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.
This 3rd edition brings many improvements, including nearly 100 new
exercises (including many interactive exercises providing instant feedback), a
new section on trees in the graph theory chapter, and improved exposition
throughout. Previous editions will continue to be available indefinitely. A few
times a year, the text is updated with a new "printing" to correct errors. See
the errata list for more information.
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 will 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.
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. There is also a
cheap Kindle version available; it works great on Android tablets;
unfortunately it seems the math does not render well on Amazon's e-ink
readers.
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.

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: 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