Notre Dame REU 2002  Home Page

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The goal of this REU is to introduce undergraduate mathematics students to the pleasures and challenges of research in mathematics. It also seeks to provide them with a mathematical background  which goes beyond what is usually available in the undergraduate curriculum,  one which will prove valuable to them in any graduate work in mathematics.

This program is designed for undergraduates who have completed two or three years of an undergraduate program leading to a Batchelor's degree in Mathematics. A further requirement is that the applicant be committed to pursuing some further work in Mathematics beyond the Batchelor's degree. The successful applicants will have a desire to experience how mathematical research is done, and will have a solid background in Linear Algebra and Multivariable Calculus. They will have completed the sophomore year of studies as mathematics majors.

Contents

1. How to contact us:

                                      or you can write us at :

                                    A less reliable means is by phone:                     1-219-631-6571

Selection of Participants will begin on March 11, and preference will be given to applicants whose files are complete at that time.

HowTo Apply:

---We also need a transcript of grades from your college or university.

---You will need to fill out the application form below. You can either  mail it or send it by e-mail  to us. Send all information to the address above.

2.Dates of this year's REU:

The REU will meet in Hayes-Healy-Hurley Hall, on the campus of the University of Notre Dame. There will be an seminar room reserved for the use of students of NDREU 2002. Classes will be in Room 171. A special room of the Mathematics Library will be reserved for students of NDREU 2002.

3. Stipends:

2.Format of this year's REU:

The directors of this year's REU are Professor Frank Connolly, and Dr. Dan Isaksen. Both are topologists at the University of Notre Dame.

5.Mini-Courses for 2002:

Abelian Groups  (to be taught by Frank Connolly):  This course will familiarize the student with the notion of a group, but with special attention to the category of Abelian Groups. Topics will include: Groups; Subgroups and Quotient Groups; Homomorphisms; Direct Sums and Direct Products; Free Abelian Groups; Cyclic Groups; the Structure Theorem for Finitely Generated Abelian Groups; The functor Hom; The Tensor Product of two abelian groups;  Rings and Modules.

Topology and the Fundamental Group  (to be taught by Dan Isaksen):    This course will familiarize the student with the concept of a topological space with special attention to surfaces and the fundamental groups of manifolds of dimensions two and three. Topics will include: Topological Spaces and Metric Spaces; Connectedness and Compactness; Separation Properties; Continuous Functions; Loops, Homotopy, and the Fundamental Group of a topological space; Van Kampen's Theorem;  the fundamental group of a surface and of a knot complement;

6.Research Problems for 2002:

• Hamiltonian Graphs
• Surgery Obstruction Groups

Surgery Obstruction Groups  (to be led by Frank Connolly):        The main goal of this project will be to compute the Grothendieck group of nonsingular quadratic forms of the polynomial ring Z[t], and the polynomial ring Q[t].  This is the so called Quadratic Witt Group of Z[t] (or Q[t]). Because of recent work it turns out that these are closely connected with the functor UNIL( ; ,  ),  introduced in the Topological theory of Surgery, 30 years ago, but still poorly understood today.  Indeed, it is now clear that a calculation of these is more or less equivalent to a calcuation of UNIL(Z; Z,Z) or UNIL(Q; Q,Q). No knowlege of topology is required, but the student should have a good background in Linear Algebra, and a working knowlege of Abelian Groups will eventually emerge as desirable.

7.Application Form

Date:

Name:

Social Security #:

Are you  a United States Citizen ?

Birth date:

Expected date of graduation:

Name of your institution:

Overall GPA:

Math GPA:

Your address at college:
 
 

Your telephone number at college:

e-mail address:

Dates of your Spring Break in 2002
 

Home Address and phone number:
 
 

Address, phone number, e-mail address during your Spring Break:

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Name, address, and phone numbers of TWO persons (college mathematics professors) who will write references for you:

1.

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2.

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If you wish, you may identify yourself as belonging to one or more of the following groups which are under-represented in the mathematical sciences (just
circle, underline, or put parentheses around the appropriate attributes):

............Women..........American Indians...........Blacks.........

....... Hispanics.........Native Alaskans............Native Pacific Islanders..........

Please provide the following information (on a separate page):

Titles of college mathematics courses completed & textbooks used:

Titles of college mathematics courses in which you are presently enrolled & textbooks you are using:

On a separate page provide the following essay:

In a brief essay of perhaps one typed page describe your mathematical interests and career goals, including your interest in, and preparation for,  graduate study in mathematics. You might indicate in this essay which of the two research projects described above interests you most.

8. History of this REU.

          During the twelve graduating classes beforeSUMR existed, (1978--1989), apparently only one member of the Notre Dame mathematics undergraduate program (M. Mast),  successfully pursued a pure mathematics Ph.D.   In  the first seven  graduating classes (1990--1996) after SUMR started,  there were, on average, two SUMR students per year, and  eleven of those fifteen early students earned Ph.D.'s in Mathematics. In the last five years, (1997--2001), the program has graduated thirteen  students, of whom eleven are working towards Ph.D.'s in Mathematics or Physics in the next few years. The program
has gradually grown larger. Four excellent students from the class of 2003 have just been admitted into SUMR.  Of the seven current students in SUMR, all are expected to pursue Ph.D.'s in Mathematics.

        The complete list of all students who have participated in SUMR for at least one year, and the records they have established,  is attached at the end of this section.

        A fundamental feature of SUMR has always been to introduce students to advanced mathematical subjects which would be of use to them in graduate school but which are usually unavailable to undergraduates.  Yearlong seminar topics in recent years include  Morse Theory, Characteristic Classes, Algebraic Number Theory, and Lie Groups.  But SUMR has gradually put more and more emphasis on independent work as well. All participants of SUMR must now write several term papers, as well as a very substantial Senior Thesis.  In order to give more emphasis to this aspect of independent work, we started the summer program, Notre Dame Research Experience in Mathematics,  two years ago.   This program turned out very well. Of the four participants in NDREM 2000, three have graduated  and are  pursuing Ph.D.'s in mathematics at Oxford,  Berkeley, and Columbia.  Two  of the four became   Rhodes Scholarship Competition  finalists, one was a George C. Marshall Scholarship  winner, one was a NSF Graduate Fellowship winner, two  won Honorable Mention in the NSF Competition, and two were Goldwater Scholarship winners .  We also expect excellent things from the participants in the 2001 summer  program.

 Graduates of SUMR, 1990-2001

 David Hurtubise (1990):  Stanford University , Ph.D., Mathematics.
 David Schmitz (1990):  University of Chicago, Ph.D., Mathematics.
David Letscher (1991): University of Michigan, Ph.D., Mathematics.
Martin Mohlenkamp (1991): Yale University,  Ph.D., Mathematics.
Reed Solomon (1991):Cornell University, Ph.D., Mathematics.
Tao Chen (1992):Stanford University, Ph.D., Applied Mathematics.
Margaret Conroy (1992):University of Michigan, M.S., Mathematics.
Tom Nevins (1992): University of Chicago, Ph.D., Mathematics.
Kevin Chouinard (1993): University of Virginia, Ph.D., Mathematics.
Yuhui Ren   (1993): University of Illinois, M.S.,   Electrical Engineering.
 Anthony Vazzana  (1993): University of Michigan, Ph.D., Mathematics.
 Tim Culver  (1994):  Duke University (declined Michigan), M.S., Mathematics.
Mary Donohue (1994):  Wharton School of Business, M.B.A.
 Kevin Hartshorn  (1994):  UC Berkeley, Ph.D., Mathematics.
Dana Powell  (1996):   Stanford University, Ph.D., Mathematics.
Chris Dwyer (1997): University  of Wisconsin,  Mathematics.
Jeff Beh (1998):  University of Pennsylvania, Mathematics.
Aaron Couture (1998):  Notre Dame  (declined Yale), Physics.
Helga Schaffrin (1999):  New York Univ. (declined Chicago),  Mathematics.
Brian Dean (1999):   Johns Hopkins Univ.  (declined Yale), Mathematics.
 Eric Hatfield (1999):  Washington University at St. Louis, Medicine.
Amanda Mueller(1999): Harvard Univ.(declined  Princeton), Mathematics.
 Richard Siefring (2000):  New York University, Mathematics.
 Sami Assaf (2001):  UC Berkeley,  Mathematics.
Matthew Hedden (2001):   ColumbiaUniv.(declined Chicago),  Mathematics.
 Michael Munn (2001):  SUNY, Stony Brook,  Mathematics.
David Swinarski (2001): Baliol College, Oxford,  Mathematics.
Sonja Mapes (2002): Current senior.
CariAnne McCullough (2002):  Current senior.
Andrew Nerlinger  (2002):   Current senior.
Kathleen Ponto (2002):  Current senior.
Kathryn Hylden (2003):  Current junior.
 Nicholas Mastronardi (2003): Current junior.
 Donovan McFerron (2003): Current junior.
 Kevin Thomas (2003):  Current junior.

Winners of the NSF Graduate Fellowship:     Assaf, Hartshorn, Hurtubise, Mohlenkamp, Mueller, Schmitz.
Winners of the NSF Postdoctoral Fellowship:     Solomon,  Mohlenkamp, Nevins.
Winner of the George C. Marshall Scholarship:    Swinarski.
Winner of the Fulbright Scholarship:     Conroy.
Winner of the NDSEG Fellowship:    Nevins.
Winners of the Goldwater Scholarship:     Beh, Hurtubise,  Ponto, Siefring,  Swinarski, Vazzana.
Honorable Mention in the NSF Graduate Fellowship Competition:     Couture,  Letscher, Nevins, Siefring, Swinarski.
Runners-up or Honorable Mention in the Alice Schaefer Scholarship Competition:      Assaf,  Mapes, Mueller, Ponto.
Rhodes Scholarship Finalists:    Hedden, Swinarski.