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National Alliance for Doctoral Studies in the Mathematical Sciences ISU REU
and
Mathematics and Computing Research Experiences for Undergraduates at Iowa State University
supported by the
National Science
Foundation
through
DMS 0750986, DMS 0502354, DMS
0353880
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ISU MATH REU
ISU STAT
REU ISU Math/Stat REU09 Homepage
The Iowa
State University Department of
Mathematics offers the summer program Mathematics and
Computing Research Experiences for
Undergraduates (ISU Math REU), sponsored by the National Science
Foundation through an REU-site grant and the National Alliance grant and the Iowa
State University Department of
Statisics offers the ISU Stat REU, sponsored by the National Science
Foundation through the National Alliance grant.
Summer 2009 REU
Tentative Information for 2010
- Dates: June 6, 2010 to July 31, 2010
- Compensation: Students will receive support for
travel
to and
from Ames, on-campus lodging at (probably in Frederiksen Court student
apartments), some meals and food money, and
a stipend of $3200 ($400 per week).
Questions:
For questions about the application process or
general information,
contact REU@math.iastate.edu
with "REU" in the subject of the email.
For questions about a specific project, contact
the mentor for that project.
For other scientific
questions, contact the Director,
Prof. Leslie Hogben,
LHogben@iastate.edu with the word "REU" in the subject of the
email.
Telephone contact: Department of
Mathematics,
515-294-1752 (ask for Kristy).
Sorry, we cannot accept any
applicants who are not US citizens or permanent residents.
In 2010 all student must be nominated by an Alliance mentor or must be a member of an under-represented minority.
ISU Math REU
REU09 Homepage
REU06 Homepage
REU05 Homepage
REU04 Homepage
The ISU Math REU varies in size and scope. In 2009 we ran the larger version of the program. In 2010 we will offer the smaller version that is limited to students nominated by National Alliance mentors.
Participants spend eight weeks working on research projects as
part
of active research groups at ISU. The
projects are in a variety of mathematical areas, representing the
diverse
research
interests of the ISU Mathematics Department, such as mathematical
biology, linear algebra, dynamical systems, numerical analysis, and
graph theory, all utilizing
computational
methods.
At the beginning of the summer the mentors
explain the necessary background to the students and there are
presentations
on writing in LaTeX and using Matlab. During most of the program,
students conduct research, meeting daily with their faculty
and
graduate student mentors. In addition to their own research,
students attend weekly REU Seminars, where they hear faculty lectures
on a variety of mathematical topics and presentations related to
attending
graduate school. The REU concludes with a symposium of
student
reports.
Participants are provided a stipend,
accommodation
in University student housing, travel and some meals, and will
have the opportunity to participate in social activities for REU
students, both Math REU and campus-wide ISU REU activities
(see general information).
More information about
the ISU Math REU can be found in the article
in the Proceedings of the Conference in Promoting Undergraduate
Research in Mathematics or on the pages from prior years (REU06, REU05, REU04). Students in the REU often publish their
results (list
of papers).
Students who are U.S. citizens or permanent
residents
and will be undergraduates in Fall 2010 and are nominated by a National
Alliance mentor or are a member of an under-represented minority will
be eligible to apply for
summer 2010 through the National Alliance website.
Applicants
should have completed at least two years of undergraduate mathematics
courses
including at least two semesters of calculus and two subsequent
courses,
including at least one course involving reading and writing
proofs. Most projects also require specific courses such as
linear algebra or
differential
equations.
Women and under-represented minorities are
particularly
encouraged
to apply.
All students in the REU regardless of
funding source will live and work together in a diverse environment.
Tentative Math Project Descriptions 2010
More wil be listed and the details will be filled in by January 2010;
some of the current descriptsions are from 2009 but 2010 projects will
be similar
Sign Pattern Matrices Dr. Minnie Catral and Prof.
Leslie Hogben
A
sign pattern is a
matrix whose entries are elements of {+, -,0}; it describes
the set of real matrices whose entries have the signs in the
pattern. More detail about this project later. Students
involved in this
project
will be part the ISU
Combinatorial Matrix Theory Research Group; more
information
is available on that page. This group regularly publishes its
results. The summer 2004, 2005, 2006 groups all published papers
that have appeared in in Linear Algebra and Its
Applications and Electronic
Journal of Linear Algebra (see list of papers); the 2009 group has papers in preparation. Linear
algebra is a pre-requisite for this project, graph theory is an
advantage,
and a strong theoretical mathematics background (usually including
abstract
algebra or real analysis) is expected. The software we use is
Mathematica and/or Sage,
but you can learn that here.
Algebraic Combinatorics Group
Prof. Sung
Yell Song
Combinatorics could be described as the art of enumerating and
arranging objects according to specified rules, and it deals with
analyzing discrete objects and finding optimal configurations
satisfying certain prescribed properties. This group will investigate
some problems in combinatorial design theory, algebraic graph theory,
and/or the theory of association schemes.
They could be (1) the existence and construction problem of
combinatorial designs of certain type (similar to the project done by 2004
group, see also list of
papers), (2) the characterization problem of certain class
of distance-regular graphs (similar to the project done by 2005 group), and (3) the classification problem
of association schemes having certain properties.
These problems are related to various arrangements of the elements of a
set into subsets according to prescribed rules. Students participating
this group will learn combinatorial design theory, algebraic graph
theory or the theory of association schemes depending on the choice of
research theme in addition to some common basics. For instance, in
connection with problem
(2), one of the things researchers in algebraic graph theory try to do
is understand the combinatorial meaning of the eigenvalues of the
adjacency matrix of a graph. The problems along this line concern
connected components, paths, independent sets, maximal cliques, and
decompositions of a graph into factors, all of which are basic terms in
algebraic graph theory.
Some knowledge in linear algebra, abstract algebra, combinatorics and
graph theory will be beneficial but not required.
Markov Chains and Dynamical Systems Prof. Wolfgang Kliemann
When we think of Markov chains (on a finite state space) we think of
concepts like communicating classes, irreducibility and recurrence that
can be analyzed using linear algebra (eigenvalues, eigenvectors etc)
and products of matrices. Dynamical systems, on the other hand,
with associated concepts like periodic orbits, limit sets, and chaos,
seem deeply rooted in analysis and topology. In this project we will
try to construct some connections between Markov chains and dynamical
systems to see if concepts and results in one of the two areas give us
a better understanding of the other topic. In particular, we will
construct several dynamical systems from a given Markov chain and see
what attractors/repellers and chaotic behavior of these systems mean
for the chain. The main connection is, of course, symbolic dynamics
and, more surprisingly, also some ideas from the theory of control
(orbits, control sets etc).
This project is suitable for students with a first course in linear
algebra and some knowledge of analysis/topology; background in
probability/statistics would certainly be a plus, but is not required.
Depending on the interest of the participants, we may begin looking at
some applications of this circle of ideas, such as stability of hybrid
systems, i.e. engineering systems in
continuous time (given by ordinary differential equations) that are
subject to random perturbations in discrete time (e.g. from the sensors
and information processing components of the system).
ISU Stat REU
REU09 Homepage
Participants in the ISU Stat REU attend a workshop for the first four weeks of the prgoram and then begin work on research projects with faculty mentors. Sample 2009 projects are listed. Check back in January 2010 for 2010 projects
ISU Stat Project Descriptions 2009
Development of Statistical and Computational Methods for the
Identification of Differentially Expressed Gene Categories, Dan
Nettleton
Microarray technologies allow researchers to simultaneously measure the
expression of thousands of genes in multiple biological samples.
By examining how genes change expression across different types of
samples or samples collected under different conditions, researchers
gain clues about how genes
act together to carry out important biological processes. Genes
can be organized into groups based on past research. Genes in a
group may share a function or act together in the same biological
process. Researchers often wish to learn whether known groups of
genes change their behavior in response to new conditions. This
summer research project involves the development of statistical and
computational methods for assessing evidence of group expression change
in response to stimuli. The project will involve mathematics,
statistics, and computation. Although biological data will be
used, no special background in biology is required.
Snacks & Statistics: Modeling nutrition education programs to impact public policy Mack Shelley
Child nutrition programs are essential for improved child health,
students’ achievement at school, and better life circumstances for
children and their family members. One of the leading efforts at
enhancing child nutrition is the Pick a better snackTM & ACT
program, which provides school-based education about the benefits of
nutrition and physical activity. In Iowa, this program is provided by
the Department of Public Health’s Iowa Nutrition Network, which uses a
social marketing model to deliver nutrition and health messages with
support from community-based public and non-profit agencies. We will
attempt to determine the optimal combination of traits of schools and
students that can maximize the effect of this nutrition education
program. We will do this by applying multilevel statistical methods
(Hierarchical Linear Models) using data collected from school sites in
Iowa. These models will be estimated to predict self-reported student
physical activity, nutrition knowledge, preference/exposure to
different fruits and vegetables, self-efficacy, and fruit and vegetable
consumption. Using data over several years, we will examine the
“Level-2” effects of differences in nutrition project implementation,
teachers, urbanicity, project intensity, and socioeconomic status
(measured by the percentage of students eligible for free and
reduced-price lunch), and the “Level-1” effects of student differences
based on grade level and student demographics. The results of these
models will be used to derive implications for public nutrition policy
and to suggest recommendations for how the program can be improved to
yield better outcomes for students, families, and schools.
Histograms and Taut-strings Dan Nordman
Histograms (http://en.wikipedia.org/wiki/Histogram) are a fundamental
graphic used to describe and summarize a data set, roughly indicating
which values occur in the data and how often (i.e., the distribution of
the data). Despite their common use, there is no generally
accepted manner to construct a histogram. Recently, Davies and
Kovac (2004) introduced the so-called taut-string histogram, which
creates a histogram by pulling an imaginary ``string” tightly through a
``tube” (created around the empirical distribution function). The
taut-string histogram has interesting mathematical properties, some of
which are known, but never rigorously proven. This project
in mathematical statistics seeks to formally prove some of these
properties (perhaps using calculus) and explore statistical properties
of taut-string histograms through simulation.