Notes for UCL COMP0147 Discrete Mathematics Course. Latest compiled PDF version available at (https://github.com/jieyouxu/COMP0147-Discrete-Mathematics-Notes/releases).

• Foundations
  • Sets
  • Binary Relations
    • Equivalence Relations
  • Modular Arithmetics
  • Functions
    • Injections
    • Surjections
    • Bijections
  • Cardinality of Sets
  • Groups
    • Symmetric Group
    • Permutations
      • Sign of Permutations
      • Order of Permutations
    • Abstract Groups
    • Lagrange's Theorem
  • Euclid's Algorithm
    • Solving Linear Congruences
    • Fermat's Little Theorem
    • Euler Totient Function
    • Application of Public Key Cryptography
• Linear Algebra
  • Correspondence between Linear Maps and Matrices
  • Associativity and Non-commutativity of Matrix Manipulation
  • Gaussian Elimination
  • Inverting Matrices
  • Determinants
  • Eigenvalues and Eigenvectors
• Counting
  • Counting Fundamental Principles
  • Multiplication Principle
  • Inclusion-exclusion Principle