WOMEN IN MATH -
WIM SCHOLARS PROGRAM
- Bingqian Lu, Supervisor: Anna Mazzucato.
Title: Monte Carlo simulations and option pricing.
Description: Monte Carlo simulation is a legitimate and widely used technique for dealing with uncertainty in many aspects of business operations. The purpose of this paper is to explore the application of this technique to the stock volality and to test its accuracy by comparing the result computed by Monte Carlo Estimate with the result of Black-Schole model. In addition, we used Mathematica, a mathematical computer software application, we tested the relationship between the sample size and the accuracy of Monte Carlo Simulation and provide numerical and geometrical evidence for our conclusion.
- Paige Carlton, Supervisor: Andrew Belmonte.
Title: Saffman-Taylor Fingering.
Description: Researching Saffman-Taylor Fingering. Injecting liquids of different densities and observing the patterns of fingering. Later will infuse particles into the liquids and observe how the particles affect fingering and the air bubbles formed.
- Jacquelyn Kirchner, Superviser: Jason Morton.
Title: Petascale Experimental Mathematics.
Description: Jacquelyn will study approaches for using supercomputer hardware such as the Blue Waters machine, as well as commodity clusters, to solve problems in computational algebraic geometry. Specifically, she will be attempting to solve computationally certain implicitization problems that have resisted both mathematical and small-scale computational approaches.
- Yixuan Shi, Junior, Supervisor: Jenny Li.
Title: Mathematical models on monetary policy and open market operation analysis.
Description: Many countries now face the economical crisis problem. A very powerful tool for government to balance their economy is using monetary policy. A well-build mathematical model will provide a decisive help on formulating proper policy. Bubble problem, hyper deflation problem, and many economic issues can be well presented and fixed via mathematical models. I hope to development a certain way to solve those economic problems. Moderate adjusting the interest rate and the amount of liquidity in a nonlinear way may achieve equilibrium in a dynamic economic and a steady positive growth rate. Project report.
- Paige Elizabeth Pfeffer, Junior, Supervisor: Jenny Li.
Title: Optimization problems arising from economics and finance
Description: Economics and finance are concerned with decisions making, i.e. making a choice among alternatives in a way to maximize or minimize something. For example, a company wants to maximize their profit while minimizing cost with consumers maximizing there utility (represents happiness) and financial intermediaries maximizing their investment returns. The corresponding mathematical model can be an optimization problem with many variables; stochastic and dynamic with equality or inequality constraints. Professor Jenny Li and I are going to investigate a particular problem arising from a banking firm model from economics.
- Amber L. Reardon, Junior, Supervisor: Alexei Novikov.
Title: Front propagation in reaction-diffusion equations
Description: The objective of this project is to understand the behavior of solutions of the reaction-diffusion equations. The project comprises two parts: rigorous analytical study of the Kolmogorov-Petrovsky-Piskunov-Fisher equations and numerical simulations of reaction-diffusion equations in 1-dimensional heterogeneous media using MATLAB. Project report.
- Anna Auker , Freshman, Supervisor: James Sellers.
Title: Properties of recurrent Sequences
Description: As part of a small group, Anna will participate in a study of recurrences and related properties (such as divisibility of Fibonacci numbers and related families.
- Kristina Colladay, Senior, Supervisor: Andrew Belmonte.
Title: Mathematical modeling of biodiesel production
Description:Biodiesel is a fuel esentially interchangeable with petroleum diesel, produced by chemical reaction from mo0st vegetable oils. We are studying the coupled Oridnary Differential Equations models for this reaction, and comparing it with our own biodiesel production experiments in the Pritchard Fluid Lab.
- Christine Cushwa, Senior, Supervisor: Diane Henderson and
Title: Numerical look at Mathieu's equation.
Description: We studied differential equations with non-constant coefficients, concentrating on the Mathieu equation for which we conducted a numerical investigation.
- Fara Delitsky, Freshman, Supervisor: Anna Mazzucato and
Title: Numerical methods for elliptic equations and linear algebra
Description: We study the properties of the stiffness matrix associated to the discretization of the Laplace equation. Our approximation space is defined in terms of a partition of unity. We want to obtain a fast method for solving the resulting linear system. We will consider the effect of changing the basis of the Finite Element space.
- Noopur Pathak, Sophomore, Adviser: Luen-Chau Li.
Title: Zero-preserving isospectral flows
Description: We plan to construct isospectral flows on symmetric matrices which preserve zero patterns and which converge to diagonal matrices. We hope to be able to use such flows to compute the eigenvalues of some classes of structured matrices.