Discrete Mathematics

Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math and computer science majors. The book is especially well-suited for courses that incorporate inquiry-based learning. Since Spring 2013, the book has been used as the primary textbook or a supplemental resource at more than 200 colleges and universities around the world (see the partial adoptions list). The text is endorsed by the American Institute of Mathematics' Open Textbook Initiative and is well reviewed on the Open Textbook Library.

After many years of development, I am pleased to announce that the 4th edition of Discrete Mathematics: an Open Introduction is now available, here and on Runestone Academy.

The new edition brings many improvements and a new organization of content. In particular, the book now starts with logic and proofs, then practices those proofs with graph theory. The second half of the book contains material on counting (with a new "application to probability" section) and sequences. Over the last few years, I have found that students have more success with this arrangement. There is also a stronger emphasis on discrte structures, which should make the book more useful for students in computer science, while still focusing on understanding mathematical concepts essential for math majors and future math teachers.

There is more interactivity as well. More interactive exercises (which you can give students credit for if you create a course with the book on Runestone Academy; it is completely free for you and your students) and some interactive Sage and Python code to explore some topics.

Online homework sets are available through Runestone Academy (free), Edfinity (inexpensive) or as WeBWorK sets from the author (the WeBWorK exercises are available in the Contrib folder of the OPL as well).

Please contact the author with feedback and suggestions, or if you are decide to use the book in a course you are teaching. You can also easily submit feedback about an error or typo by creating a GitHub issue.

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, and work well with screen readers for visually impaired students. 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.

A print version will be available late spring 2025, released by CRC Press. The online version will remain available and free forever, and the book is still released under a Creative Commons License (but note the new Non-Commercial addition to the license).

PreTeXt (and LaTeX) source

The source files for this book are available on GitHub.

Instructor and student resources

There are a number of videos instructors have made for classes they taught using the book. Check out the playlists below. If you make videos or know of others, please share them.

• Mathematical Visual Proofs. Beautifully animated videos illustrating ideas from the book.
• Dr. Trevor Bazett's Course. A complete course that uses the textbook as a basis for the videos.

If you are using the book in a class you are teaching, instructor resources are available by request. Just contact the author. You can also request WeBWorK homework sets if you have access to a WeBWorK server.

We also have a google group for instructors teaching discrete math, especially with the book. It would be lovely to discuss teaching strategies with you all there. Let's build a community!

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. Originally designed to support future math teachers, the text has a friendly and informal tone, and puts an emphasis on understanding the included concepts, rather than simply memorizing procedures. The book has also been successfully used in courses catering to computer science students, who also benefit from the deeper understanding it promotes.

Four main topics are covered: Logic, graph theroy, counting, sequences. Along the way, proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The 4th edition has a stronger emphasis on discrete structures, including sets, functions, and relations. 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:

• Over 750 exercises, including many with solutions and hints. Exercises range from easy to quite involved, with many problems suitable for homework.
• Investigate! and preview 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

License

Discrete Mathematics: an Open Introduction, 4th edition by Oscar Levin is licensed under CC BY-NC-SA 4.0

You are free to download, use, and print as you wish to, for noncommercial purposes. 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 and release your modified version under a compatible license.

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.