Undergraduate Research Opportunities

For undergraduate research opportunities, we usually refer students to the AMS website, our headline, and our SMALL webpage on other programs. Prof. Vélez has put together the following excellent list of programs with special features. Comments are most welcome either below or by emailing Frank Morgan.
Summer REU programs
by William Yslas Vélez, University Distinguished Professor of Mathematics, The University of Arizona, Tucson, Arizona
Information about summer REU programs are available at the NSF website and also on the AMS website.
Most of these programs are for students in their junior year who have completed at least one proof-intensive course and at least some upper division course work in algebra, analysis or linear algebra.
I have read over the descriptions of the proposed activities for the REU sites. I have commented on programs that fit certain needs of undergraduates. In particular, I looked for those programs that students who had not started upper division courses could apply to. Many REU sites do not list the minimum prerequisites or I may have overlooked some so please look carefully at both websites.
Most of the summer REU programs that appear on the NSF REU require some computing background, so I will not list it separately as a requirement. This computing requirement may consist of either programming skills in some language or facility with some computational package.
For Secondary Mathematics Education Majors 
1. Illinois State University will recruit eight undergraduate mathematics education majors.
Programs that have a research component in mathematics education 
1. George Mason University. “The participants in this subprogram will learn about current software to create interactive computer-based demonstrations, issues of interfaces and controls, and how to evaluate effectiveness. Studying the research work related to student conceptual issues in the curriculum will influence the design intent.”
2. Marquette University. “Relational Thinking Strategies of Pre-Service Mathematics Teachers and Their Students.”
For students who have completed two semesters of calculus 
1. Arizona State University, Mathematical and Theoretical Biology Institute. The site says that students who have completed at least their sophomore year and have completed two semesters of calculus can apply.
2. St. Mary’s College of Maryland. They stipulate, “but have not taken any upper-level mathematics courses.”
For students who have completed three semesters of calculus and linear algebra 
1. Mount Holyoke College.
2. Central Michigan University. Does not require third semester calculus.
For students who have completed three semesters of calculus, differential equations, and linear algebra 
1. Northern Arizona University.
2. University of North Carolina, Asheville. “…we strongly encourage students who have completed no more than one or two years of a typical undergraduate mathematics program to apply.”
Industrial Mathematics 
1. Worchester Polytechnic Institute.
2. Institute for Pure and Applied Mathematics. Research in Industrial Projects. Students who graduate in May can apply. International students can also apply.
International Opportunities 
1. DIMACS. “A small number of REU participants are selected to participate in an extension of the research experience. These students will travel to DIMATIA, at Charles University in Prague, Czech Republic, and will participate in the Midsummer Combinatorial Workshop as well as additional REU program activities.”
2. Institute for Pure and Applied Mathematics. Eight US students will be selected for the program in Hong Kong.
Mathematics and the Biological Sciences 
1. Cold Spring Harbor Laboratory. Of course a background in the biological sciences is required.
2. Virginia Polytechnic Institute and State University. Systems Biology.
3. Dordt College. Statistical Genetics
4. Emory University. Biostatistics.
5. University of Pittsburgh, School of Medicine.
6. University of Wisconsin, Biostatistics.
7. University of Wisconsin, Computational Biology. Requires one year of calculus.
8. MBI Undergraduate Summer Research Program. Mathematical Biology.
Programs for Women 
1. The Carleton College Summer Mathematics Program for Women. This program requires second semester calculus and linear algebra.
2. Summer EDGE program. For women who have graduated and plan to pursue graduate studies in mathematics.
3. Institute for Advanced Study Program for Women.
Programs with a focus on under-represented students 
1. Committee on Institutional Cooperation.
2. MSRI-UP.
Almost all REU programs are for students who are undergraduates. I did find some for students who graduate in May 2012.
Programs where graduate can apply 
1. Summer EDGE program. For women who have graduated and plan to pursue graduate studies in mathematics.
2. Institute for Pure and Applied Mathematics. Research in Industrial Projects. Students who graduate in May can apply. International students can also apply.
Many of the national labs have internship programs. These internship programs can be for the summer or for a semester. As one example look at the following.
National labs 
1. Argonne National Labs.