Levin O. Discrete Mathematics: An Open Introduction

3rd ed. — Independently published, 2019. — 407 p. — ISBN: 978-1792901690.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 over 470 exercises, including 275 with solutions and over 100 with hints. There are also Investigate! activities throughout the text to support active, inquiry based learning. In addition to lots of minor corrections, both to typographical and mathematical errors, this third edition includes a few major improvements, including:More than 100 new exercises, bringing the total to 473. The selection of which exercises have solutions has also been improved, which should make the text more useful for instructors who want to assign
homework from the book.
A new section in on trees in the graph theory chapter.
Substantial improvement to the exposition in chapter 0, especially the section on functions.
The interactive online version of the book has added interactivity.
Currently, many of the exercises are displayed as WeBWorK problems, allowing readers to enter answers to verify they are correct.