MATHEMATICS AND COMPUTING RESEARCH EXPERIENCES FOR UNDERGRADUATES AT IOWA STATE UNIVERSITY supported by the National Science Foundation (DMS-0353880)

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 frequently 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, some travel and meal expenses, 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).

Students who are U.S. citizens or permanent residents and will be undergraduates in Fall 2008 are eligible to apply  in early 2008 for summer 2008.  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 minorities are particularly encouraged to apply.  Women may also wish to apply to the Iowa State University Program for Women in Science and Engineering (PWSE) in addition to applying, in 2008, directly to the REU.  Minorities may  apply for summer 2008 to the AGEP/Alliance program. This page (that you are reading) describes only the application process for positions funded by the Department of Mathematics NSF REU site grant (direct application to the REU); PWSE and AGEP/Alliance programs offer additional sources of funding (and thus additional opportunities to be selected) for REU positions, including the projects listed on this page.  

General Information for 2006 (N/A in 2008)

• Dates: June 4, 2006 to July 29, 2006
  
• Compensation: Students will receive some support for travel to and from Ames, on-campus lodging at (probably in Frederiksen Court student apartments)  and some meals during the eight weeks of the REU, and a stipend of $2500.

E-mail: REU@math.iastate.edu
 

Telephone contact: Department of Mathematics, 515-294-1752 (ask for Kristy).

Fax: 515-294-5454 (address to REU)

Mailing address:
Summer Research Experiences for Undergraduates
Department of Mathematics
Carver Hall
Iowa State University
Ames, IA 50011
 

How to Apply: (2006) Not yet available for 2009   

Instructions to the applicant:   E-mail (REU@math.iastate.edu) with "REU (your last name)" as the subject of the e-mail is the preferred form of submission for all materials except the transcript, and is required for the information and statement that you submit.  Attachments may be used for formatted materials.  An e-mail body should contain plain text only- no graphics or styles.  The following attachment formats are accepted: PDF, MSWord, LaTeX, Postscript.   All attachments should contain your last name in the file name and at the beginning of the document.    Please suggest submission of letters of recommendation by e-mail.  US Mail or fax is acceptable for letters of recommendation if the writer of the letter prefers this format, but we ask you to offer electronic submission as an option to people who recommend you, as all materials will be reviewed in electronic format.  The official transcript should be sent  via US Mail (address below) directly from your institution.

Please submit the following materials to complete your application:

• The following Basic Information, numbered as shown, in the body of an e-mail to REU@math.iastate.edu with "REU (your last name)" as the subject:
• 1a. full name
• 1b. citizenship (and residency status if not US Citizen)
• 1c. e-mail address
• 1d. telephone number(s)
• 1e. mailing address

Please note: at least 1 of your e-mail and phone numbers must be able to reach you within 24 hours on any business day during the month of March.  If necessary, supply back-up contact information.
 
• 2a. undergraduate institution(s) and expected graduation date
• 2b. List of all college mathematics courses taken or in progress, with grades if completed
• 2c. GPA in mathematics courses
Use the following scales to compute this averages: A+=4.3, A = 4, A-=3.7, B+=3.3, B=3, B-=2.7, etc.  Use plus/minus grading as stated unless your school does not report +/- on the transcript, in which case, use A = 4.0, B = 3.0, etc.
• 2d. If you have participated in a previous NSF sponsored REU, list institution and date.
• 3a. projects that most interest you (up to three, please read the project descriptions on this web-site)
• 3b. if there are any projects you would not be interested in, please state this also.
• 4a,b. name and (e-mail or phone number) of people who will write letters of recommendation fro you

• A one to two page Personal Statement  with your name in it (either as an attachment to the e-mail or in the e-mail body) explaining:

1) Your relevant background and experience, including a) prior research experience and/or mathematics project(s) you have done (if any), b) other mathematically or computationally relevant job(s) you have held such as tutoring, etc., c) what experience you have with computer operating systems (e.g., Mac OS 9, Windows XP) and software (e.g.,  Mathematica, Matlab, programming languages), and d) what interested you in your advanced mathematical course work (beyond basic calculus).
2) Why you are interested in the projects that you identified above.
3) What your goals are and why you feel you would benefit from our program.
The Personal Statement, in contrast to the Basic Information, should not use numbering and need not use the listed order.  See also Advice to the applicant.
The personal statement must have your name both inside it and as part of the file name if it is an attachment.
 
• Your current undergraduate transcript (official).  The transcript should include all grades received for work completed by Feb. 1, 2005 and should be mailed (USPS) by your institution(s) directly to the mailing address:

Summer Research Experiences for Undergraduates 2006
Department of Mathematics
Carver Hall
Iowa State University
Ames, IA 50011
 
• Two or three letters of reference Two letters of recommendation is standard, but three will be accepted if the additional letter has significant additional information (and asking for three provides you with a greater likelihood we will actually get two, the minimum number needed for us to consider your application).  At least one must be from a college or university mathematics professor who has taught you in a formal course.  Prior research experience is not required; however, if you have prior relevant research experience, such as another REU, one of the letters must be from your previous mentor or program director. All letters should be from mathematicians, statisticians, computer scientists, biologists, chemists or other  scientists who can comment on your potential for mathematical research and/or relevant research experience.   Letters of recommendation should be sent directly by the writer via e-mail (preferred) to REU@math.iastate.edu with "REU (your last name)" as the subject,  or by fax (515-294-5454) or by US Mail to the mailing address above.

Applications will be accepted until all positions are filled, but late applicants may not be fully considered.  We usually start reading applications on the day of the deadline.

Project Descriptions (2006)

• basic theory of nonlinear dynamical systems and chaos,
• dynamic reliability, bridging the gap between nonlinear dynamics, random processes, and their statistical behavior.
Both topics will include numerical computations of system behavior in low dimensions.

Numerical Analysis Prof. Roger Alexander  Problems to be addressed will be chosen from one of the following areas having to do with numerical methods for stiff initial value problems in ordinary differential equations (ODEs). As background, students should have completed a basic course in numerical methods or scientific computing, and be familiar with a numerical software system such as Matlab. 
Design of Runge-Kutta formulas. A Runge-Kutta formula is specified by an s by s coefficient matrix A and an s-vector b of weights. The coefficients are determined by a set of conditions, expressible as polynomials in the coefficients, for the formula to have a desired order of accuracy. The resulting polynomial system of equations must be solved in parametric form in order to optimize the formula. The Groebner basis technique using a computer algebra system such as Maple or Singular is essential for managing the large computations.
Analysis of Test Problems. A number of excellent test problems have been collected or devised to examine the behavior of numerical ODE software. However, it is not sufficient merely to compare different codes, for the "standard" code's results may be contaminated by excessive numerical errors. Analytical approximations, using singular perturbation techniques, can provide a rigorous standard for the evaluation of numerical software.
Ill-conditioning of Linear Systems. Solving stiff ODEs requires implicit methods, which must be evaluated by a simplified Newton method on each integration step. The linearized equations are badly conditioned. Further ill-conditioning can appear in the neighborhood of a rest point of the ODE. How is it that codes can deliver an accurate approximate ODE solution under these conditions?


Combinatorial Matrix Theory  Prof. Leslie Hogben  Combinatorial matrix theory uses graphs and other combinatorial techniques to study matrices or families of matrices. The  2006 combinatorial matrix group will work on some aspect of combinatorial matrix theory, possibly on matrix completions, minimal rank/maximum multiplicity of of a graph or sign pattern, or spectrally arbitrary sign patterns. 
Matrix completions: A matrix completion problem for a pattern involves determining whether a pattern of entries (described by a digraph) has the property that any partial X-matrix can be completed to and X-matrix, for X a specific type of matrix. 
Minimum rank: The graph of a symmetric matrix A has an edge between i and j if a_ij is nonzero.  Finding the maximum multiplicity of eigenvalue 0 among symmetric matrices having a given graph is equivalent to finding the minimum rank among symmetric matrices having the given graph. 
Sign patterns: 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.
Students involved in this project will be part the ISU Combinatorial Matrix Theory Research Group; more information is available on that page. The summer 2003 and 2004 groups have a combined paper about matrix completions that will appear in Linear Algebra and Its Applications. The summer 2005 group has submitted a paper about spectra of matrices described by a tree or tree sign pattern. 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, but you can learn that here.

Matrix Stability  Prof. Leslie Hogben  A real square matrix is stable if all its eigenvalues have negative real part.  Stable matrices play a vital role in many applications including differential equations. There are many interesting generalizations of stability, and counter examples to conjectures can be found computationally.  This project will explore various types of matrix stability.  Linear algebra is a pre-requisite for this project and a strong theoretical mathematics background (usually including abstract algebra or real analysis) is expected.  The software we use is Mathematica, but you can learn that here.

Biomolecular Modeling and Simulation Prof. Zhijuan Wu  Three possible projects in biomolecular modeling and simulation have been designed for the REU students in this group during summer 2006:
(1) Develop optimization methods for constructing protein structures that can fit given sets of distance constraints. The work is related to distance based protein modeling.
(2) Solve linear systems of ordinary differential equations to obtain estimates on fluctuations of protein structures around their stable states. Identify "hot" versus "cold" spots along protein backbones.
(3) Align protein structures and estimate the fluctuations of the structures within the structural ensembles via RMSD (root-mean-square deviation) and DME (distance matrix error) calculations.
The projects require the knowledge in linear algebra, optimization, and ordinary differential equations. The general knowledge in molecular biology is helpful for the understanding of the biological importance of the problems, but is not required.


Modeling Cancer Mathematically Prof. Khalid Boushaba, Prof. Howard Levine, Prof. Michael Smiley      Metastases are the main cause of mortality in cancer.  The surgical removal of a primary tumor is often followed by a rapid growth of secondary tumors (metastases) that may have been dormant in a distant organ for many years. This project models this phenomena using a model that focuses on the idea that secreted growth factors from the primary tumor have a rather short half life and thus cannot diffuse very far without degrading or binding to the extra cellular matrix (ECM) and becoming deactivated whereas secreted inhibitors have a much longer half life and thus able to diffuse over longer distances.  The model uses the principles of chemical kinetics, random walks and systems of differential equations to describe those processes.  The participating students will begin by learning the some of the relevant cell biology and organic chemistry.  They will learn many modeling ideas and simulations  techniques.  Knowledge of Calculus of several variables and ordinary differential equations is required, and at least six credit hours of Biology/Chemistry is preferred.

(taken from http://www.hosppract.com/issues/1999/01/eckhardt.htm)

Advice to the Applicant

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 pre-requisites
• do identify projects that match your background and interests and explain why you are interested in that project in you application

General preparation:

Take the hardest math 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 study abroad program.

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, as we can teach this if needed when you arrive: Matlab, Mathematica, statistical software, 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 (however, the vast majority of students selected are at least mathematical juniors, although many are chronological sophomores). 

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

Leslie