Introduction to Mathematical Proofs

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 when 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.