The Undergraduate Mathematics Research Club The University of Texas at Austin

 Education
The Undergraduate Mathematics Research Club, or Math Club, is a student group sponsored by the UTAustin Mathematics Department and formed under the auspices of the Geometry Group RTG grant from the National Science Foundation. It is open to all students interested in mathematics, and especially caters to the UTAustin pure and applied mathematics communities. Our goal is to enhance the undergraduate math experience by exposing students to beautiful mathematics, interesting research, and helpful information.
Speakers include UT faculty, graduate students, and undergraduates, as well as researchers visiting as part of the RTG program. In addition to talks on pure and applied math, we will also hold information sessions on topics like applying to graduate school, things to do over the summer (REUs, Math Camps, etc.), and how to use the computer resources in the math department.

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The Top Ten Reasons Everyone Should Study Topology
Professor Vick explains why you should drop everything you're doing and start studying topology.

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Fiber Bundles and Symmetry Groups
Geometric and topological objects frequently come in families parameterized by other such objects. Depending on how intricate and/or symmetrical these objects are, the families can be "twisted.'' We will investigate the source of this behavior in concrete cases, and outline a program to understand such twisting in a large range of cases using topology.

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Reliable Communication and Linear Algebra
Professor Voloch will speak about how linear algebra is used in the theory of errorcorrecting codes, which are extensively used in telecommunications. He will also cover the modern ideas that go into the new "lowdensity parity check" (LDPC) codes, as well as the mathematical challenges associated with them.

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Surprising Circles, Archimedes, Onions, and Calculus
Cool insights about circles and basic geometry give magical proofs to some calculus results such as the derivative and integral of sin(x). In fact, some basically calculus insights preceded calculus itself by a couple thousand years. For example, Archimedes used ideas about levers and limits to deduce the equation for the volume of the sphere.

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Fully Conservative Characteristic Methods for Transport
Professor Todd Arbogast presents his topic "Fully Conservative Characteristic Methods for Transport"

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Making Tracks: A Mathematician Plays with Trains
Suppose we are given a set of segments of track from a toy train, and wish to make interesting designs which are simple closed curves. What options are available to us? Surprisingly, even a simple question like this leads us to use tools from linear algebra and number theory, and serves as a model for more general questions about positioning objects in space.