Undergraduate Research Initiative

In an effort to further improve its undergraduate component and to respond to numerous specific inquiries, the Department of Mathematics at University of Rochester is starting this fall an undergraduate research initiative, which wants to challenge and offer support to interested students in undertaking mathematical research projects. This initiative intends to complement in a nice way well-known summer research opportunities - REU's. Involvement in a research project can serve as a culminating experience in an undergraduate mathematics major, an enriching opportunity for a mathematics minor, and an excellent way of getting a flavor of what it means to be a research mathematician.

What is mathematical research?

In order to have a starting point of discussion let us take the definition of 'research' from the Merriam-Webster Dictionary: "a careful or diligent search; a studious inquiry or examination; an investigation or experimentation aimed at the discovery and interpretation of facts, revision of accepted theories or laws in the light of new facts, or practical application of such new or revised theories or laws; the collecting of information about a particular subject." Here are some examples as they apply to Mathematics:

a brand new theorem
a new proof or an improvement of a previously known result
a resolution of a long standing conjecture
a numerical investigation for a theoretical problem
a survey of advances (state of the art) on a particular topic
a mathematical modeling of a real world problem

In what concerns undergraduate mathematical research, one can take a look at UMAP (the journal of undergraduate mathematics and its applications) and at the following journals published by the Mathematical Association of America, which are all a good source of project ideas:

Necessary background

In order to give yourself a better chance at succeeding in this activity, we feel that one should have a solid knowledge and understanding of the concepts discussed in the foundational courses:

Equivalent courses may be substituted (e.g., 141-143 for 161-162, or the 17X Quest series). Of course, it is highly recommended for interested students to take also 200 level classes before or at the time of starting the project. There might be projects though where one can get by with less than what it's specified above, but this needs to be discussed in detail with the advisor.

Ideas for projects

The following list contains links to websites that have titles, abstracts or even full versions of previous undergraduate research projects:

REU projects and a set of ideas at University of Michigan
REU projects at University of Chicago in 2007 and 2006
REU projects at UCLA
LMS undergraduate project archive
Furman University Electronic Journal of Undergraduate Mathematics
Recent senior theses in Mathematics at Princeton, Harvard, Cornell, and Harvey Mudd

Local contacts and support

Interested students should contact one of the following advisors, depending on the research area of the project:

Research field	Advisor	Office	E-mail
Algebra and Number Theory	Douglas Haessig	Hylan 813	chaessig@math.rochester.edu
Analysis	Alex Iosevich	Hylan 909	iosevich@math.rochester.edu
Geometry	Sema Salur	Hylan 1005	salur@math.rochester.edu
Mathematical Physics and Probability	Shannon L. Starr	Hylan 1017	sstarr@math.rochester.edu
Topology	Frederick Cohen	Hylan 1002	cohf@math.rochester.edu

If unsure about the research field or for any other questions, please contact Coordinator of Undergraduate Research, Alex Iosevich.