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This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.
Chapters 0–3 cover fundamental operations involving sets and the principle of mathematical induction, and standard combinatorial topics: basic counting principles, permutations, combinations, the inclusion-exclusion principle, generating functions, recurrence relations, and an introduction to the analysis of algorithms. Applications are emphasized wherever possible and more than 200 exercises at the ends of these chapters help students test their grasp of the material.
Chapters 4 and 5 survey graphs and digraphs, including their connectedness properties, applications of graph coloring, and more, with stress on applications to coding and other related problems. Two important problems in network optimization ― the minimal spanning tree problem and the shortest distance problem ― are covered in the last two chapters. A very brief nontechnical exposition of the theory of computational complexity and NP-completeness is outlined in the appendix.
- Sales Rank: #616476 in eBooks
- Published on: 2012-04-30
- Released on: 2012-04-30
- Format: Kindle eBook
About the Author
V. K. Balakrishnan is Professor Emeritus at the University of Maine.
Most helpful customer reviews
25 of 26 people found the following review helpful.
Excellent introduction to Discrete Mathematics
By Carlos Ordonez
I was misled by the low price thinking this would be a bad book. But I was Mathematics. The reason for which I bought this text book is because it has many proofs and in particular it includes the proofs of a couple of theorems I had been looking for. The presentation is formal but clear. The author includes plenty of excercises and answers are provided for odd numbered ones. So far I haven't found errors or typos. The book has enough material to be used in a two semester course sequence. I would give it a relations, total and partial orders, logic, combinatorics, regular languages, graphs, number theory, algorithm analysis and even NP-completeness. This book should be useful for both Math and CS students.
22 of 24 people found the following review helpful.
Excellent Text
By Robert Street
As with any Dover text, it is important to remember that this text is designed to teach the material, not to coddle the reader. This text provides broad and deep coverage of the various topics that fall under discrete mathematics (set theory, boolean logic, graph theory, etc.) with clarity and simplicity. This book is not designed to help you pass a test, but is instead designed to help you grasp and understand the topic, which it does very well. Easily the best book I own on this topic (I often joke that the author covered my first semester course on discrete math in the first chapter!).
8 of 8 people found the following review helpful.
A good supplement, but not a guide for a new learner
By Jadrian Miles
This book is full of great examples and loads of practice problems. Its descriptions, for students fairly comfortable with mathematical writing, are concise and no-nonsense, which can be great. It makes a good reference, in that way, but the book doesn't do much to guide your intuition. It's also full of tiny mistakes (seemingly due to rushed editing) that should be no problem for an advanced student or someone working closely with another guide to the subject (a teacher, tutor, or other textbook). But for learners who might struggle with the material, these mistakes in the book can really interrupt understanding. (As a result, I chose not to assign this book to my students.)
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