## Mathematics & Computer Science

## Upcoming Events

### '14 Spring Semester

**On April 22**, Pi Mu Epsilon reception at Hoffman House for this year's inductees to the honor society.

**On March 20**, Colloquium Series presentation by Dr. Gabriel Feinberg of Haverford College: Pythagorean Triples and Geometry. A Pythagorean triple is a triple of positive integers a, b, and c such that a2+b2 = c2. Some well-known examples include (3,4,5), (5,12, 13), and (8,15,17), but there are infinitely many more. In this talk, we will see two methods for describing all Pythagorean triples, and the geometry behind them. The first method will be classical, relying on Euclidean geometry, while the second will appeal to ideas from non-Euclidean geometry.

**On March 5**, (At Temple University) Presentation by
Daniel File, visiting assistant professor of mathematics. This is part two of a two-part lecture at the Temple University Number Theory Seminar. His talk is titled "Test Vectors and Central L-values for GL(2) II.

**On February 26**, Colloquium Series presentation by Dr. Robert Vallin of Slippery Rock University on Mathematical Card Magic: A rising swell of research is being devoted to topics such as juggling, the game of SET, Sudoku & KenKen Puzzles, and more. What unites these topics is that they fall under the umbrella term Recreational Math. This talk will look at the recreational topic of playing card tricks that are based on mathematical ideas. We will show some tricks, explore the mathematics behind them, and see how they can lead to something new under the sun.

**On February 26**, (At Temple University) Presentation by
Daniel File, visiting assistant professor of mathematics. This is part one of a two-part lecture at the Temple University Number Theory Seminar. His talk is titled "Test Vectors and Central L-values for GL(2) I. He will give two lectures describing recent work with Kimball Martin and Ameya Pitale in which they compute the central value of the base change L-function for a cuspidal automorphic representation of GL(2).

**On February 21**, Colloquium Series presentation by Dr. Patrick Williams of Muhlenberg College: Mathematics On Your Mind.
Wondering what those math courses are preparing you for? A career in neuroscience, of course! In this talk, I'll introduce a few of the many ways in which interesting mathematical challenges—and mathematicians—permeate the field of neurophysiology. We'll focus on one critical issue, dimensionality reduction, and look at how it factors into the creation of a brain-controlled neuroprosthetic limb.

**On February 7**, Colloquium Series presentation by Allison Davidson of Purdue University: What Makes a Pólya Urn Scheme Tenable and Why Is That Important?
Pólya urns are statistical models that use colored balls to simulate a growth or decay process. Pólya urns that can be repeated indefinitely, regardless of the events that take place, are known as tenable urns. In identifying the specific conditions required for tenability, one can assess the tenability of any Pólya urn scheme, and thus the sustainability of the specific growth or decay model it represents.

**On February 3**, Colloquium Series presentation by Dr. Thomas LoFaro,
Clifford M. Swanson Professor of Mathematics at Gustavus Adolphus College: Finding Hubs & Authorities from Network Connectivity. Jon Kleinberg's HITS (Hypertext Induced Topic Search) algorithm was originally designed to rank web pages in a manner similar to the PageRank algorithm used by Google. HITS assigns a pair of weights to each page that measures both the quality of the information on the page (the authority weight) and the access to information that it provides (the hub weight). This feature makes HITS applicable to the analysis of social networks and other non-internet specific networks. In this talk I will describe the HITS algorithm, discuss network structures where HITS fails to converge to a meaningful result, and propose a modification to the algorithm that addresses this shortcoming.

**On January 27**, Colloquium Series presentation by Dr. Robert Bosch, Robert and Eleanor Biggs Professor of Science at Oberlin University:
Opt Art. Optimization is concerned with optimal performance—finding the best way to complete a task. It has been put to good use in a great number of diverse disciplines: advertising, agriculture, biology, business, economics, engineering, manufacturing, medicine, telecommunications, and transportation (to name but a few). In this lecture, we will showcase its amazing utility by demonstrating its applicability in the area of visual art, which at first glance would seem to have no use for it whatsoever! We will begin by describing how to use integer programming to construct a portrait out of complete sets of double nine dominoes. We will then describe how high quality solutions to certain large-scale traveling salesman problems can lead to beautiful continuous line drawings. We will conclude by presenting other examples of Opt Art—art constructed with the assistance of optimization techniques.