Olympia Nicodemi’s "Discrete Mathematics: A Bridge to Computer Science and Advanced Mathematics" (1987) is designed to transition university students from calculus to rigorous, proof-based mathematical reasoning. The text emphasizes structural clarity and recursive thinking, covering foundational areas such as combinatorics, graph theory, and Boolean arithmetic. Learn more about the text at books.google.com. A Bridge to Computer Science and Advanced Mathematics
Here’s a detailed review of "Discrete Mathematics" by Olympia Nicodemi based on its content, style, and typical reception among students and instructors.
Many discrete math books relegate recursion to a single section, often as a prelude to induction. Nicodemi makes recursion a recurring theme from the very first chapters. She uses recursive definitions not as a programming trick but as a fundamental way to define mathematical objects (strings, trees, sequences). By the time the student reaches induction, it feels like a natural extension of recursive thinking, not a magical leap. Discrete Mathematics by Olympia Nicodemi
What makes Nicodemi’s text a feature rather than a mere reference is its ability to generate genuine astonishment.
Take the humble pigeonhole principle: If you have more pigeons than holes, at least one hole has two pigeons. Trivial, right? Nicodemi transforms this triviality into a scalpel. In her hands, the principle proves that at a party of six people, there are either three mutual friends or three mutual strangers. The mundane becomes the magical. The discrete becomes the sublime. the recurrence beneath the population model
Students who work through this book don’t just learn math; they learn how to think in structures. They learn to see the graph beneath the social network, the recurrence beneath the population model, the Boolean algebra beneath the circuit board. The world becomes a lattice of logical relations.
Counting is often harder than it looks. Nicodemi navigates the student through permutations, combinations, and the Pigeonhole Principle. The inclusion of basic probability ties these counting methods to real-world applications. a mathematics major
If you are a computer science student, a mathematics major, or a self-taught programmer looking to level up your logical thinking, you have inevitably encountered the term Discrete Mathematics.
Often described as the "math of computing," it is the foundation upon which algorithms, cryptography, and data structures are built. But finding the right resource to learn it can be tricky. Some textbooks are dry and impenetrable; others are so superficial they leave you with more questions than answers.
Today, we are taking a close look at "Discrete Mathematics" by Olympia Nicodemi—a textbook that has earned a reputation for being a gentle yet rigorous introduction to this complex subject.
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.