Opportunities for Independent Work and Research
The Mathematics Department offers opportunities for independent study in specialized areas with a faculty mentor when the student has developed an appropriate background and interest. Independent work can be an important part of the undergraduate educational experience.Students who become involved in independent study projects or research in mathematics most often do so in the junior or senior years after taking several advanced courses. Students usually need the tools from one or more of these courses, and sometimes such projects grow out of ideas presented in classes. However, a few students have acquired significant knowledge in a "niche" of mathematics (e.g., number theory) during math summer camps, high school study, or prior reading, and could pursue independent work earlier. During the fall semester of the junior year, majors are invited to a group meeting to discuss projects or other ideas for capstones--for example, participation in a "senior seminar" in which students read and make presentations.
Some ideas for possible work are linked, below, to this page. The suggestions will also give you an idea of the sorts of things some faculty are interested in.
Independent work might lead to graduation with Latin Honors. However, in any case, a senior (or "capstone" project) can be a valuable experience and a interesting addition to a resume and letters of recommendation. Sometimes student work can be published in undergraduate research journals (such as, for example, the Rose-Hulman Undergraduate Math Journal). Although more unusual, such work may even be publishable in research journals.
Students involved in the Honors Statistics Program have the opportunity to do a practicum, which consists of hands-on field work under the supervision of a professional mentor--either a faculty mentor or a mathematical scientist in industry or at a government research facility. For example, students can undertake a practicum with Washington University faculty in the mathematics department, at the medical school, or in other Arts & Sciences departments such as biology, economics or psychology.
Majors can also propose interdisciplinary projects involving another department if there are faculty in both departments who are will to co-sponsor the work. In that case, an advisor in one of the departments will be designated as the "primary" advisor and, for procedure's sake, that deparment will recommend Latin Honors for the student. (Latin Honors are attached to the AB degree and are, technically, a College award not a "departmental" award. See the Latin Honors web page for more information.)
Recent Projects and Honors Work in Mathematics
An Elementary Proof of a Generalization of Brun's Theorem
(Advisor: Professor Brian Blank)
Explorations of a Generalization of the Descent Statistic
(Advisor: Professor John Shareshian)
An Inquiry into the Optimality of Diseases
(Advisor: Professor John McCarthy)
On the Row Sums of the Character Tables of GL(2,q)
(Advisor: Professor John Shareshian)
Randomly Generated Covering and Almost-Covering Arrays
(Advisor: Professor JohnShareshian)
Polygonal Billiards and Markov Chains
(Advisors: Professors Renato Feres and Al Baernstein)
On the Algebraic Topology of Finite Spaces
(Advisor: Professor John Shareshian)
An Application of Harmonic Functions in Estimating the Conversion Rate of a Heterogeneous Catalyst
(Advisor: Professors Renato Feres and Al Baernstein)
Refinable Functions in L^2(R) with Composite Symmetry
(Advisor: Professors Guido Weiss and Edward Wilson)
The Complexity of Pebbling and Cover Pebbling
(Advisor: Professor Mohan Kumar)
Methods for Characterizing Doubly Invariant Subspaces
(Advisor: Professor John Shareshian)
Use of the Pigeonhole Principle in an Attempt to Solve a Problem of Moreto
(Advisor: Professor John Shareshian)
Finite Groups Associated with Composition Dilation Wavelets
(Advisor: Professors Guido Weiss and Edward Wilson)
Patterns of Progression from Psychiatric Disorders to Alcohol Use Disorders:
A Unique Method of Analysis
(Advisor: Professor Edward Spitznagel)
Studies of Dependence and Asymptotic (In)dependence in a New Family of Bivariate Distributions
(Advisor: Professor Al Baernstein)
Approaches to the Virtual Positive Betti Number Conjecture
(Advisor: Professor Rachel Roberts)
A New Framework for Removing Gaussian and Impulse Noise
The Algebraic Structure of OP(P)
(Advisor: Professor Nik Weaver)
Utilization of Census Data 2000 in California
(Advisor: Professor Edward Spitznagel)
Differentiable Paths in the "Hawaiian Earring"
(Advisor: Professor Renato Feres)
Survival Analysis of Framingham Data
(Advisor: Professor Edward Spitznagel)
Consistency of the Continuum Hypothesis
(Advisor: Professor Nik Weaver)
Analysis of the RSA Cryptosystem and the Use of
Elliptic Curves in Cryptography
(Advisor: Professor Mohan Kumar)
Wavelets on the Integers
(Advisor: Professors Guido Weiss and Edward Wilson)
Polynomials over Fp Whose Values are Squares:
An Explication of a Paper of Umberto Zannier
(Advisor: Professor Mohan Kumar)
Basic Ideas in Ramsey Theory
(Advisor: Professor Steven Krantz)
Heegaard Splittings, Computation of Homology, and
Encoding of 3-Manifolds in Computer Usable Form
(Advisor: Professor Rachel Roberts)
An Introduction to Ramsey Theory
(Advisor: Professor Steven Krantz)
A Survey of Topics in Heat Kernels and Dirac Operators
(Advisor: Professor Renato Feres)
The Wave Equation on the Sierpinski Gasket
(Advisor: Professor Al Baernstein)
Nonlinear Methods of Optimization
(Advisor: Professor Edward Spitznagel)
A Proof of Dirichlet's Theorem
(Advisor: Professor Mohan Kumar)
Yahtzee Revisited
(Advisor: Professor Steven Krantz)
The St. Petersburg Paradox
(Advisor: Professor Stan Sawyer)
Triple Distinct Edge-Intersecting Hypergraphs
(Advisor: Professor Steven Krantz)
The Smale Conjecture for Complex Polynomials
The Bootstrap Technique Applied to the Kappa Statistic
(Advisor: Professor Al Baernstein)
(Advisor: Professor Edward Spitznagel)
Faculty Ideas for Independent Work or Research Projects in Mathematics
W.U. students often take advantage of research experiences offered around the country during summer months. Examples include
There are also summer research opportunities which attempt to increase opportunities and participation of women in the field, for example,Research Experiences for Undergraduates
REU in Industrial Mathematics and Statistics
Research Opportunities in Applied Mathematics
Director's Summer Program, National Security Agency
Other possibilitiesDuring the regular school year, a number of majors have chosen to participate in an intense mathematical semester (or year) of study in the premier Budapest Semesters Program.Carlton/St. Olaf Program
George Washington University ProgramAll of these study opportunities experiences can lead to projects that often can be continued as independent study or research when students return to return to Washington University. Sometimes these are suitable for honors or capstone projects.
You can learn about some of the research interests of the faculty on the Department's faculty web page and additional links availble there.
Undergraduate majors interested in independent work in mathematics should talk with their major advisor or make direct contact with a faculty member whose general interests seem to fit. Students may also contact the Chair of the Undergraduate Committee, Professor Ron Freiwald for advice.