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008 101213t2011 flua f b 001 0 eng d
020 _a9781420093643 (hardcover : alk. paper)
020 _a1420093649 (hardcover : alk. paper)
039 9 _a201107140054
_bVLOAD
_c201106101630
_dfauzi
_c201012131602
_dtraining
_y201012131602
_ztraining
040 _aUMP
090 _aQA9.54 .G86 2011
100 1 _aGunderson, David S.
245 1 0 _aHandbook of mathematical induction :
_btheory and applications /
_cDavid S. Gunderson
260 _aBoca Raton, FL :
_bCRC Press,
_cc2011
300 _axxv, 893 p. :
_bill. ;
_c27 cm.
490 1 _aDiscrete mathematics and its applications
504 _aIncludes bibliographical references and indexes
505 0 _aWhat 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 -- 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
520 _a"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."--Publisher’s description
650 0 _aProof theory
650 0 _aInduction (Mathematics)
650 0 _aLogic, Symbolic and mathematical
650 0 _aProbabilities
830 0 _aCRC Press series on discrete mathematics and its applications
999 _aVIRTUA40
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