By Olympia Nicodemi | Discrete Mathematics

In the crowded field of undergraduate mathematics textbooks, most tend to blend together: a predictable march of definitions, worked examples, and problem sets. Rarely does a text dare to challenge not just what students learn, but how they think. Olympia Nicodemi’s Discrete Mathematics is one of those rare exceptions.

★★★★☆ (4.5/5) Best for: Motivated undergraduates and instructors seeking a discovery-based approach. Avoid if: You need quick answers, heavy CS applications, or extensive hand-holding. Discrete Mathematics by Olympia Nicodemi

Nicodemi’s book occupies the niche between Epp’s gentle introduction and Hammack’s pure-proof focus, with a distinctive voice that rewards repeated reading. No book is perfect. Some readers find Nicodemi’s insistence on discovery frustrating when they simply need a clear statement of a theorem. The lack of an extensive answer key can be a genuine obstacle for independent study. Additionally, the book’s publication history (originally by Pearson, now harder to find) means it lacks modern online resources like companion websites or video playlists. In the crowded field of undergraduate mathematics textbooks,

There is also a notable absence of algorithmic thinking. While graph theory appears, there is no discussion of search algorithms, complexity, or data structures—topics that many current discrete math courses include to serve CS majors. Olympia Nicodemi’s Discrete Mathematics is not the best-selling textbook on the market, nor is it the most up-to-date. But for the right student—one who wants to learn not just what mathematicians know but how they think—it is a hidden gem. ★★★★☆ (4

First published as part of a series aimed at fostering mathematical maturity, Nicodemi’s book is not a lightweight survey of topics for computer science majors, nor is it a dry collection of proofs. Instead, it is a carefully crafted bridge from computational calculus to the abstract reasoning required for advanced mathematics. This article explores what makes this textbook distinctive, its core strengths, and why it remains a valuable—if underappreciated—resource. The most striking feature of Nicodemi’s approach is its insistence on active learning . Many discrete math texts present a theorem, give a proof, and then ask students to repeat the pattern. Nicodemi inverts this process. She frequently introduces a problem or a pattern, guides the student through examples, and then asks: What do you notice? Can you state a general rule?