Special Mathematics Classes: Capstones
MTH 396 and MTH 496 Prerequisites:
Completion of MTH 309, MTH 310, and MTH 320 (or the honors equivalent), cumulative GPA of at least 2.0, average of at least 2.0 across MTH 309, MTH 310 and MTH 320 and approval of the capstone instructor. Note: e-mail notification will be given once your override has been issued.
Fall Semester 2011: MTH 496 - Random and Pseudorandom Sequences taught by Jonathan Hall
Description: Almost everyone would agree that flipping a coin a large number of times produces a random sequence of heads and tails, that is, 0’s and 1’s. But what exactly does it mean for a sequence to be random? Sequences that behave randomly are of great use in cryptography (one-time-pad, quantum cryptography), communication (mobile phones, the Global Positioning System), and elsewhere (dithering of digital images). Therefore it is important to be able to construct large sets of sequences that individually and collectively appear random. The course will deal with the properties, construction, analysis, and applications of such sets of sequences. The methods will include probability, analysis, and geometry; but the main tools are algebraic, particularly linear recursions and finite fields.
Spring Semester 2012: MTH 496 - Introduction to Chaos taught by T.Y. Li
Textbook: Introduction to Chaos by Kathy Alligood, Tim Sauer and James Yorke
Description: Chaotic behavior in dynamical system exists everywhere. It often crosses many disciplinary boundaries. In this course, we will give an introduction to some of the most fundamental elements with names, such as, attractors, basins, saddles, homoclinic point, cascades, and horseshoes. The goal is to help you learn what to look for in your own studies of dynamical systems of the world and universe.
Spring Semester 2012: MTH 396 - High School Mathematics from and Advanced Viewpoint. Instructor to be announced.