On Monday November 16th, at 3:30 PM in Math 357, Dr. Robert Vallin of Lamar University will be talking about “Mathematics and Card Magic.” This talk will be accessible for all students and Dr. Vallin is an excellent speaker. (flyer in PDF form)
Abstract: Recreational Mathematics is about doing mathematics for fun, rather than research. It covers many topics including games, puzzles, juggling, art, and more. It has had no greater champion than Martin Gardner, who wrote the Mathematical Games column for “Scientific American” for 25 years. In this talk we will look at several card tricks that are based on mathematics and were introduced to the world at large by Gardner, and show some of the workings behind them. We will further see how one particular trick relates to some known ideas and leads to developing new mathematics.
Our next colloquium will be on Monday November 9th at 3:30 PM in Math 357. Dr. Nick Long will be talking about “Easy Unsolved Algebra Problems.” This talk will be accessible and interesting for students with experience or interest in linear algebra.
Abstract:Dynamical systems is a branch of mathematics that uses many tools from many different areas of mathematics to help describe the behavior of changing systems. Symbolic Dynamics deals with the changes that can be described by infinite sequences of symbols. For example, the data on computers is stored and manipulated as a long sequences of zeros and ones but can exhibit interesting behaviors like chaos. We will look at some problems that can be stated in basic linear algebra terms, but the answers are still mostly or partially unknown. All that is needed to solve them is another good idea. (flyer in PDF form)
On Monday September 21st at 3:30 PM in Math 357, Dr. Mark Webb will be giving our first colloquium of the semester on “Edge Ideals.” Be sure to invite any students who have an interest in algebra.
How many distinct triangles can you find in the graph above? What about graphs that aren’t complete? One interesting solution involves associating the graph with a collection of polynomials – called the edge ideal. This association allows one to use algebra to study graphs. In this talk, we will present a hands-on approach to this field, using SAGE to compute examples and explore recent results and open problems in this area.
On Monday, February 23rd at 3:30 PM in Math 357, Marcus Webb will talk about “The Freshman’s Dream.” Abstract: Let A be an m by n matrix with entries in some finite field – the integers modulo a prime p, for example. What happens to the kernel of A when we raise each entry to the p’th power? In this talk, we will answer this question and consider its generalization to matrices with entries in a commutative ring of prime characteristic. For such rings, every freshman’s dream is true: (a+b)p=ap+bp, and we will explore some of the remarkable consequences of this equality. (flyer in PDF form)
On Monday February 16th at 3:30 in Math 357, Dr. Jonathan Mitchell will be talking about “The Effect of a State-Dependent Delay on a Weakly-Damped Nonlinear Oscillator.” Abstract: We consider a weakly-damped nonlinear oscillator with state-dependent delay which has applications in models for lasers, epidemics, and micro-parasites. We begin by introducing a nonlinear oscillator stemming from the usual predator-prey system and analyzing the evolution of its energy. We will incorporate a constant time lag in the production of the predator population and show that sufficiently large delay can cause oscillations to persist via an Hopf bifurcation. We then consider a variable delay which will depend on the relative size of the prey population. Specifically, we find conditions on the functional form of the delay in which the branch of periodic solutions will be either sub- or super-critical as well as an accurate estimation of the amplitude. (flyer in PDF form)
On Monday, February 9 at 3:30 in Math Building 357, Dylan Poulsen of Baylor University will be talking about “Stability and Control of Dynamic Equations on Time Scales.” Abstract: From cruise-control systems to rocket dynamics, control theory forms a foundation for our modern society. Much of control theory relies on updates to the system occurring at uniform, predictable moments in time. As control systems become distributed over large scales or become controlled by low-speed devices, the uniformity and predictability of the time domain cannot be guaranteed. In this talk, we outline an approach to controlling linear systems on non-uniform and random time domains using a new branch of mathematics called time scales. We will derive a stability theory for this case, and then we will apply the theory in finding the optimal control policy. (Flyer in PDF form)
On Monday November 3rd at 3:30 in Math 357, Dr. Qin Shing from the Department of Mathematics and Center for Astrophysics, Space Physics and Engineering Research at Baylor University will be talking about “Numerical PDEs and the Legacy of ADI and LOD Methods”.
Abstract: Numerical partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations. They involve computational methods including the finite difference and finite element, finite volume, spectral, meshless, domain decomposition, multigrid, and in particular, splitting methods. The ADI and LOD approaches are two of them with extraordinary features in structure simplicity, computational efficiency and flexibility in applications. They look similar, but are fundamentally different. Naturally, they lead to different ways of operations, and offer different strategies in computational realizations. This talk will provide an insight into the glorious history of these numerical methods, and discuss some of their latest reinforcements including applications for highly oscillatory waves. (Flyer in PDF form)
About Dr. Qin Sheng: Dr. Sheng received his BS and MS in Mathematics from Nanjing University in 1982, 1985, respectively. Then he acquired his Ph.D. from the University of Cambridge under the supervision of Professor Arieh Iserles. After his postdoctoral research with Professor Frank T. Smith, FRS, in University College London, he joined National University of Singapore in 1990. Since then, Dr. Sheng was on faculty of several major universities till his joining Baylor University, which is one of the research institutions and the second largest private university in the United States. Dr. Sheng has been interested in splitting and adaptive numerical methods for solving linear and nonlinear partial differential equations. He is also known for the Sheng-Suzuki theorem in numerical analysis. He has published over 95 refereed journal articles as well as 6 joint research monographs. He has been an Editor-in-Chief of an SCI journal, International Journal of Computer Mathematics, published by Taylor and Francis in London since 2010. He gives invited presentations, including keynote lectures, in international conferences every year. Dr. Sheng’s projects have been supported by several U.S. research agencies. He currently advises 3 doctoral students and 1 postdoctoral research fellow. He also serves on Panelist Boards for several research agencies including the National Science Foundation, USA.