Mathematical Induction

A Powerful and Elegant Method of Proof

Titu Andreescu, Vlad Crisan (Autoren)

Buch | Hardcover

432 Seiten

2017
Xyz Press (Verlag)
978-0-9968745-9-5 (ISBN)

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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.

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.

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

Erscheinungsdatum	14.08.2017
Verlagsort	TX
Sprache	englisch
Maße	152 x 229 mm
Gewicht	758 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
Themenwelt	Sozialwissenschaften ► Pädagogik
ISBN-10	0-9968745-9-3 / 0996874593
ISBN-13	978-0-9968745-9-5 / 9780996874595
Zustand	Neuware