verlag
Chapman and Hall/CRC
Erscheinungsdatum
2016
Sprache
Englisch
ISBN 10 
113819901X
ISBN 13 
9781138199019
Einband
Taschenbuch
Anzahl der Seiten
921
Kontakt zum Hersteller
CRC Press
https://www.routledge-ny.com

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