MATHEMATICAL INDUCTION. A POWERFUL AND ELEGANT METHOD OF PROOF

• 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
• Other Books from XYZ Press

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.