Combinatorics (Wiley Series in Discrete Mathematics and Optimization)

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Product Description

A mathematical gem� freshly cleaned and polished

This book is intended to be used as the text for a first course in combinatorics. the text has been shaped by two goals, namely, to make complex mathematics accessible to students with a wide range of abilities, interests, and motivations; and to create a pedagogical tool, useful to the broad spectrum of instructors who bring a variety of perspectives and expectations to such a course.

Features retained from the first edition:

• Lively and engaging writing style
• Timely and appropriate examples
• Numerous well-chosen exercises
• Flexible modular format
• Optional sections and appendices

Highlights of Second Edition enhancements:

• Smoothed and polished exposition, with a sharpened focus on key ideas
• Expanded discussion of linear codes
• New optional section on algorithms
• Greatly expanded hints and answers section
• Many new exercises and examples

Combinatorics (Wiley Series in Discrete Mathematics and Optimization) Review

There is no question that combinatorics is becoming more important in the practice of computer science. While some of the most important techniques are covered in discrete mathematics courses, there is not enough breadth or depth in the coverage. As a consequence, one of my goals this upcoming year is to convince my colleagues at Mount Mercy to add a course in combinatorics to the curriculum. As part of the proposal, I need to create a list of resources and a sample schedule of topics to be covered. To begin this process, I studied several combinatorics texts and decided that this one was the best.
There are six chapters, and the titles are:

 Chapter 1 The mathematics of choice
=623; Chapter 2 The combinatorics of finite functions
 Chapter 3 Polya's theory of enumeration
᠒3; Chapter 4 Generating functions
1623; Chapter 5 Enumeration in graphs
 Chapter 6 Codes and designs

The coverage is thorough and the sequence has been structured to make the last four chapters independent. This necessitated the duplication of some definitions and theorems, but it is a sensible strategy. There is more than enough material for a one-semester course, so this increases the options available to an instructor. I often skip chapters in a textbook in order to cover a topic I consider critical and find it very helpful when the author repeats key definitions and theorems.
The style is mathematically rigorous, the approach is that of a mathematics textbook with the sequence being: theorem, proof, example(s). A large number of exercises are given at the end of each section and solutions/hints to the odd numbered ones are included. It is a sound combinatorics text and the one that I would most likely use if I ever teach such a course.

Published in Journal of Recreational Mathematics, reprinted with permission.

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