--- title: Discrete Mathematics description: Discrete mathematics studies mathematical structures that are countable or distinct rather than continuous. Learners will understand logic, set theory, combinatorics, and graph theory, which form the mathematical foundation of computer science. category: mathematics subcategory: discrete-math difficulty: beginner, intermediate, advanced url: /subject/discrete-mathematics --- # Discrete Mathematics Discrete mathematics studies mathematical structures that are countable or distinct rather than continuous. Learners will understand logic, set theory, combinatorics, and graph theory, which form the mathematical foundation of computer science. ## Available Resources 4 Books • 6 Courses • 3 Websites ## Websites ### 1. Art of Problem Solving Discrete Math The Art of Problem Solving wiki's entry point for discrete mathematics, defining the field and branching into combinatorics, graph theory, set theory, number theory, and abstract algebra. Written for competition students, with links into AoPS problem archives. **Difficulty:** Beginner | **Price:** Free **Link:** https://artofproblemsolving.com/wiki/index.php/Discrete_Mathematics **Tags:** discrete-mathematics, combinatorics, graph-theory, number-theory, competition-math ### 2. discretemath.org Discretemath.org is an educational resource focused on discrete mathematics. It provides tutorials, notes, and practice problems on core topics such as logic, set theory, combinatorics, graph theory, and algorithms to help learners master discrete math concepts. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://discretemath.org **Tags:** websites, mathematics-statistics, mathematics ### 3. oeis.org OEIS is the Online Encyclopedia of Integer Sequences, a searchable database of integer sequences. It provides each sequence’s terms, definitions, formulas, references, and cross-links, plus tools to identify sequences from terms and explore related patterns. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://oeis.org **Tags:** websites, mathematics-statistics, mathematics ## Books ### 1. Discrete Mathematics: An Open Introduction **Author:** Oscar Levin A free, open-licensed undergraduate textbook covering counting and combinatorics, sequences and recurrence relations, symbolic logic, proof techniques including induction, and graph theory, with many worked exercises. Readers build the discrete foundations needed for computer science and upper-level mathematics. **Difficulty:** Beginner | **Price:** Free **Link:** https://discrete.openmathbooks.org/dmoi3.html **Tags:** discrete-mathematics, combinatorics, graph-theory, symbolic-logic, mathematical-induction ### 2. Discrete Mathematics and its Applications - Kenneth Rosen **Author:** Kenneth H. Rosen Standard undergraduate textbook covering logic, proof techniques, set theory, counting, recurrences, and graphs, with a number theory chapter on divisibility, modular arithmetic, primes and RSA. Extensive exercise sets follow each section for self-study practice. **Difficulty:** Beginner | **Language:** English | **Price:** Paid **Link:** https://amzn.to/4k8ABBR **Tags:** discrete-mathematics, proof-techniques, combinatorics, modular-arithmetic, textbook ### 3. Discrete Mathematics and Its Applications **Author:** Kenneth H. Rosen Standard undergraduate discrete mathematics textbook covering logic, proof, sets, functions, algorithms, number theory, counting, relations, graphs and trees, with thousands of exercises. Its relations chapter develops equivalence relations, partial orders, closures and matrix representations to a level suited to computer science study. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0072424346?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, discrete-math ### 4. Introduction to Discrete Mathematics **Author:** Robert J. McEliece, Robert B. Ash, Carol Ash 1989 undergraduate textbook from Caltech and Illinois authors introducing sets, relations, functions, combinatorics, graphs, number theory, recurrences and Boolean algebra with an applied, computing-oriented slant. Readers gain working fluency with the discrete structures underlying algorithms and coding theory. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0394358198?tag=edmonddante07-20 **Tags:** discrete mathematics, combinatorics, graph theory, number theory, boolean algebra ## Courses ### 1. Algorithmic Aspects of Machine Learning (MIT 18.409) **Author:** Ankur Moitra Designing machine learning algorithms with provable guarantees: nonnegative matrix factorization, topic models, tensor decomposition, sparse recovery, dictionary learning and learning mixture models. Moitra's detailed lecture notes, which read as a complete monograph, and problem sets teach rigorous analysis of learning algorithms. **Difficulty:** Advanced | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-409-algorithmic-aspects-of-machine-learning-spring-2015/ **Tags:** provable-algorithms, matrix-factorization, tensor-decomposition, sparse-recovery, learning-theory ### 2. Mathematics for Computer Science (MIT 6.042J) **Author:** Tom Leighton, Marten van Dijk Discrete mathematics for computer science with an emphasis on definitions and proofs: logic, induction, sets and relations, graph theory, modular arithmetic, asymptotics, counting and discrete probability. 25 lecture videos, problem sets and exams with solutions build fluency in writing proofs. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-fall-2010/ **Tags:** discrete-mathematics, mathematical-proofs, induction, graph-theory, combinatorics, discrete-probability ### 3. Theory of Computation (MIT 18.404J) **Author:** Michael Sipser Sipser's course on automata, computability and complexity: regular and context-free languages, decidability, reducibility, the recursion theorem, time and space complexity, NP-completeness, hierarchy theorems, probabilistic computation and interactive proofs. 25 lecture videos, slides, problem sets and exams support rigorous proof-based study. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-404j-theory-of-computation-fall-2020/ **Tags:** automata-theory, computability, decidability, complexity-theory, np-completeness ### 4. Dynamic Systems and Control (MIT 6.241J) **Author:** Emilio Frazzoli, Munther Dahleh Analysis and control of linear time-invariant systems modeled by ordinary differential equations: state-space models, input-output response, feedback interconnections, stability and performance. Provides lecture notes, the full open textbook, and problem sets with solutions for designing controllers with guaranteed properties. **Difficulty:** Advanced | **Price:** Free **Link:** https://ocw.mit.edu/courses/6-241j-dynamic-systems-and-control-spring-2011/ **Tags:** linear-systems, state-space, stability, feedback-control, robust-control ### 5. Probabilistic Systems Analysis and Applied Probability (MIT 6.041SC) **Author:** John Tsitsiklis Modeling and analysis of uncertainty: probability models, discrete and continuous random variables, Bayesian inference, limit theorems and random processes. Designed for independent study, with lecture videos, slides, recitation and tutorial problems, problem sets and exams with solutions, and TA problem-solving videos. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/ **Tags:** probability, random-variables, bayesian-inference, limit-theorems, random-processes, statistical-inference ### 6. Discrete Mathematics **Author:** Dominik Scheder Dominik Scheder's proof-based course on sets, functions and relations, enumerative combinatorics, graph theory, and network flows and matchings, each concept paired with a fully proved non-trivial result. Learners read formal statements and write rigorous proofs of their own. **Difficulty:** Intermediate | **Language:** English | **Duration:** 11 weeks of study, 3-5 hours per week. | **Price:** Free **Link:** https://www.coursera.org/learn/discrete-mathematics **Tags:** discrete-math, combinatorics, graph-theory, network-flows, proofs --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/discrete-mathematics