Discrete Mathematics: An Open Introduction

Note, this is the corrected Fall 2015 edition. A new, much improved (and cheaper) 2nd edition is now available.

This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. 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 proof" 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. The book contains 299 exercises, all with solutions (or at least a hint), as well as 45 additional more involved problems suitable for homework. There are also Investigate! problems throughout the text to support active, inquiry based learning.

While there are many fine discrete math textbooks available, this text has the following advantages:

• It is written to be used in an inquiry rich course.
• It is written to be used in a course for future math teachers.
• It is open source, with low cost print editions and free electronic editions.