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About this product
- DescriptionHandbook 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 tation 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.
- Author BiographyDavid 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.
- Author(s)David S. Gunderson
- PublisherTaylor & Francis Ltd
- Date of Publication15/10/2009
- Series TitleDiscrete Mathematics and its Applications
- Series Part/Volume Numberv. 58
- Country of PublicationUnited States
- ImprintChapman & Hall/CRC
- Content Note38 black & white illustrations, 9 black & white tables
- Weight1746 g
- Width178 mm
- Height254 mm
- Spine46 mm
- Series Edited byKenneth H. Rosen
- Format DetailsUnsewn / adhesive bound
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