What's Next?
Continue Your Discrete Math Journey
Deeper Theory
- Abstract Algebra — groups, rings, fields, and Galois theory (the algebra beneath cryptography).
- Automata & Formal Languages — finite automata, context-free grammars, Turing machines, and decidability.
- Compilers — apply formal languages directly: build a lexer, parser, and evaluator.
Applied Directions
- Algorithms — sorting, graph algorithms, dynamic programming — all analyzed with the combinatorics from this course.
- Cryptography — RSA, elliptic curves, and zero-knowledge proofs all rest on number theory and discrete probability.
- Information Theory — entropy, Huffman coding, and channel capacity require combinatorics and probability.
References
- Discrete Mathematics and Its Applications by Kenneth Rosen — the standard undergraduate textbook, thorough and clear.
- Concrete Mathematics by Knuth, Graham & Patashnik — advanced combinatorics and generating functions, written for CS students.
- Introduction to the Theory of Computation by Sipser — formal languages and computability built on the foundations here.
- MIT 6.042J — MIT's discrete math for CS, full lecture notes and problem sets free online.