2011-2012 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.

Determining Cayley Tables from Cayley Graphs

Jesse Howe

Wednesday, October 26th

$jesse$

Cayley graphs give a visual representation of the partial structure of a group. A Cayley table represents the complete structure of a group. In a Cayley graph, the elements of a group become vertices and the edges represent right multiplication by the elements of the set S, where S is everything in G except the identity. Using diagrams and tables, I will discuss when is it possible to take the graph of a group and generate complete information (Cayley table) about the structure of that group, from partial information (Cayley graph), and what characteristics of the given group dictate whether or not this is possible.

Optimizing a Line of Best Fit

Samantha Shell

November 18

$samantha shell_1.jpg$

This work continues the collaboration with chemists at DU who use MatLab programs to analyze data, plot the data, and then calculate curves that fit the data. The goal of this project is to write optimization code so the user can change a specified parameter and the program will automatically adjust the other corresponding variables to make a better fit line. I plan on using a smaller set of data to get the techniques down and demonstrate in my final talk, but the ultimate goal is to apply these techniques and cod to the MatLab program so the researchers at DU will be able to use it in the near future. I also hope to get more data from them to make sure everything really does work the way it should.

Baseball's "Pythagorean Theorem"

Erika Espinoza

November 22, 2011

$erika_e$

The famous theorem relates sides of a right triangle. Let's see how a variation applies to the diamond of America's sport.

Diophantine Equations in Chemistry

Christian Collins

Friday Dec. 2

$christian$

Diophantine equations are equations with integer solutions. Surprisingly, these can be useful for decomposing a complex chemical reaction into individual steps.