Department of Mathematics and Philosophy

Undergraduate Research - Combinatorics

Faculty


Adeleke Samson Adeleke

Areas of Interest: Algebra, Combinatorics, Differential Equations

Description: The material could be on any topic beyond the contents of Math 355 (Combinatorics), Math 421 (Abstract Algebra), and Math 333 (Ordinary Differential Equations). In more detail, the Math 355 course introduces applications of counting and graphs to computer science, chemistry, operations research, etc. The Math 421 course covers the basics of abstract algebra of groups, ranges, and fields, an aesthetically satisfying subject while Math 333 on Differential Equations models down-to-earth phenomena across a broad spectrum.

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Blackford Tom Blackford

Areas of Interest: Algebraic coding theory, algebra, combinatorics

Description: Coding theory involves the transmission of encoded information across a noisy communications channel. It has been used in telegraphs, computers, CD-players and cash registers. It provides mathematical algorithms to correct errors in transmission. Often information is transmitted as blocks of binary digits, and an algebraic structure is put on these blocks. This leads to formation of special types of codes including cyclic, negacyclic, and quasi-cyclic codes. Techniques in linear and abstract algebra are used in decoding and error-correcting.

I am looking for a student who is interested in studying algebraic coding theory and in particular cyclic codes and their generalizations. I will provide any abstract algebra that is needed.

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Mei Yang Mei Yang

Areas of Interest: Algebra and Combinatorics

Description: For students who have taken the introductory combinatorics course and learned the basic enumeration techniques and graph theory, there are many directions you may further explore. Here are a few suggestions:

(1) Compare advantages and disadvantages of different techniques by solving problems using more than one method.

(2) Investigate the relationships among different techniques. For instance, how to get generating functions from recurrence relations, or vice versa.

(3) You may further study the generating function method, which nowadays is the main language of enumerative combinatorics. Topics range from compositions of generating functions, generating functions in several variables, and application of generating functions to enumeration of trees, and various kinds of graphs.

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