2013-2014 Seminar Series
Student presentations given during the 2011-2012 academic year. All talks are at noon in Hurst 101 (some exceptions apply) Each year senior mathematics majors participate in a seminar series. The students are responsible for learning about an advanced mathematics topic not generally covered in the curriculum. Each student has a faculty adviser, writes a paper, and gives a presentation. The presentations are open to all.
Modeling Sickle Cell Anemia: Genetic Distributions in a Population
I will be looking at mathematical models of allele frequencies and their resulting genotypes and phenotypes in a population. Beginning with the Hardy-Weinberg model, we will build upon it to show the complexity of real life models using difference equations and understanding stability of fixed points. These concepts will be applied to sickle cell anemia, which is one of few diseases to be positively selected for, to better understand how it will exist in a population.
Stabilizing an Inverted Pendulum
The inverted pendulum on a cart is a classic example of an optimal control theory problem. I will be deriving the equations of motion and investigating stabilization of the system using control theory techniques.
Nifty Matrix Decompositions
A matrix and a complex number are often thought of as two very different ideas. However, certain matrix factorizations demonstrate that matrices are quite similar to complex numbers. This uncanny connection produces some insightful results, which we will explore theoretically and visualize with illuminating pictures.
Designing a Recommender System
Have you ever wondered how Pandora chooses such excellent (or terrible!) songs for you on your radio? So did I! Using collaborative filtering techniques, I designed an algorithm like what I believe Pandora might use by calculating the similarity of different songs.