The Induction Book (Aurora: Dover Modern Math Originals) by Steven H. Weintraub

By Steven H. Weintraub

Mathematical induction — in addition to its equivalents, entire induction and well-ordering, and its quick final result, the pigeonhole precept — represent crucial facts concepts. each mathematician knows mathematical induction, and each scholar of arithmetic calls for a seize of its ideas. This quantity offers an creation and a radical publicity to those evidence options. aimed toward scholars of arithmetic in any respect degrees, the textual content is especially appropriate for classes in mathematical induction, theorem-proving, and problem-solving.
The remedy starts off with either intuitive and formal reasons of mathematical induction and its equivalents. the following bankruptcy offers many difficulties along with effects to be proved by means of induction, with options passed over to allow teachers to assign them to scholars. difficulties differ in trouble; the vast majority of them require little historical past, and the main complex contain calculus or linear algebra. the ultimate bankruptcy positive factors proofs too complex for college students to discover on their lonesome, a few of that are well-known theorems by means of famous mathematicians. For those attractive and demanding theorems, the writer presents expositions and proofs. The textual content concludes with a precious Appendix delivering the logical equivalence of many of the types of induction.

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