Başlık:
Handbook of Mathematical Induction : Theory and Applications
Yazar:
Gunderson, David S., author.
ISBN:
9780429147937
Basım Bilgisi:
First edition.
Fiziksel Tanımlama:
1 online resource
Seri:
Discrete Mathematics and Its Applications
İçerik:
chapter 1 What is mathematical induction? -- chapter 2 Foundations -- chapter 3 Variants of finite mathematical induction -- chapter 4 Inductive techniques applied to the infinite -- chapter 5 Paradoxes and sophisms from induction -- chapter 6 Empirical induction -- chapter 7 How to prove by induction -- chapter 8 The written MI proof -- part Part II: Applications and exercises -- chapter 9 Identities -- chapter 10 Inequalities -- chapter 11 Number theory -- chapter 12 Sequences -- chapter 13 Sets -- chapter 14 Logic and language -- chapter 15 Graphs -- chapter 16 Recursion and algorithms -- chapter 17 Games and recreations -- chapter 18 Relations and functions -- chapter 19 Linear and abstract algebra -- chapter 20 Geometry -- chapter 21 Ramsey theory -- chapter 22 Probability and statistics -- part Part III: Solutions and hints to exercises -- chapter 23 Solutions: Foundations -- chapter 24 Solutions: Inductive techniques applied to the infinite -- chapter 25 Solutions: Paradoxes and sophisms -- chapter 26 Solutions: Empirical induction -- chapter 27 Solutions: Identities -- chapter 28 Solutions: Inequalities -- chapter 29 Solutions: Number theory -- chapter 30 Solutions: Sequences -- chapter 31 Solutions: Sets -- chapter 32 Solutions: Logic and language -- chapter 33 Solutions: Graphs -- chapter 34 Solutions: Recursion and algorithms -- chapter 35 Solutions: Games and recreation -- chapter 36 Solutions: Relations and functions -- chapter 37 Solutions: Linear and abstract algebra -- chapter 38 Solutions: Geometry -- chapter 39 Solutions: Ramsey theory -- chapter 40 Solutions: Probability and statistics.
Özet:
"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.
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Kütüphane | Materyal Türü | Demirbaş Numarası | Yer Numarası | Durumu/İade Tarihi | Materyal Ayırtma |
|---|---|---|---|---|---|
Arıyor... | E-Kitap | 544049-1001 | QA9.54 G863 2014 | Arıyor... | Arıyor... |