Read more about Discrete Mathematics: An Open Introduction - 3rd Edition

Discrete Mathematics: An Open Introduction - 3rd Edition

(5 reviews)

Oscar Levin, University of Northern Colorado

Copyright Year: 2016

ISBN 13: 9781534970748

Publisher: Oscar Levin

Language: English

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CC BY-SA

Reviews

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Reviewed by Nachimuthu Manickam, Professor, DePauw University on 12/18/20

This book covers all the important topics such as set theory, logic, counting techniques, number theory, graph theory etc. These are the topics normally covered in any typical discrete math course. The "investigate" part for each concept is an... read more

Reviewed by John Salisbury, Adjunct Instructor, Rogue Community College on 8/25/20

I have not taken discrete mathematics so I am not sure what all the areas are but it's over 400 pages long and seems to cover in good depth the topics that it covers. It appears to have a comprehensive index and it also has a "list of symbols"... read more

Reviewed by Elena Braynova, Professor, Worcester State University on 6/30/20

Almost every CS program requires students to take a Discrete Mathematics course. The textbook covers most of the topics usually discussed in a Discrete Mathematics course such as Counting Techniques, Recurrence Relations, Set Theory, Logic, Graph... read more

Reviewed by John Salisbury, Mathematics Instructor, Rogue Community College on 4/11/17

There are many topics in discrete mathematics. This book does a fine job of covering numerous topics in this area, including among several other topics, symbolic logic, counting, sets, and a short section on number theory. There is very good... read more

Reviewed by Namita Sarawagi, Associate Professor, Rhode Island College on 4/11/17

This textbook, “Discrete Mathematics: An Open Introduction”, by Oscar Levin, provides a good overview of topics in Discrete Mathematics. The primary focus of this text is not to provide a rigorous mathematical foundation for Computer Science... read more

Table of Contents

0 Introduction and Preliminaries 1

  • 0.1 What is Discrete Mathematics?
  • 0.2 Mathematical Statements
  • 0.3 Sets

1 Counting

  • 1.1 Additive and Multiplicative Principles
  • 1.2 Binomial Coefficients
  • 1.3 Combinations and Permutations
  • 1.4 Combinatorial Proofs
  • 1.5 Stars and Bars
  • 1.6 Advanced Counting Using PIE
  • 1.7 Chapter Summary

2 Sequences

  • 2.1 Definitions
  • 2.2 Arithmetic and Geometric Sequences
  • 2.3 Polynomial Fitting
  • 2.4 Solving Recurrence Relations
  • 2.5 Induction
  • 2.6 Chapter Summary

3 Symbolic Logic and Proofs

  • 3.1 Propositional Logic
  • 3.2 Proofs
  • 3.3 Chapter Summary

4 Graph Theory

  • 4.1 Definitions
  • 4.2 Trees
  • 4.3 Planar Graphs
  • 4.4 Coloring
  • 4.5 Euler Paths and Circuits
  • 4.6 Matching in Bipartite Graphs
  • 4.7 Chapter Summary

5 Additional Topics

  • 5.1 Generating Functions
  • 5.2 Introduction to Number Theory

Ancillary Material

About the Book

Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. The textbook has been developed while teaching the Discrete Mathematics course at the University of Northern Colorado. Primitive versions were used as the primary textbook for that course since Spring 2013, and have been used by other instructors as a free additional resource. Since then it has been used as the primary text for this course at UNC, as well as at other institutions.

About the Contributors

Author

Oscar Levin is an Associate Professor at the University of Northern Colorado in the School of Mathematical Sciences. He has taught mathematics at the college level for over 10 years and has received multiple teaching awards. He received his Ph.D. in mathematics from the University of Connecticut in 2009.