MATH 785 - Sets and Methods in Discrete Mathematics

(3 units)

Ramsey Theory, Extremal Combinatorics, Partial Orders, Combinatorial Designs; Probabilistic Method, Linear Algebraic and Polynomial Method, Geometric and Topological Method.

Maximum units a student may earn: 3

Prerequisite(s): MATH 485 or MATH 685 or Instructor’s Approval

Grading Basis: Graded
Units of Lecture: 3
Offered: Every Spring - Odd Years

Student Learning Outcomes
Upon completion of this course, students will be able to:
1. demonstrate understanding of Ramsey-theoretic arguments and also come up with new Ramsey-type problems in their fields on interest.
2. demonstrate understanding of the nature and tools of Extremal problems in Combinatorics as well as come up with new extremal problems while dealing with mathematical structures in their fields of interest.
3. demonstrate a deeper understanding of richer structures like that of Posets and Designs and generalize other problems to the setting of these richer structures.
4. understand and apply various modern techniques like, Probabilistic, Algebraic and Topological techniques while working with problems in Discrete Math and/or their respective fields of interest.
5. import modern tools from other areas of Mathematics and apply it in Discrete Math problems.

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