Olympia Nicodemi's textbook, Discrete Mathematics: A Bridge to Computer Science and Advanced Mathematics
Counting and Combinatorics: She illustrates how simple counting principles (like the Pigeonhole Principle or permutations) are actually the engines behind complex computer algorithms.
While the world of computing has changed drastically since the book's release, the underlying mathematics has not. Discrete Mathematics by Olympia Nicodemi remains a strong choice for: Discrete Mathematics by Olympia Nicodemi
Exercise Difficulty Variation
While many exercises are excellent for learning proofs, a few are too challenging for beginners without hints. Some instructors supplement with additional problem sets.
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. Some instructors supplement with additional problem sets
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.
If you are looking for a text that makes discrete math feel like a conversation with a wise, encouraging mentor—rather than a competition with an indifferent syllabus—this is the one. Logic and Sets:
Exploring networks and the relationships between discrete objects. Boolean Algebra: Foundations for digital logic and computer arithmetic. Logic and Sets: