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Full Description
This book serves as a very good resource and teaching material for anyone who wants to discover the beauty of Induction and its applications, from novice mathematicians to Olympiad-driven students and professors teaching undergraduate courses. The authors explore 10 different areas of mathematics, including topics that are not usually discussed in an Olympiad-oriented book on the subject. Induction is one of the most important techniques used in competitions and its applications permeate almost every area of mathematics.
Contents
Foreword
A Brief Overview of Induction
Theory and Examples
Introductory Notions
Variants of Induction
Paradox of Induction
Well-Ordering and Transfinite Induction
Proposed Problems
Sums, Products, and Identities
Theory and Examples
Proposed Problems
Functions and Functional Equations
Theory and Examples
Proposed Problems
Inequalities
Theory and Examples
Proposed Problems
Sequences and Recurrences
Theory and Examples
Proposed Problems
Number Theory
Theory and Examples
ThepandönpùTechnique
Divisibility
Representations
Proposed Problems
Combinatorics
Theory and Examples
Partitions and Configurations
Graph Theory
Combinatorial Geometry
Proposed Problems
Games
Theory and Examples
Proposed Problems
Miscellaneous Topics
Geometry
Examples
Proposed Problems
Induction in Calculus
Examples
Proposed Problems
Induction in Algebra
Examples
Proposed Problems
Solutions
A Brief Overview of Induction
Sums, Products, and Identities
Functions and Functional Equations
Inequalities
Sequences and Recurrences
ContentsNumber Theory
Combinatorics
Games
Miscellaneous Topics
Geometry
Induction in Calculus
Induction in Algebra
Notations and Abbreviations
Bibliography
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