Faculty Research Areas

Arnold Adelberg (Professor Emeritus)

Jeffrey Blanchard (Assistant Professor), Applied Mathematics, Applied and Computational Harmonic Analysis, Wavelets, Compressed Sensing.

Marc Chamberland (Myra Steele Professor of Natural Sciences), Experimental Mathematics, Classical Analysis, Number Theory, Dynamical Systems, Differential Equations.

Christopher French (Associate Professor)

Gene Herman (Professor Emeritus)

Charles Jepsen (Professor Emeritus)

Jeffrey Jonkman (Associate Professor)

Shonda Kuiper (Associate Professor)

Joseph Mileti (Assistant Professor), Computability theory, reverse mathematics, set theory, Ramsey theory, and the interaction of mathematical logic with algebra and combinatorics. 

Tom Moore (Professor, SFS)

Emily Moore (Professor, SFS)

Jennifer Paulhus (Assistant Professor), algebraic number theory, arithmetic geometry, elliptic and hyperelliptic curves, representation theory, Jacobian varieties.

Christopher Olsen (Assistant Professor)

Karen Shuman (Associate Professor), Analysis, Harmonic Analysis, Iterated Function Systems.

Royce Wolf (Associate Professor), Algebraic Topology, Combinatorial Group Theory, Knot Theory, Spherical Virtual Knot Theory, Quandles.

Departmental Publications

A chronological list of publications authored by faculty and students from the Department of Mathematics and Statistics: Publications authored by faculty and students from the Department of Mathematics and Statistics (PDF, updated 6-Dec-2011). If you have access to MathSciNet, click here for up to date publications indexed by the AMS.

Research Opportunities at Grinnell

Current MAPs (Summer 2011)

  • The K-selection problem on GPUs (with Prof. Blanchard) The classic problem of finding the Kth largest element in a list has been extensively studied with many available algorithms and even parallel algorithms. The twist in this MAP will be developing, analyzing, and implementing a parallel K-selection algorithm on graphical processing units (GPUs). GPUs recent adoption of IEEE standard error correction have propelled them to the forefront of high performance computing with three of the top four supercomputers from the Top500 list being CPU-GPU heterogeneous machines. Prerequisites: Any math course above MAT 215 , familiarity with at least one programming language (preferably C, C++, and/or Matlab)
  • Finite Product Identities / Multiplicative Partitions (with Prof. Chamberland) For the summer of 2011, Prof. Chamberland proposes to have three students working on projects related to product identities. There are two broad areas of study: Finite Product Identities, and Multiplicative Partitions. To work on these projects, students will need to have taken either MAT 218, MAT 321 or MAT 316. Read full description of Prof. Chamberland's research projects here.
  • NCAA Cross Country Championship Selection (with Professors W. Freeman and Jonkman) The teams competing in the NCAA Division III national cross country meet consist of 16 automatic qualifiers and 16 teams chosen by an NCAA selection committee. Members of the committee have expressed strong support for trying to make the process more objective by using statistical models to assess the process and find patterns associated with success at the national meet. We will use the data available to the selection committee to try and find models that predict success at the national meet. The MAP participants will present the results to the NCAA selection committee at the fall 2011 NCAA Championships in Oshkosh, Wisconsin. Prerequisites: MAT 209 or MAT 336. Additional statistical modeling experience, particularly MAT 310, is preferred.
  • Assessment of the CDC's BRFSS Survey (with Prof. Jonkman) The primary source of state-level health estimates in the United States is the BRFSS, a large-scale telephone survey administered by the CDC. However, the BRFSS has a low response rate (a median of 34.9% in 2009), and also omits cell-phone-only households. Despite corrections based on sampling theory, these problems may lead to systematically biased estimates. This MAP will attempt to assess whether the BRFSS produces data that are representative of the US population by comparing sample characteristics from the BRFSS to US Census data at the state level. Prerequisites: MAT 209 or MAT 336.
  • Comparing Random Sequences (with Prof. Mileti) During the 1960s and 1970s, mathematicians used computability theory to develop a precise definition for when an infinite sequence of zeros and ones is random. In the last 15 years, the theory of these random sequences has become an active area of research. This project will investigate how to define what makes one random sequence "more random" than another, and to prove results about the relationship between the various proposed definitions of this intuitive concept. Prerequisites: Math 316 (analysis) and sufficient background in computer science to be comfortable working with computable functions (CSC 341 preferred).
  • Computing the measure of the overlap for one-dimensional iterated function systems (with Prof. Shuman) 2 students, both of whom ideally should have taken Math 218 (combinatorics), Math 316 (analysis), or their equivalents. We continue the work begun by Pengjun Shen, Ernest Boateng-Abebresse, Talent Takundwa, and Klevi Xhaxho in 2008 and 2010 to compute measurements associated with specific iterated function systems (fractals). In 2008 and 2010, our Grinnell students computed exactly the size of several sets associated with iterated function systems---the value of these measurements were not known before! At the end of summer 2010, Klevi had several conjectures about other systems, which will be the starting point for this summer's MAPs (pending approval from the Dean's office).
  • The Extension problem for Association Schemes (with Prof. French) Association schemes can be viewed as a generalization of groups; in particular, association schemes give rise to an algebra just as groups can be used to form group algebras. In this way, the representation theory of association schemes can be studied in much the same way as classical group representation theory. In understanding group theory, an early step is to understand how one can build up larger groups from smaller groups, a question often described as the extension problem. In this MAP, we will be looking at the much more difficult extension problem for association schemes. In particular, we will try to compute examples of extensions, understand their representations in terms of those of their constituent parts, and generalize the theory of group extensions as far as possible to association schemes.

Previous MAPs

External Summer Programs

Research Opportunities

  • The 2012 NSF-sponsored Explorations in Statistics Research Workshop will be hosted by UC Berkeley, June 16-24. 1-week program that introduces students to applied statistics research. Travel, room and board is provided. Participants must be permanent residents or US citizens.

Undergraduate Summer School in Mathematics

Summer Courses for Students Entering Graduate School

  • Nebraska IMMERSE IMMERSE is an intensive course for recent graduates who will begin graduate programs in the fall.
  • Enhancing Diversity in Graduate Education (EDGE) is a program "with the goal of strengthening the ability of women students to successfully complete graduate programs in the mathematical sciences, with particular inclusion of women from minority groups."

Internships