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Discrete Mathematics

Course Syllabus

  • Sets
  • relations
  • functions
  • Equivalence and Partial order relations
  • Formal logic: Propositional logic and truth tables
  • normal forms
  • Predicates and Quantification
  • Notion of proof: proof techniques
  • Mathematical Induction
  • Combinatorics: Basic counting techniques
  • The pigeonhole principle
  • countable and uncountable sets
  • recurrence relations The principle of Inclusion-exclusion
  • Graph theory: Graph terminology
  • representation of graphs
  • Isomorphism
  • trees
  • Eulerian and Hamiltonian graphs
  • Graph coloring and Planar graphs
  • Number theory: Divisibility
  • GCD
  • The Euclidean algorithm
  • The fundamental theorem of arithmetic
  • Modular arithmetic
  • Group theory: Groups
  • subgroups
  • finite groups
  • cyclic groups
  • permutation groups
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Prerequisites

  • None

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