Introduction to Discrete Mathematics via Logic and Proof

This is a textbook for undergraduate students with the primary goals being to help them learn how to read and write proofs, ease their way into abstract thinking and formal mathematical notations, and master the core concepts of discrete mathematics. The prerequisites are minimal for this book and it can be used in any introductory course on proofs and discrete mathematics, both for a mathematics-oriented as well as a computer science-oriented course.

 

A wide range of topics are included in the book, which necessarily means that some of these topics can only be discussed tangentially. Topics in logic, including Propositional Logic and First-Order Logic are discussed quite nicely in the first part of the book. In fact, these two topics cover almost 30% of the book. The reviewer liked this introduction which contained several historical remarks and context for the material, a feature which is repeated more or less, throughout the book. After this introduction, the reader is gently guided towards other topics.

 

The unique style of using the deductive perspective on mathematical logic will definitely help the students get a more balanced view of the methodology in mathematics. The material is incremental in difficulty and ends with a good primer on graph theory. In between, we get to see topics in set theory, combinatorics, functions, posets, and Boolean algebra. Many of these topics are not discussed at length due to the nature of the book as well as the intended audience, which makes the exclusion of a comprehensive bibliography guiding the readers to further material a drawback.

 

At times, the exposition felt too dry, but this might be the personal taste of the reviewer rather than a drawback of the book. Overall, the book gives a good introduction to logic and proof, using various topics in discrete mathematics. The exercises are well thought out and give additional material to think about.  The choice of topics is balanced and the overall style is easy to read.

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Manjil Saikia (manjil@saikia.in) is presently at Cardiff University, UK. He studied mathematics at Tezpur (India), Trieste (Italy) and Vienna (Austria), and manages the bilingual (Assamese and English) website Gonit Sora (https://gonitsora.com).