Department of Mathematics

University of Mississippi


      Pi Mu Epsilon Meetings

Thursday, May 4, 2017, 12:15-12:50 PM in Hume 101

Micah Milinovich
University of Mississippi

Solved and unsolved problems concerning prime numbers (pdf)
An integer greater than one is said to be prime if its only positive divisors are one and itself. The distribution of the primes has fascinated mathematicians since antiquity. In this talk, I will outline some well known solved and unsolved problems concerning the prime numbers, trying to illustrate how modern number theorists think about them.

Thursday, March 30, 2017, 12:15-12:50 PM in Hume 101

Thái Hoàng Lê
University of Mississippi

Complete Order is Impossible (pdf)
Any large enough system must contain a structured subsystem. This is the idea of Ramsey theory, a branch of combinatorics. For example, among any six people, we can find either three people who mutually know each other or three people who mutually do not know each other. In this talk, I will give a brief introduction to Ramsey theory, as well as its manifestations in other branches of mathematics such as number theory, analysis and logic.

Thursday, March 2, 2017, 12:15-12:50 PM in Hume 101

Rachna Prakash
School of Accountancy, University of Mississippi

Where Business Meets Mathematics (pdf)
In this talk I will discuss various applications of math in business with a focus on how math is applied in the discipline of accountancy. Starting with a brief introduction on the historic links between accountancy and math, I will discuss how ubiquitous math is in different fields of business. I will end with an example of how math is used in accounting research with a brief discussion of my research on climate change.

Thursday, October 27, 2016, 12:15-12:50 PM in Hume 101

Xiaotu Ma
St. Judes’ Hospital

Genomics study of relapsed pediatric B-acute lymphoblastic leukemia (pdf)
Genomics-based analysis is revolutionizing our understanding of cancers and holds the promise for understanding all diseases with a genetic-basis. In this talk, I will give a brief introduction on what we are looking for in a genomic study, from a perspective of variant detection and interpretation. I will then describe how we apply our techniques in a study of relapse ALL samples and stress the importance of detection of subtle signals from statistical perspectives.

Thursday, September 22, 2016, 12:15-12:50 PM in Hume 101

Welcoming meeting (pdf)
We welcome you to the first Pi Mu Epsilon meeting of the 2016-17 school year! At this meeting, we will discuss the goals of Pi Mu Epsilon, future events, and how to join. To finish up, we will have graduate students from the math department answer questions about graduate school and how to apply to graduate programs.

Thursday, April 21, 2016, 12:15-12:50 PM in Hume 201

Maksym Derevyagin
University of Mississippi

Let’s Get Rational! (pdf)
I am going to discuss continued fractions, which are expressions used to represent real numbers, and Diophantine approximations. The latter deals with problems such as whether a given real number is rational or irrational; if the number is irrational then the problem is to determine how well it can be approached by rational numbers.

Thursday, March 24, 2016, 12:15-12:50 PM in Hume 201

Gerard Buskes
University of Mississippi

From A (luminum Carbonate via kitchen cloth) to Z (ebra) (pdf)
We will discuss 1) a mathematical object that connects the Musee du Conservatoire des Arts et Metiers in Paris with Oxford, Mississippi, 2) a mathematical object found in Dutch kitchens, and 3) an animal from Africa.

Thursday, February 18, 2016, 12:15-12:50 PM in Hume 201

Samuel Lisi
University of Mississippi

The Hairy Ball Theorem (pdf)
Imagine a soccer ball entirely covered in hair. The Hairy Ball Theorem says that you can’t comb the hair flat everywhere — there will always have to be a tuft of hair sticking up somewhere. This famous theorem of topology was first stated by Poincaré (late 1800s) and proved by Brouwer in 1912. A different way of saying this is that if you consider the Earth and look at the windspeed at each point, there is at least one place where the wind is not blowing. This will lead us into an exploration of some basic topological properties of surfaces and their relationship to dynamical systems.

Thursday, December 3, 2015, 12:15-12:50 PM in Hume 101

James Reid
University of Mississippi

Mathematics and the Movies (pdf)
We will view and discuss several short clips from movies that present mathematics in a correct, incorrect, and in a humorous fashion.

Thursday, November 12, 2015, 12:15-12:50 PM in Hume 101

NOVA documentary “The Proof” (pdf)

Tuesday, October 27, 2015, 12:20-12:50 PM in Hume 101

Jo Howard
Special Guest (pdf)

Tuesday, April 21, 2015, 12:15-12:55 PM in Hume 101

Jo Howard

Relating Mathematical Studies to Life Applications (pdf)
Jo Howard graduated from the University of Mississippi with degrees in mathematics in 1967. She has since worked on applying mathematics to a number of fields including: designing trajectories for Boeing that put a man on the moon in 1969, programming the space simulator in Houston, Texas, and data management systems in the oil and gas industries.

Friday, April 10, 2015, 12:00-12:50 PM in Hume 101

William Staton
University of Mississippi

Powerful Numbers (pdf)
We will call a positive integer “powerful” if for every prime p, if p divides n, then p^2 divides n. That is, every prime in the factorization of n appears to at least the second power. We will discuss some algebraic properties of the set of powerful numbers to emphasize an important property of primes. Then we will show that there are infinitely many pairs of consecutive powerful numbers, such as 8 and 9.

Thursday, March 26, 2015, 12:15-12:50 PM in Hume 101

Eleanor Anthony
University of Mississippi

PME Induction and Student Talk (pdf)
Come and join us as we welcome new members to the Pi Mu Epsilon Honor Society and elect officers for 2015. Eleanor Anthony will give a short talk on her undergraduate mathematics research.

Thursday, February 19, 2015, 12:15-12:50 PM in Hume 101

Samuel Lisi
University of Mississippi

Morse Theory on Surfaces (pdf)
Have you ever wondered how many holes your doughnut has? We will see how calculus can tell us something about the topology of a surface.

Thursday, November 13, 2014, 12:15-12:50 PM in Hume 201

Joshua Adam Gray
University of Mississippi

Metadata, Social Networks, and Paul Revere (pdf)
Dr. Kieran Healy, a sociologist at Duke University, wrote an article last summer discussing how “metadata” from colonial America could have been used to identify Paul Revere as a key figure of the American Revolution before it began. Dr. Gray will discuss the graph theory underlying some of these ideas and how it pertains to modern social networks.

Thursday, October 16, 2014, 12:15-12:50 PM in Hume 201

Sam Watson
Massachusetts Institute of Technology

Schramm-Loewner Evolutions (pdf)
Dr. Watson will explain in non-technical terms why the study of “conformally invariant two-dimensional statistical physics models” is compelling and beautiful.

Thursday, May 1, 2014, 12:15-12:50 PM in Hume 201

Amanda Hall
University of Mississippi

The Tutte Polynomial Formula for the Class of Twisted Wheel Graphs (pdf)
Amanda will talk about her SMBHC Senior Thesis this Thursday. Come to here about her research and the research process.

Thursday, April 3, 2014, 12:15-12:50 PM in Hume 201

James Reid
University of Mississippi

A Beautiful Mind, Equilibria, and Traffic (pdf)
We will explore the life and works of John Nash, the subject of the popular movie A Beautiful Mind. In particular, we will discuss the concept of Nash-Equilibria and its implications to the flow of vehicular traffic.

Thursday, February 27, 2014, 12:15-12:50 PM in Hume 201

Organizational Meeting: Induction of New Members and Officer Elections (pdf)

Thursday, December 5, 2013, 12:15-12:50 PM in Hume 101

Caroline Turnage-Butterbaugh
University of Mississippi

Gaps Between Primes (pdf)
Caroline will talk about some recent exciting results in number theory, starting with Yitang Zhang’s theorem on prime gaps, the Polymath project that grew from it, and the Maynard-Tao result that improved upon this work. She will also talk about a conjecture of Erdös and Turán that she proved recently as joint work with William Banks and Tristan Freiberg from the University of Missouri.

Thursday, October 31, 2013, at 12:15 PM in Hume 101

Sooyeon Lee, Catherine Putnam, Stephan Roberts, Christopher Schwanke, Caroline Turnage-Butterbaugh
University of Mississippi

Graduate Studies in Mathematics (pdf)
Are you considering going to graduate school in mathematics? Do you wonder what graduate school in mathematics is like? Do you have questions about applying to graduate schools? If you’ve answered yes to any of these questions, come ask a panel of five of the math department’s graduate students anything you’d like to ask about graduate school!

Thursday, September 12, 2013, at 12:15 PM in Hume 101

Sandra Spiroff, Jonathan Broom, Travis Dirle, Adam Flaherty, and Thomas Naugle
University of Mississippi

“There’s ca$h in math”-an overview of the SMILE program at LSU (pdf)
Come hear about the summer SMILE program at Louisiana State University and how you can earn a stipend while learning mathematics, for example, Jordan decomposition and the Z-transform, or associating graphs to commutative rings. An overview of the program will be given by Dr. Spiroff, followed by the students briefly describing their summer projects.

Thursday, April 25, 2013, at 12:15 PM in Hume 101

Sam Cole
University of Mississippi

“The Hardest Logic Puzzle Ever” and Logical Connectives (pdf)
In 1986 logician George Boolos published “The Hardest Logic Puzzle Ever”, a variation on the classic “Knights and Knaves” puzzle. Boolos’ puzzle is as follows: “Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.” In order solve this puzzle the logical connectives encountered in mathematics are needed to construct questions. The properties of these connectives and the solution to many variants of this problem will be presented.

Thursday, February 21, 2013, at 12:15 PM in Hume 101

Przemo Kranz
University of Mississippi

Octonions-or how many square roots of -1 are there? (pdf)
As complex numbers are constructed out of real numbers, so quaternions are constructed out of complex numbers. Quaternions, in turn, are the building blocks of a still more “complex” set of objectsoctonions. Octonions form an eight dimensional normed division algebra, a basis of which contains seven elements whose squares are all -1.

Thursday, November 15, 2012 at 12:15 pm in Hume 101

Erwin Miña-Diaz
University of Mississippi

Inversion in Planar Geometry (pdf)
Inversion, or reflection about circles, is a transformation that generalizes the idea of reflection (mirror image) about a line. Inversion has several beautiful properties. For instance, lines and circles are transformed into lines and circles as well, and angles between curves are preserved under inversion. In this talk, we shall introduce this concept, discuss some of its most basic properties, and apply it to solve some problems in planar geometry.

Thursday, October 18, 2012 at 12:15 pm in Hume 101

Brad Cole
University of Mississippi

Drunk Cops and Robbers: How To Catch A Thief… Slowly (pdf)
The game of Cops and Robbers can be played out, in a mathematical sense, on a graph—i.e., on a set of vertices and edges, like a square, star, hexagon, or other figure. In the game, the players designated as “cop” and “robber” take turns, respectively, moving from vertex to vertex along graph edges. Should the players ever occupy the same vertex at the same time, the robber is captured and the cop wins. The theory behind these graph pursuit-evasion games has been well studied. In 2011, a version of this game was investigated where the robber is moving randomly; a “drunk” robber. This talk will explore the reversed role: the cop is now “drunk” while the robber moves perfectly. The expected capture time will be demonstrated for the simplest 1-cop win graphs (paths), 2-cop win graphs (cycles) and, time permitting the k-d-regular tree.

If this talk were a movie, then the plot would be: How would the movie Taken (or Taken 2, the sequel) work out if Liam Neeson’s character had been drinking constantly?

Thursday, September 20, 2012 at 12:15 pm in Hume 101

Christopher Schwanke, Daniel Chausse, Stephan Roberts, Michael Azlin, Caroline Turnage-Butterbaugh, Lisa Ewell, and Lynsey Cargile
University of Mississippi

Hilbert’s Hotel: A Play (pdf)
Hilbert’s Hotel is very different than other hotels, for it has infinitely many rooms! Come see the very strange things that can occur when dealing with an infinite number of objects. Things like the sign in front of the hotel, which reads: “No Vacancy – Rooms Available!”

Thursday, August 30, 2012 at 12:15 pm in Hume 101

Sandra Spiroff, Jonathan Broom, Ben Moore, and Lindsay Pittman
University of Mississippi

“I Know What You Did Last Summer” – an overview of the SMILE (Summer Math Integrated Learning Environment) program at LSU (pdf)
Are you interested in earning a summer stipend while learning some new and interesting mathematics? Then this meeting is for YOU. We will be highlighting the SMILE program at Louisiana State University and how you can apply for summer 2013. In particular, three Ole Miss students will give a brief discussion of their projects and experiences in Baton Rouge.

Thursday, April 19, 2012 at 12:15 pm in Hume 101

William Staton
University of Mississippi

Gaussian Integers and Rational Tangents of Rational Angles (pdf)

Thursday, March 8, 2012 at 12:15 pm in Hume 101

Caroline Turnage-Butterbaugh, Chris Schwanke, Kai Yu
University of Mississippi

Panel of Graduate Students to Answer Questions about Graduate School in Mathematics

Monday, November 7, 2011 at 12:15 pm in Hume 203

John Dever
University of Mississippi

Infinitesimals, Differentials, and Derivatives in Normed Vector Spaces (pdf)
By establishing properties of a certain class of functions, the infinitesimals, between normed vector spaces, the concepts of the differential and derivative are easily generalized to normed vector spaces. The relationship between differentials and directional derivatives will be discussed and properties such as the chain rule will be established.

Thursday, October 27, 2011 at 12:15 pm in Hume 203

John Estes
University of Mississippi

Paths, Independence, and Fibonacci

Thursday, September 8, 2011 at 12:15 pm in Hume 201

Sandra Spiroff, Daniel Chausse, Tanya Dewland, W. Chapman Smith
University of Mississippi

I Know What You Did Last Summer (pdf)
Come hear about the summer SMILE program at Louisiana State University and how you can earn a stipend while learning mathematics, for example, geometric constructions or the spread of HIV. An overview of the program will be given by Dr. Spiroff, followed by the students briefly describing their projects.

Thursday, April 7, 2011, at 12:15 PM in Hume 109

David Benko
University of South Alabama

eBay and the art of bidding
Bidding on eBay is easy – no math is involved, right? We will disprove the claim by demonstrating a scientific way of bidding. We will also offer some ideas that should be implemented at eBay to make it a better auction marketplace. Finally, we propose a fair system which is somewhere between socialism and capitalism. Whether you’re a buyer or seller or president of eBay, you must see this talk!

Thursday, November 11, 2010 at 12:15 in Hume 111

Zhu Cao
University of Mississippi

Elementary Theory of Partitions

Thursday, September 16, 2010 at 12:15 in Hume 111

William Staton
University of Mississippi

A 15-minute Introduction to Extremal Graph Theory

Thursday, April 8, 2010 at 12:15 pm in Hume 109

Vlad Timofte
University of Mississippi

Repeating Atomic Configurations You May Not Be Unique!

Thursday, March 4, 2010 at 12:00 pm in Hume 321

Xin Dang
University of Mississippi

PageRank — secret of Google’ success

Thursday, February 4, 2010 at 12:00 pm in Hume 321

Erwin Mina-Diaz
University of Mississippi

Kinematics Method in Planar Geometry (pdf)
From the study of Physics and Calculus, undergraduate students are quite familiar with Kinematics,”the theory of vectors and velocities”. In this talk we shall discuss how the concept of velocity and its properties can be used to solve some purely mathematical problems in planar geometry.

Tuesday, October 20, 2009 at 12:15 pm in Hume 101

Ryan Daileda
Trinity University

Factorization Beyond the Integers (pdf)
We all know that any integer can be factored uniquely into primes. What if we look at other sets which have the same axiomatic properties as the integers? Does an analogous property hold? It turns out that the answer is ‘no,’ and we will explore how badly this can fail.

Thursday, October 1, 2009 at 12:15 pm in Hume 101

James Reid
University of Mississippi

Durer’s Melencolia and Spherical Polyhedra (pdf)
Albrecht Durer (1471-1528) is regarded by some as the preeminent artist of the Renaissance in Northern Europe. Many different interpretations of the symbols included in his engraving the “Melencolia” have been given. There have been numerous interpretations of the shape of the stone block given on the left side of the figure. We investigate whether this block can be the model of a spherical polyhedron.

Thursday, September 3, 2009 at 12:15 pm in Hume 101

William Staton
University of Mississippi

Generating Functions and Integer Partitions

Thursday, April 30, 2009 at 12:15 pm in Hume 101

Sandra Spiroff
University of Mississippi

Unique Factorization and a Connection to Gambling

Thursday, April 2, 2009 at 12:15 pm in Hume 101

John Conlon
Department of Economics, University of Mississippi

Fool Asset Price Bubbles with Rational Economic Agents