Discrete Mathematics: A Bridge to Computer Science and Advanced Mathematics
by Olympia Nicodemi is a foundational textbook designed to introduce students to the non-continuous mathematical structures essential for modern computing and higher-level math. Overview and Purpose
Originally published in 1987 by West Publishing Co., this text serves as a "bridge" for first- or second-year undergraduate students. It is specifically crafted for a one-semester course, helping students transition from the continuous mathematics of calculus to the discrete reasoning required in computer science. Key Core Topics
The book covers several critical areas of discrete mathematics, emphasizing both theoretical understanding and practical application: Mathematical Reasoning:
Developing skills in deduction, formal proof, and recursive thinking. Combinatorics: Studying counting, permutations, and combinations. Graph Theory:
Exploring networks and the relationships between discrete objects. Boolean Algebra: Foundations for digital logic and computer arithmetic. Logic and Sets:
Fundamental concepts like propositional logic, set theory, and functions. Target Audience & Prerequisites
Primary audience includes computer science and mathematics majors. Prerequisites:
Students typically need at least one semester of calculus and familiarity with a high-level computer programming language to fully engage with the material. Discrete Mathematics by Olympia Nicodemi
Reviewers have noted the book's "crisp and clear" delivery of deep content, making it a classic choice for foundational study.
You can find digital versions or physical copies through retailers like or borrow it from the Internet Archive If you're studying for a specific course, would you like a summary of a particular chapter solving a practice problem from the book?
Discrete Mathematics by Olympia Nicodemi: A Comprehensive Guide
In the landscape of higher mathematics, finding a textbook that balances rigorous theory with approachable pedagogy is a rare feat. Discrete Mathematics by Olympia Nicodemi stands as a cornerstone for students and educators alike who are navigating the transition from computational calculus to the abstract world of discrete structures.
Whether you are a computer science major, a future mathematician, or an enthusiast of logical puzzles, Nicodemi’s work offers a clear roadmap through some of the most vital concepts in modern science. Who is Olympia Nicodemi?
Olympia Nicodemi is a distinguished professor of mathematics at SUNY Geneseo, known for her commitment to mathematical education and her ability to make complex topics accessible. Her approach in Discrete Mathematics reflects years of classroom experience, prioritizing student comprehension and the development of proof-writing skills. Core Themes and Coverage
The book is designed to provide a solid foundation in the "mathematics of the finite." Unlike calculus, which deals with continuous change, discrete mathematics focuses on distinct, separated values. Nicodemi covers several essential pillars: 1. Logic and Proofs
The journey begins with the language of mathematics. Nicodemi introduces propositional logic, quantifiers, and the rules of inference. The real strength here is the focus on mathematical induction and direct/indirect proofs, teaching students not just how to find an answer, but how to argue that the answer is correct. 2. Set Theory and Relations Discrete Mathematics: A Bridge to Computer Science and
Understanding how objects group together and interact is fundamental to computer science. The text explores sets, functions, and relations (including equivalence relations and partial orderings), which are the building blocks for database theory and algorithm design. 3. Combinatorics (The Art of Counting)
From basic permutations to complex combinations, Nicodemi breaks down counting principles. This section is vital for understanding probability and the complexity of algorithms. 4. Graph Theory
Graphs are used to model everything from social networks to neural pathways. Nicodemi provides a lucid introduction to vertices, edges, paths, circuits, and trees, ensuring students can visualize and manipulate these structures effectively. 5. Algebraic Structures
For those moving toward abstract algebra, the book introduces concepts like Boolean algebra, which is the mathematical backbone of digital logic and computer circuitry. Why Choose This Text? Pedagogy First
Nicodemi’s writing style is often described as "conversational yet precise." She avoids the "definition-theorem-proof" fatigue by providing ample examples that ground abstract ideas in reality. Clarity in Proof Writing
One of the biggest hurdles for students is learning how to write proofs. This textbook acts as a mentor, guiding the reader through the logic of construction, helping them move from "knowing" a fact to "proving" it. Bridge to Computer Science
While it is a math book at its heart, the applications to computer science—such as algorithm analysis and logic gates—make it an invaluable resource for CS students who need to understand the "why" behind the code. Final Thoughts
Discrete Mathematics by Olympia Nicodemi is more than just a collection of formulas; it is a training manual for logical thinking. In an age dominated by digital data and complex algorithms, the ability to think discretely is a superpower. Nicodemi provides the tools to build that power, one logic gate and one proof at a time. Clear, Conversational Writing Style Nicodemi writes in an
This section handles the language of mathematics. The explanations of set operations, partitions, and functions (injective, surjective, bijective) are clear and accompanied by helpful Venn diagrams and visual aids.
Clear, Conversational Writing Style
Nicodemi writes in an unusually engaging, almost Socratic tone. She explains why definitions matter, how proofs are constructed, and what the underlying intuition is. This makes the book readable compared to drier, definition-theorem-proof texts.
Strong Emphasis on Proof Writing
From early chapters, students are guided through logical arguments, induction, contradiction, and constructive proofs. The book doesn’t just present proofs—it teaches how to think about them. Many exercises ask for original proofs, not just computations.
Thoughtful Organization
Topics flow naturally:
Historical and Philosophical Context
Unusually for a discrete math text, Nicodemi includes brief historical notes (e.g., on Cantor, Euclid, or Boolean algebra). This helps humanize the material and shows why certain ideas emerged.
Excellent for Self-Study
Because of the explanatory style and fully worked examples, motivated readers can work through much of the book alone. Solutions to odd-numbered exercises are often provided.
Discrete Mathematics by Olympia Nicodemi is not for the faint of heart, nor is it for the student looking for a quick reference for computer science algorithms.
It is for the rebel. The student who found calculus beautiful but empty. The philosophy major who loves logic but hates notation. The future computer scientist who wants to understand why an algorithm works, not just how to code it. The math major who has grown tired of computation and hungers for proof.
In many departments, this book serves as a bridge—a gentle, rigorous bridge—from high-school algebra to the upper-division proof courses like Real Analysis or Abstract Algebra. It is the place where potential mathematicians learn to spread their logical wings.