Handbook of Mathematical Induction - David S. Gunderson

Handbook of Mathematical Induction

Theory and Applications
Buch | Hardcover
922 Seiten
2010
Chapman & Hall/CRC (Verlag)
978-1-4200-9364-3 (ISBN)
268,10 inkl. MwSt
Enables readers to prove hundreds of mathematical results. This title presents the formal development of natural numbers from axioms, which leads into set theory and transfinite induction. It covers Peano's axioms, weak and strong induction, double induction, infinite descent downward induction, and variants of these inductions.
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.

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.

THEORY: 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. APPLICATIONS AND EXERCISES: 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. SOLUTIONS AND HINTS TO EXERCISES. APPENDICES. References. Index.

Erscheint lt. Verlag 28.9.2010
Reihe/Serie Discrete Mathematics and Its Applications
Zusatzinfo 9 Tables, black and white; 38 Illustrations, black and white
Sprache englisch
Maße 178 x 254 mm
Gewicht 1880 g
Themenwelt Mathematik / Informatik Mathematik Allgemeines / Lexika
Mathematik / Informatik Mathematik Graphentheorie
Mathematik / Informatik Mathematik Logik / Mengenlehre
Technik Elektrotechnik / Energietechnik
ISBN-10 1-4200-9364-9 / 1420093649
ISBN-13 978-1-4200-9364-3 / 9781420093643
Zustand Neuware
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