This book will help you learn combinatorics in the most effective way possible - through problem solving. It contains over 200 combinatorics problems with detailed solutions.
Combinatorics is that part of mathematics that involves counting. It is therefore a fundamental part of math, and mastering it gives you wide reaching powers. The applications of combinatorics include: probability, cryptography, error correcting, games, music, and visual art. It can help you understand other parts of math from a more fundamental perspective.
The book begins with the basics of what is needed to solve combinatorics problems, including: definitions, a guide (or classification system) for solving problems based on the twelvefold way, as well as an overview of combinatorics.
The remainder of the book consists of problems and solutions. There are 2 separate groups of problems in this book. The first group consists of 82 problems, while the second group has another 124 problems (called exercises). Each group of problems begins with the easiest ones that anyone can solve and progresses to greater difficulty.
This book is good preparation for more advanced combinatorics texts such as Lovasz's Combinatorial Problems and Exercises.
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About the authors: Stefan Hollos and J. Richard Hollos are physicists by training, and enjoy anything related to probability. They are the authors of Probability Problems and Solutions, The Coin Toss: Probabilities and Patterns, Bet Smart: The Kelly System for Gambling and Investing, as well as Simple Trading Strategies That Work and Pairs Trading: A Bayesian Example, and are brothers and business partners at Exstrom Laboratories LLC in Longmont, Colorado. The websites for their work are Exstrom.com and QuantWolf.com.
Table of Contents
- Chapter 1 Introduction
- 1.1 Definitions
- 1.2 A Guide to Solving Counting Problems
- 1.3 Sum and Product Rule
- 1.4 Permutations and Combinations
- 1.5 Inclusion Exclusion Principle
- 1.6 Stirling Numbers of the Second Kind
- Chapter 2 Problems
- Chapter 3 Exercises
- Further Reading
- About the Authors
Send comments to: Richard Hollos (richard[AT]exstrom DOT com)
Copyright 2013-2014 by Exstrom Laboratories LLC