Discrete Mathematics

An Open Introduction, 3rd edition

This is the new 3rd edition of the book. The previous version is available at the 2nd edition's site.

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. Since Spring 2013, the book has been used as the primary textbook or a supplemental resource at multiple universities around the world. The text is endoursed by the American Institute of Mathematics' Open Textbook Initiative and is well reviewed on the Open Textbook Library.

This 3rd edition brings many improvements, including nearly 100 new exercises, a new section on trees in the graph theory chapter, and improved exposition throughout, as well as many corrections to previous errors. Previous editions will continue to be available indefinitely.

Please contact the author with feedback and suggestions, or if you are decide to use the book in a course you are teaching.

Get the book

The entire book is available for free as an interactive online ebook. This should work well on all screen sizes, including smart phones. Hints and solutions to examples and exercises are hidden but easily revealed by clicking on their links. Some exercises also allow you to enter and check your work, so you can try multiple times without spoiling the answer.

For offline use, a free pdf version, suitable for reading on a tablet or computer, is available for download. This should be searchable and easy to navigate using embedded links. Hints and solutions (when available) can be accessed by clicking on the exercise number, and clicking on the number of the hint or solution will bring you back to the exercise.

If you prefer a physical copy, an inexpensive print version of the text is available on Amazon. This should be cheaper than printing the entire book and binding it yourself. Page numbers match the pdf version.

PreTeXt (and LaTeX) source

The source files for this book are available on GitHub.

About the book

The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proofs" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.

Four main topics are covered: counting, sequences, logic, and graph theory. Along the way, proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. An introductory chapter covering mathematical statements, sets, and functions helps students gain familiarity with the language of mathematics, and two additional topics (generating functions and number theory) are also included.

While the book began as a set of lecture notes, it now contains a number of features that should support its use as a primary textbook:

  • 473 exercises, including 275 with solutions and another 109 with hints. Exercises range from easy to quite involved, with many problems suitable for homework.
  • Investigate! activities throughout the text to support active, inquiry based learning.
  • A full index and list of symbols.
  • Consistent and helpful page layout and formatting (i.e., examples are easy to identify, important definitions and theorems in boxes, etc.).

About the author

Oscar Levin is an associate professor at the University of Northern Colorado. He has taught mathematics at the college level for over 10 years and received multiple teaching awards. He received his Ph.D. in mathematical logic from the University of Connecticut in 2009.


Creative Commons License
Discrete Mathematics: An Open Introduction by Oscar Levin is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. You are free to download, use, print, and even sell this work as you wish to. You can also modify the text as much as you like (create a custom edition for your students, for example), as long as you attribute the parts of the text you use to the author.

If you are interested in using parts of the book combined with another text with a similar but different license (GFDL, for example), please reach out to get permission to modify the license.