Mathematics Research Experiences for Undergraduates at Iowa State University

Investigacion en Matematicas y Estadisticas
supported by the National Science Foundation through
DMS 0750986, DMS 0502354,
DMS 0353880
and the ISU Department of Mathematics

ISU MATH REU 2013    ISU MATH REU 2011     ISU Math/Stat REU10        ISU Math/Stat REU09      
ISU MATH REU 2006     
ISU Math REU05        ISU Math REU04         ISU Math REU03
ISU REU Publications                
ISU Math REU will be offered in summer 2015 
2015 General Information
2015 projects (not yet available)   2015 application (not yet available)

ISU Math REU general information

Participants spend eight weeks working on research projects. The
projects are in a variety of mathematical areas, representing the diverse research interests of faculty in the ISU Mathematics Department, such as
graph theory, numerical analysis, linear algebra, probability, and dynamical systems.   Students will work in teams as part of active research groups at ISU.  This is a research group based REU and all participants collaborate with others; if you prefer to work alone this REU is not a good fit for youThere is no workshop component to this REU.  It is all research, although faculty and graduate students help the participants acquire relevant research background.  Students are selected by project and each of the projects lists its prerequisites. 

At the beginning of the summer the mentors explain the necessary background to the students.  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 on such topics as using LaTeX and attending graduate school, but the focus is on research and there is no workshop or class component to this REU.   The REU concludes with a symposium of student reports. Many projects submit papers for publication (list of papers) and students frequently present their REU research at conferences. 

Participants are provided a stipend, accommodation in University student housing, some travel reimbursement 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.  This is a large diverse REU and some activities are multicultural.  We particularly welcome applications from members of under-represented groups.

More information about the ISU Math REU can be found in the article that appeared in Involve, Vol. 7 (2014) No. 3 Special Issue: Proceedings of the Trends in Undergraduate Research in Mathematical Sciences Conference 2012, and an older  article in the Proceedings of the Conference in Promoting Undergraduate Research in Mathematics 2006, or on the web pages from prior years (linked above). 

Photo from Summer 2013 REU 

2015 Information

The ISU Math REU will be offered in 2015.  This is the place additional information about 2015 will be announced as it becomes available.  Please check back later for more 2015 information.

We cannot fund anyone who is not a US citizen or permanent resident.  We cannot accept anyone we do not fund (with the possible exception of Iowa State students).

Math Project Descriptions 2015

under construction
Algebraic Graph Theory Group  Dr. Sung-Yell Song,

Combinatorial Matrix Theory Group  Dr. Leslie HogbenDr. Michael Young,
Minimum rank, maximum nullity, and zero forcing on a graph

The graph of a real symmetric matrix A=[a_ij] has an edge between i and j if and only if a_ij is nonzero.  Finding the maximum multiplicity of eigenvalue 0 among symmetric matrices having a given graph is the same as finding the maximum nullity and is equivalent to finding the minimum rank among symmetric matrices having the given graph.  Initially a subset Z of the vertices of a graph G are colored blue and the remaining vertices are colored white.  The color change rule is that if a blue vertex v has exactly one white neighbor w, then change the color of w to blue.   The set Z is a zero forcing set if after applying the color change rule until no more changes are possible, all the vertices of G are blue.  The zero forcing number is the minimum size of a zero forcing set.  The zero forcing number is an upper bound for the maximum nullity of a graph, and arose independently in the study of control of quantum systems in physics, where it is called graph infection or propagation.   This project will investigate problems related to minimum rank, maximum nullity, and zero forcing number.

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 (see list of papers).

Linear algebra is a prerequisite 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 Sage and Mathematica, so knowing one or both of these in advance is helpful, but you can learn one or both of here.

Advice to the Applicant

Students frequently ask what information is most helpful to us in making decisions and what they should do to improve their chances of selection.   Here is some advice based on what has happened previously (do not be discouraged if you can't follow all of it- not all successful applicants do) and some of it is my (Leslie's) opinion. 

Follow directions. We require certain specified documents, NOT in your resume.  Answer the eligibility questions and what projects interest you question on the application site correctly- these are important and determine who reads the application.

Writing the personal statement
Our program has a strong project-fit element to the selection process: the project mentors have great influence on who is picked.  So the best advice I can give you specific to our program is
    read the project descriptions carefully
    don't ask for a project for which you do not have the necessary prerequisites
    do identify all projects that match your background and interests, and explain why you are interested in that project in you application
This is of course in addition to answering the rest of the questions we ask.

General preparation:
Take the hardest mathematics courses available.  We are looking for people who seek challenges and love math.  We are also looking for a strong foundation in proof-based (theoretical) courses in which you read and write proofs- in some colleges this is all math courses, in others the first proof course might be abstract or linear algebra.  Having taken more theoretical courses is always good, whatever area.  Work hard in your math courses- having a high GPA in math courses definitely helps (we are also somewhat interested in science courses, but are not interested in non math/science grades).  Other ways to demonstrate mathematical interest include taking the Putnam Exam, membership in Pi Mu Epsilon, or participation in a selective mathematics program (e.g., study abroad).

In addition to mathematics courses, some projects may have requirements in other fields of study (e.g., biology).

All of the following are useful skills (if you have them, say so), but are less important than your math background, as we can teach this if needed after you arrive: Matlab, Mathematica, Sage, ability to write in LaTeX.

Get to know at least one or two faculty members at your college well- letters of recommendation play an important role in selection.

Being a freshman is a disadvantage, but we will consider you (unlike some programs) provided you are at least a mathematical sophomore, i.e., will have completed 2 years of college mathematics (calculus and above) by summer 2013.

A final suggestion- apply to several REUs, as no applicant, however outstanding, can be certain of admission to one specific REU program.

ISU Math Homepage  
Web page maintained by Leslie Hogben