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.
← Previous