This successful book has one goal: to help students develop the necessary skills to write clear, correct, and concise proofs. The beautiful proofs found in this new edition will encourage many students to study higher mathematics.

Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers.

It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow while writing proofs.

The third edition includes a new Chapter 10, Proofs from Combinatorics. This unique chapter, authored by Prof. Bóna, offers instructors a choice to include coverage of combinatorics, which, for many students in this course, might be an introduction. Readers will encounter counting arguments, combinatorial proofs of identities, and proofs from graph theory. In this chapter, many of the exercises introduce classic material that is not covered in the text. This helps the instructor spend more time on combinatorics if the instructor prefers to do so.

The first two editions of this successful textbook were authored by Charles E. Roberts Jr. Miklós Bóna picks up his legacy with this revision and a new revision of Roberts’ Elementary Differential Equations (CRC Press), now in its third edition.

Charles E. Roberts Jr. (deceased) was Professor Emeritus in the Department of Mathematics and Computer Science at Indiana State University. He is remembered as a master teacher and prolific researcher. His book, A Mathematical Introduction to Proofs, is also published by CRC Press.

Miklós Bóna received his Ph.D. in mathematics from the Massachusetts Institute of Technology in 1997. Since 1999, he has taught at the University of Florida, where, in 2010, he was inducted into the Academy of Distinguished Teaching Scholars. Professor Bóna has mentored numerous graduate and undergraduate students. He is the author of six books and more than 100 research articles, mostly focusing on enumerative and analytic combinatorics. His book, Combinatorics of Permutations, won a 2006 Outstanding Title Award from Choice, the journal of the American Library Association. He is also an Editor-in-Chief of the Electronic Journal of Combinatorics and two book series at CRC Press.