MAT 227 - Discrete Mathematics in Computer Science [SUN# MAT 2227]

1. Determine the validity of complex arguments using formal logic notation.
2. Demonstrate competency in formal proof-writing techniques including direct and indirect methods of proofs.
3. Solve problems involving real world applications.

1. Utilize propositional and elementary predicate calculus.
2. Utilize the algebra of sets.
3. Demonstrate basic counting techniques.
4. Define and write direct and indirect proofs.
5. Define relations, functions, sequences and their properties.
6. Determine the digraph and matrix of a relation.
7. Apply big-oh notation.
8. Write induction proofs.
9. Provide recursive definitions and use recurrence relations.
10. Apply some or all of the above topics to computer science.

1. Logic
   1. Propositional forms
   2. Quantifiers
2. Set Theory
   1. Description and notation
   2. Venn diagrams
   3. Set operations
   4. Subsets and power set
3. Counting Techniques
   1. Factorials, permutations, and combinations
   2. Inclusion-exclusion principle
   3. Binomial coefficients
4. Proof techniques
   1. Direct proofs; proofs by cases
   2. Indirect proofs:  by contrapositive and by contradiction
   3. Rules of inference
5. Relations and Functions
   1. Cartesian products and ordered pairs
   2. Functions
      1. Domain, codomain, and range
      2. Inverse images
      3. One-to-one and onto functions
   3. Sequences and sigma notation
6. Binary Relations
   1. Reflexive, antireflexive, symmetric, antisymmetric, and transitive relations
   2. Graphs and digraphs of relations
   3. Adjacency matrix of a relation
   4. Equivalence relations, equivalence classes, and partitions
7. Big-Oh Notation
   1. Definition
   2. Relation to computer programming
8. Mathematical Induction
   1. Inductive proofs
   2. Strong vs. regular induction
   3. Inductive definitions
9. Recursion
   1. Recursive definitions
   2. Recurrence relations
   3. Explicit solutions