Discrete Mathematics: An Open Introduction

(2 reviews)

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Oscar Levin, University of Northern Colorado

Pub Date: 2016

ISBN 13: 978-1-5349707-4-8

Publisher: Independent

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Reviewed by John Salisbury, Mathematics Instructor, Rogue Community College, on 4/12/2017.

There are many topics in discrete mathematics. This book does a fine job of covering numerous topics in this area, including among several other … read more

 

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Reviewed by Namita Sarawagi, Associate Professor, Rhode Island College, on 4/12/2017.

This textbook, “Discrete Mathematics: An Open Introduction”, by Oscar Levin, provides a good overview of topics in Discrete Mathematics. The primary … 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 Planar Graphs 
  • 4.3 Coloring 
  • 4.4 Euler Paths and Circuits 
  • 4.5 Matching in Bipartite Graphs
  • 4.6 Chapter Summary

5 Additional Topics 

  • 5.1 Generating Functions 
  • 5.2 Introduction to Number Theory 

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(s)

Oscar Levin is an Assistant 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.