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Handbook of Mathematical Induction - Theory and Applications (Paperback)
Loot Price: R1,684
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Handbook of Mathematical Induction - Theory and Applications (Paperback)
Series: Discrete Mathematics and Its Applications
Expected to ship within 12 - 17 working days
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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.
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