Oct 20, 2019
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:
- Use deduction and techniques of problem solving.
- Use Mathematical Induction.
- Use sets, relations and Cartesian product of sets.
- Use binary relations, equivalence relations and partial orders.
- Use functions, injections, surjections, bijections.
- Use the Pigeonhole principle.
- Use the fundamental counting principle.
- Use permutations and combinations.
- Use probability.
- Use permutations and combinations with unlimited repetition.
- Use the Binomial theorem.
- Use the Multinomial theorem.
- Use the Principle of inclusion-exclusion.
- Use graph models.
- Use Isomorphic, complete and bipartite graphs.
- Use the degree of a vertex and related theorems.
- Use walks, paths, trails, circuits of a graph.
- Use Eulerian and Hamiltonian graphs.
- Use planar and nonplanar graphs.
- Use trees, spanning trees.
- Use minimum length paths, minimum weight trees
- Use optimal binary trees.
- Use generating functions.
- 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:
- Interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics.
- Represent mathematical information symbolically, visually, numerically and verbally.
- Employ quantitative methods such as arithmetic, algebra, geometry, or statistics to solve problems.
- Estimate and check mathematical results for reasonableness.
- Recognize the limitations of mathematical and statistical methods.
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