MATH 235 - Discrete Mathematics

1. Discuss fundamental mathematical structures including functions (surjections, injections, inverses, composition), relations (reflexivity, symmetry, transitivity, equivalence), and sets (complements, Cartesian products, power sets).
2. Apply the basics of counting including counting arguments, the pigeonhole principle, cardinality, countability, permutations and combinations, and recurrence relations.
3. Demonstrate knowledge of basic logic including propositional and predicate logic.
4. Demonstrate the use of logical connectives, truth tables, and normal forms (conjunctive and disjunctive).
5. Apply logical concepts such as validity, universal and existential quantification, modus ponens, and modus tollens.
6. Analyze problems using digital logic including logic gates, flip-flops, counters, and circuit minimization.
7. Demonstrate formal proofs including use of implication (converse, inverse, contrapositive, negation, and contradiction), the structure of formal proofs (direct, counterexample, contrapositive, and contradiction), mathematical and strong induction, recursive mathematical definitions, and well orderings.
8. Solve problems involving random events in finite probability spaces.
9. Demonstrate Bayes’ rule for conditional probabilities.
10. Illustrate the idea of mathematical expectation.

• Functions
• Elementary combinatorics
• Sets
• Propositional logic
• Predicate logic
• Proof techniques
• Relations
• Discrete probability

 
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Course Addendum - Syllabus (Click to expand)