Handbook of Mathematical Induction: Theory and Applications

ISBN-13: 9781420093643 / Angielski / Twarda / 2010 / 921 str.

David S. Gunderson;Kenneth H. Rosen

Opis

Enables readers to prove hundreds of mathematical results. This book 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.

Spis treści

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.

O autorze

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.