| Handbook of Mathematical Induction: Theory and Applications Contributor(s): Gunderson, David S. (Author) |
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ISBN: 1420093649 ISBN-13: 9781420093643 Publisher: CRC Press OUR PRICE: $266.00 Product Type: Hardcover Published: September 2010 Annotation: This comprehensive handbook enables readers to prove hundreds of mathematical results. It presents the formal development of natural numbers from axioms, which leads into set theory and transfinite induction. The book covers Peano's axioms, weak and strong induction, double induction, infinite descent downward induction, and variants of these inductions. It also contains numerous exercises highlighting the various levels of difficulty of an inductive proof, the variety of inductive techniques available, and the scope of results provable by mathematical induction. The final section includes solutions to all exercises in long form so that no steps are omitted. |
| Additional Information |
| BISAC Categories: - Mathematics | Set Theory - Computers | Operating Systems - General - Mathematics | Logic |
| Dewey: 511.36 |
| LCCN: 2010029756 |
| Series: Discrete Mathematics and Its Applications |
| Physical Information: 1.8" H x 7.2" W x 10.1" (3.80 lbs) 922 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |