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🧮 CS285 — Discrete Math for Computing

This course builds the mathematical foundation required for computing. It covers logic, sets, functions, number theory, counting, relations, and proof techniques that are used throughout computer science.

This section contains structured study material including chapter-based notes, explanations of core concepts and proof techniques, and a cheat sheet for revision and quick reference. The goal is a clear, practical resource for understanding discrete mathematics and preparing for exams and problem-solving tasks.

🧭 How to Use This Section

Depending on where you are in the course, use this section differently.

If you are following the course, start from Chapter 1 and continue in order — the chapters build on each other deliberately. If you are revising, go directly to the cheat sheet and the chapters you find most challenging. If you are practicing problem solving, use the chapter notes as references for definitions, theorems, and methods.

🗂 Course Chapters

  • 1⃣ Chapter 1 — Logic, Sets & Functions

    Propositional logic, truth tables, logical equivalences, predicates, quantifiers, and rules of inference.

  • 2⃣ Chapter 2 — Basic Structures

    Set operations, injective/surjective/bijective functions, sequences, summations, and matrices.

  • 3⃣ Chapter 3 — Number Theory & Cryptography

    Divisibility, modular arithmetic, primes, the Euclidean algorithm, and an introduction to classical cryptography.

  • 4⃣ Chapter 4 — Induction & Recursion

    Mathematical induction, recursive definitions, and structural induction.

  • 5⃣ Chapter 5 — Counting

    Basic counting rules, permutations, combinations, and binomial coefficients.

  • 6⃣ Chapter 6 — Advanced Counting

    Recurrence relations and techniques for solving them.

  • 7⃣ Chapter 7 — Relations

    Properties of relations, matrix and graph representations, closures, and equivalence relations.

🗒 Study & Revision Material

In addition to the chapter notes, this section includes a cheat sheet for quick revision and condensed explanations of key definitions, rules, and techniques. These are designed to support both deep understanding and efficient exam preparation.

Step Topic
1 Logic, sets, and functions — build the foundation first
2 Basic structures and number theory
3 Induction and recursion — referenced throughout the course
4 Counting and advanced counting techniques
5 Relations and their representations
6 Cheat sheet for revision and quick recall before exams

About This Material

These notes are based on my own coursework and personal study. The focus is on clarity, structure, and practical understanding. Content will continue to be refined and expanded over time.