A Brief Journey in Discrete Mathematics. 1st ed. 2020

種類:

電子ブック

責任表示:

by Randolph Nelson

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Nelson, Randolph.
• SpringerLink (Online service)

ISBN:

9783030378615 [3030378616]    

注記:

1. Introduction -- 2. Let Me Count the Ways -- 3. Syntax Precedes Semantics -- 4. Fearful Symmetry -- 5. All that Glitters is not Gold -- 6. Heads I Win, Tails you Lose -- 7. Sums of the Powers of Successive Integers -- 8. As Simple as 2+ 2 = 1 -- 9. Hidden in Plain Sight -- 10. Running off the Page -- Appendix A. Tools of the Trade -- Appendix B. Notation and Identities Derived in the Book -- Bibliography -- Index.
The goal of this book is to showcase the beauty of mathematics as revealed in nine topics of discrete mathematics. In each chapter, properties are explored through a series of straightforward questions that terminate with results that lie at the doorstep of a field of study. Each step along the way is elementary and requires only algebraic manipulation. This frames the wonder of mathematics and highlights the complex world that lies behind a series of simple, mathematical, deductions. Topics addressed include combinatorics, unifying properties of symmetric functions, the Golden ratio as it leads to k-bonacci numbers, non-intuitive and surprising results found in a simple coin tossing game, the playful, trick question aspect of modular systems, exploration of basic properties of prime numbers and derivations of bewildering results that arise from approximating irrational numbers as continued fraction expansions. The Appendix contains the basic tools of mathematics that are used in the text along with a numerou

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