David S. Gunderson

Handbook of Mathematical Induction (eBook, PDF)

Theory and Applications

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 921
• Erscheinungstermin: 9. Januar 2014
• Englisch
• ISBN-13: 9781420093650
• Artikelnr.: 57081363

Autorenporträt

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.

Inhaltsangabe

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.