MATH-220 Discrete Structures

In this course, students will develop skills in fundamental mathematical concepts related to computer science. The course will discuss elements of set theory, relations, functions, propositional logic, permutations, combinations, probability, proof techniques, and elementary graph theory. Selected applications will be included.

Credits

3

Prerequisite

MATH-181 or equivalent

Hours Weekly

3 hours weekly

Course Objectives

1. 1. Develop simple direct and indirect proofs.
2. 2. Provide proofs by mathematical induction; use summations including geometric and
   arithmetic series.
3. 3. Define and construct unions, intersections, disjoint sets, symmetric difference, Venn
   Diagrams, DeMorgan’s Laws, power sets, cardinality, countable and uncountable
   sets.
4. 4. Use elementary propositional logic, construct truth tables, and use connectives;
   identify valid and invalid arguments.
5. 5. Define function; define injective, surjective and bijective functions.
6. 6. Define algorithm and distinguish between functions and algorithms.
7. 7. Define, graph, and diagram binary relations, recurrence relations, and 2nd order
   recurrence relations.
8. 8. Solve elementary problems involving permutations, combinations, and the pigeonhole
   principle.
9. 9. Determine probabilities of events in simple spaces; use the binomial theorem in
   probability.
10. 10. Define and identity elementary properties of paths, connected graphs, Eulerian and
    Hamiltonian graphs, and trees.

Course Objectives

1. 1. Develop simple direct and indirect proofs.
2. 2. Provide proofs by mathematical induction; use summations including geometric and
   arithmetic series.
3. 3. Define and construct unions, intersections, disjoint sets, symmetric difference, Venn
   Diagrams, DeMorgan’s Laws, power sets, cardinality, countable and uncountable
   sets.
4. 4. Use elementary propositional logic, construct truth tables, and use connectives;
   identify valid and invalid arguments.
5. 5. Define function; define injective, surjective and bijective functions.
6. 6. Define algorithm and distinguish between functions and algorithms.
7. 7. Define, graph, and diagram binary relations, recurrence relations, and 2nd order
   recurrence relations.
8. 8. Solve elementary problems involving permutations, combinations, and the pigeonhole
   principle.
9. 9. Determine probabilities of events in simple spaces; use the binomial theorem in
   probability.
10. 10. Define and identity elementary properties of paths, connected graphs, Eulerian and
    Hamiltonian graphs, and trees.