Colloquium 9/12: Dr. Jackie Jensen-Vallin on “Conway Notation and Gilbreath Knots”

On Monday September 12th at 3:30 in Math Building 357, Dr. Jackie Jensen-Vallin will be giving a talk on “Conway Notation and Gilbreath Knots.” This talk will be interesting and accessible for all levels of students. (flyer in PDF form)

Abstract: A knot is an embedding of a circle in three-dimensional space. The classification question – do two projections of knots represent the same knot – is a large question in knot theory, and many invariants have been developed to address this.  We will focus our invariant discussion on the Conway notation and explore knots whose Conway notation correspond to Gilbreath sequences.  A Gilbreath sequence is a sequence of (traditionally) natural numbers a_1, a_2, a_3, …, a_n such that all subsequences  a_1, a_2, …, a_m   with m≤ n contain consecutive natural numbers. We will ask if all knots can be built from Gilbreath sequences, and consider many examples.

Colloquium 4/11: Dr. Jonathan Mitchell on “Techniques for Analyzing Nonlinear Oscillators”

Next Monday, April 11, at 3:30 in Math 357, Dr. Jonathan Mitchell will be talking about “Techniques for Analyzing Nonlinear Oscillators.”

Abstract: To the chagrin of many scientists, we live in a nonlinear world. We tend recognize patterns and formations in all sorts of contexts not the least of which is in the physical sciences. Many of the periodic motions we observe can be described using various systems of nonlinear differential equations. The aim of this talk is to highlight some of the techniques that are used to analyze such nonlinear oscillators as well as discuss some of the open questions on which we hope to shed some light in the future. (Flyer in PDF form)

Colloquium 4/4: Dr. Lesa Beverly on “The Best Kept Secret: SFA Professional Development of Mathematics Teachers”

Next Monday (April 4th) at 3:30 PM, Dr. Lesa Beverly will give a presentation titled “The Best Kept Secret: SFA Professional Development of Mathematics Teachers.”

Abstract: The Department of Mathematics and Statistics has a strong history of training mathematics teachers. In this presentation, we will explore the externally funded programs that have been a part of our departmental focus since 2000, including those that have been housed in the STEM Research and Learning Center. Successes and lessons learned from these experiences will be shared. Current projects, outreach efforts, and future opportunities will also be discussed. (flyer in PDF form)

Colloquium 2/15: Dr. Tracy Weyand on “The Spectra of the Magnetic Schrodinger Operator on Graphs”

On Monday at 3:30 PM in Math 357, Dr. Tracy Weyand of Baylor University will be talking about “The Spectra of the Magnetic Schrodinger Operator on Graphs.

Abstract: In the most general sense, a graph represents a relationship between a set of objects. Applications appear in chemistry, physics, engineering, computer science, and social science to name a few. In most applications, the relationship between objects (vertices) is represented by an operator that acts on functions whose domain is the graph. My research focuses on studying the spectra and corresponding eigenfunctions of such operators.

Throughout this talk, we will consider two types of graphs: discrete and metric. Eigenvalues of the magnetic Schrodinger operator on both types of graphs can be considered functions of the magnetic flux on the graph. Viewing the eigenvalues as functions, we have been able to determine their Morse index (a measure of stability). This result has led to progress on several other problems including the inverse problem (information the eigenvalues provide about the structure of a graph) and the location of Dirac cones (touching points) in the spectral bands (as well as properties of the corresponding eigenfunctions there).

(flyer in PDF form)

Colloquium 12/10: Dr. Seth Oppenheimer on “A Collection of Models and Applications”

On Thursday December 10th at 3:30 PM in Math 357, Dr. Seth Oppenheimer will be talking about “A Collection of Models and Applications.” This talk will be descriptive and nontechnical, accessible to undergraduates who understand a derivative as a rate of change. (Flyer in PDF form)

Abstract:Mathematics can be used to describe a wide variety of phenomena with great precision.  An applied mathematician, through discussion, careful listening, and a willingness to ask simple questions, can take the verbal description of what an investigator or experimentalist thinks is happening in his or her observations and build a clean mathematical model that is subject to analysis.  Such models sometimes lead to a quick rejection of the investigators theory.  Sometimes they lead to questions that require more experimental work and the model’s refining.  Often, interesting mathematical questions arise that require their own explorations.  Sometimes deep and difficult mathematics is needed and sometimes only a deep understanding of simple mathematics. The point is, mathematics can be a subtle probe in a variety of areas.  However, it is frequently the case that only someone coming out of deep engagement with mathematics can make full use of mathematics in a scientific setting.

In my career I have had the good fortune to work with excellent collaborators in both mathematics and in several areas of science and engineering.  This has allowed me to work on a variety of cool applications as well as giving me the tools to find some interesting problems independent of disciplinary investigators. Often this work has involved the creation of novel mathematical models and their analysis.  We will take a journey through nearly thirty years of fun applications that show the power of mathematics to illuminate problems in several areas and the realization via collaboration that the whole is often greater than the sum of the parts.

This talk will be descriptive and nontechnical, accessible to undergraduates who understand a derivative as a rate of change.

 

Colloquium 11/16: Dr. Robert Vallin on “Mathematics and Card Magic”

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.

Colloquium 11/9: Dr. Nick Long on “Easy Unsolved Algebra Problems”

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)