Updated 2021 by Alan Doerr, Kenneth Levasseur, University of Massachusetts Lowell.
An Instructor's Guide is available, including
chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; suggested coverage times; detailed solutions to most even-numbered exercises; sample quizzes, exams, and final exams.
Updated 2020 by Oscar Levin, University of Northern Colorado.
An introduction to topics in discrete math and as the "introduction to proofs" course for math majors. Four main topics are covered: counting, sequences, logic, and graph theory. Proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. An introductory chapter covering mathematical statements, sets, and functions and two additional topics (generating functions and number theory) are also included.
Exercises, activities, and an index.
2017 by Mitchel T. Keller, Washington and Lee University
William T. Trotter, Georgia Institute of Technology.
Covers the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete structures (graphs, digraphs, posets, interval orders), and discrete optimization (minimum weight spanning trees, shortest paths, network flows). Introduces discrete probability, Ramsey theory, combinatorial applications of network flows, and a few other topics.
2015 by Harris Kwong, SUNY Fredonia. Covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Exercises provided. Topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity.
