MAT 250 - Discrete Mathematics
Sets, functions, mathematical induction, relations, partially ordered sets, combinatorics including permutations, the pigeonhole principle, binomial and multinominal coefficients, recurrence relations, generating functions, the principle of inclusion-exclusion. Graph theory, including paths and connectedness, minimum length paths, Eulerian and Hamiltonian graphs, graph isomorphisms, trees, planar and nonplanar graphs.
Prerequisite: MAT 182 Calculus II
4 Class Hours
Learning Outcomes of the Course:
Upon successful completion of this course the student will be able to:
1. Use deduction and techniques of problem solving.
2. Use Mathematical Induction.
3. Use sets, relations and Cartesian product of sets.
4. Use binary relations, equivalence relations and partial orders.
5. Use functions, injections, surjections, bijections.
6. Use the Pigeonhole principle.
7. Use the fundamental counting principle.
8. Use permutations and combinations.
9. Use probability.
10. Use permutations and combinations with unlimited repetition.
11. Use the Binomial theorem.
12. Use the Multinomial theorem.
13. Use the Principle of inclusion-exclusion.
14. Use graph models.
15. Use Isomorphic, complete and bipartite graphs.
16. Use the degree of a vertex and related theorems.
17. Use walks, paths, trails, circuits of a graph.
18. Use Eulerian and Hamiltonian graphs.
19. Use planar and nonplanar graphs.
20. Use trees, spanning trees.
21. Use minimum length paths, minimum weight trees.
22. Use optimal binary trees.
23. Use generating functions.
24. Use recurrence relations and find their solutions.
In the context of the course objectives listed above, upon successful completion of this course the student will be able to:
1. Interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics.
2. Represent mathematical information symbolically, visually, numerically and verbally.
3. Employ quantitative methods such as arithmetic, algebra, geometry, or statistics to solve problems.
4. Estimate and check mathematical results for reasonableness.
5. Recognize the limitations of mathematical and statistical methods.
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