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.
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.
… a treasure trove for anyone who is … interested in mathematics as
a hobby, or as the target of proof automation or assistance. It
could also be the basis for a crosscutting course in mathematics,
based on seeing how one can apply a single proof technique across
the field.
— Simon Thompson in Computing News, May 2011Gunderson started out
collecting some induction problems for discrete math students and
then couldn't stop himself, thereafter assembling more than 750 of
the addictive things for this handbook and supplementing them with
a grounding in theory and discussion of applications. He offers
500-plus complete solutions, and many of the other problems come
with hints or references; unlike other treatments, this handbook
treats the subject seriously and is not just a ‘collection of
recipes’. It’s a book that will work well with most math or
computing science courses, on a subject that pertains to graph
theory, point set topology, elementary number theory, linear
algebra, analysis, probability theory, geometry, group theory, and
game theory, among many other topics.
—SciTech Book News, February 2011… a unique work … the ostensibly
narrow subject of mathematical induction is carefully and
systematically expounded, from its more elementary aspects to some
quite sophisticated uses of the technique. This is done with a
(very proper!) emphasis on solving problems by means of some form
of induction or other … any of us who regularly teach the
undergraduate course aimed at introducing mathematics majors to
methods of proof quite simply need to own this book. … In this boot
camp course, it is imperative that problems should be abundant,
both in supply and variety, and should be capable of careful
dissection. Gunderson hit[s] the mark on both counts … Gunderson’s
discussions are evocative and thorough and can be appreciated by
mathematicians of all sorts … [he] develop[s] the requisite
surrounding material with great care, considerably enhancing the
value of his book as a supplementary text for a huge number of
courses, both at an undergraduate and graduate level … a very
welcome addition to the literature …
—MAA Reviews, December 2010
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