For most undergraduates, the "math" they know is a continuous blur. Calculus. Differential equations. The smooth, slippery slope of real numbers sliding into infinity. It is the mathematics of motion, of speed, of the analog hum of the universe. It is also, for many, the mathematics of anxiety.
But there is another world. A world without limits. A world without continuity. A world made of sharp edges, clear truth tables, and the satisfying click of a logical lock falling into place. This is the world of discrete mathematics—and no guide opens the gate quite like Olympia Nicodemi’s quietly revolutionary textbook, Discrete Mathematics.
If most math books are highways designed to get you from Point A (ignorance) to Point B (competence) as fast as possible, Nicodemi’s book is a labyrinthine garden. It asks you to slow down. To sit on a bench. To stare at a single sentence until its logical structure reveals itself like a hidden cathedral. Discrete Mathematics by Olympia Nicodemi
Overall Rating: ★★★★☆ (4/5)
Best for: Students who want a proof-oriented, conceptual introduction to discrete math, especially those in mathematics, computer science theory, or liberal arts math majors.
Not ideal for: Those seeking a purely computational, algorithm-focused, or application-driven text.
Let’s address the elephant in the room: Olympia Nicodemi’s exercises are hard. They are not the "Find the next three terms in the sequence" type. A typical Nicodemi exercise might read: For most undergraduates, the "math" they know is
"Given the recursive definition of the Fibonacci numbers, prove that the sum of any ten consecutive Fibonacci numbers is divisible by 11. Is this true for every integer divisor? Explain."
These questions require not just computation, but exploration. Many exercises have no single correct answer; they ask for conjectures, counterexamples, or generalizations. This is infuriating for students who want a quick answer key, but it is transformative for students who want to think like mathematicians. Let’s address the elephant in the room: Olympia
The chapters on graph theory are particularly strong. Nicodemi avoids the common trap of treating graph theory as a series of algorithms (BFS, DFS, Dijkstra). Instead, she focuses on graph properties: planarity, coloring, and path structure. The combinatorial proofs of graph theorems (e.g., Euler’s formula for planar graphs) are presented with geometric intuition followed by rigorous algebra. A student who works through Nicodemi’s graph theory chapters will understand why a graph is 2-colorable if and only if it is bipartite—not just how to test for bipartiteness.
Olympia Nicodemi is a Professor Emerita of Mathematics at the State University of New York (SUNY) College at Geneseo. Unlike modern textbook authors who are often hired by publishing houses to compile existing curricula, Nicodemi is a working mathematician and educator who wrote her book based on how she actually taught the course.
Her background is in algebra and number theory, and that DNA is woven throughout the text. She is famously known for her Socratic teaching style—answering questions with questions, pushing students to discover structure rather than memorize it. The textbook reads exactly like a Nicodemi lecture: clear, patient, but relentlessly logical.