Rose-Hulman Undergraduate Mathematics Conference
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Dr. Bryan Shader Dr. Travis Kowalski

Dr. Bryan Shader
University of Wyoming

Not available yet.

Title: Communication Complexity
Abstract: Consider the following problem: two people each have a binary string of length n. They would like to know whether or not their strings are equal. What's the minimum amount of information that they must exchange to do this?

As another problem: two people each have a set of numbers. They would like to know the average of their combined list of numbers. What's the minimum amount of information they need to exchange to do this?

The problems above are examples of the relatively young field of communication complexity. In this talk we will survey the resulting linear algebraic and combinatorial problems that arise from Communication Complexity, and describe some surprising, recent results in Communication Complexity.

Title: Up with determinants
Abstract: In a 1995 paper Down with Determinants in the American Mathematical Monthly Sheldon Axler described how linear algebra can be done better without determinants. He also indicated that determinants "play an honorable role in some areas of research". This talk will highlight some interesting, combinatorial and algebraic instances where the determinant is an "indispensable tool".


Dr. Travis Kowalski
South Dakota School of Mines and Technology

Travis Kowalski (travis.kowalski@sdsmt.edu) earned his Ph.D. from the University of California at San Diego in 2002. He joined the mathematics faculty at the South Dakota School of Mines and Technology in 2004. His academic interests include complex analysis, applications of power series, and the cultural and historical roots of mathematics. He also enjoys drawing cartoons and visual wordplay, spending time with his wife and two daughters, and panicking at the ever-increasing size of his "To do" list.

Title: Sineseeing: a sightseeing voyage with sine
Abstract: The sine function is an indispensible tool of mathematics, but underneath its gentle periodic waves lies an endless trove of mathematical treasures. In this talk, we plan on taking a dive into the sinusoidal sea to locate some of them, including a clever rule of thumb for approximating its values, a remarkably hidden pi inside it, and a beautifully simple (or is it beautifully complex?) formula for the sine of a single degree, both here on Earth and elsewhere in the Solar System. Along the way, we'll investigate the rich, multicultural history of the sine function and even, with a little luck, get a glimpse of its future too.