C959: Discrete Math

  1. Logic and proofs 20% of final
  • Propositions and truth tables
  • propositional statements
  • logical equivalences
  • laws of propositional logic
  • predicates and quantifiers
  • proofs

2. Sets and Functions 10% of the final

  • Set, subsets, and power seats
  • Set operations
  • Cartesian product of sets
  • Set partitions
  • Overview of functions
  • Function properties

3. Boolean Algebra and Boolean Functions 15% of final

  • Boolean operations
  • Boolean expressions and equivalents
  • Boolean functions
  • Disjunction and conjunctive normal forms
  • Simplifying Boolean expressions
  • Digital logic, circuits, and gates

4. Matrix Operations 10%

  • Types of matrices
  • Matrix addition and multiplication
  • Inverse matrices
  • Elementary matrix operations
  • Gaussian elimination and invertibility

5. Finite and Infinite Series 10%

  • Geometric and arithmetic sequences
  • Increasing, decreasing, and monotone sequences
  • Infinite sequences
  • Sum of finite and infinite series
  • Convergence and divergence

6. Relations 15% of the final (the hardest one apparently)

  • Binary relations, sets, and properties
  • Binary relation properties and directed graphs
  • Graph powers and matrix multiplication
  • Partial order relations and Hasse diagrams
  • Strict order relations
  • N-ary relations

7. Graphs and Trees 20% of the final

  • Undirected graphs
  • Graph isomorphism
  • Paths, cycles, and connectivity
  • Trees and their properties
  • Tree traversals and spanning trees