Handbook of Mathematical Induction: Theory and Applications

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.