Department of Mathematics and Computer Science
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Tue, September 29, 2015: The Mathematics of Voting

Speaker: Dr. Adam Graham-Squire
From: 5:30PM-6:30PM
Room: Congdon 138

Unfortunately, all of your civics classes have been lies - it turns out that democracy is a sham. In this talk, we will look at the difficulty in creating fair voting systems and numerous voting methods that could improve those difficulties. In particular, we will look at the Instant Runoff Voting (IRV) system and look at how it has been applied in municipal voting in the U.S. From a mathematical perspective, we will analyze the theoretical drawbacks to IRV, and discuss what research students and faculty here at HPU have done to investigate how prevalent those drawbacks are in real-world election data. The research that we have conducted touches on both mathematical voting theory as well as Computer Science.

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Tue, October 28, 2014: Right triangles and a million dollars

Speaker: Jim Brown, Clemson University
From: 3:30PM-4:30PM
Room: Phillips 218

One of the wonderful things about number theory is there are many problems that are easy to state, but extremely difficult to make any significant progress on. One such problem is the congruent number problem. We say a positive integer N is a congruent number if there is a right triangle with rational side lengths that has area N. For example, 6 is a congruent number via the 3-4-5 triangle. Can you find another right triangle with rational side lengths and area 6? How about one with area 5? In this talk we will explore the problem of finding a simple method for determining if a given integer N is a congruent number. Surprisingly this is related to an open problem whose resolution carries a reward of one million dollars! Clemson Graduate school information discussion will follow the talk.

Fri, November 02, 2012: Sine-like functions and their applications to geometry, algebra, and algebraic number theory

Speaker: Brett Tangedal (UNCG)
From: 12:00PM-1:00PM
Room: Congdon Hall 127

The lemniscatic sine function is related to the unit lemniscate in the same way that the usual sine function is associated to the unit circle. The sine function dates back to antiquity whereas the lemniscatic sine function was first defined by Gauss in the late 1790's and it became the first elliptic function to ever be studied. We will consider these sine-like functions side by side and study their parallel applications to certain problems in geometry, algebra, and algebraic number theory.

Tue, October 02, 2012: Helping with the math on "A Beautiful Mind"

Speaker: Dr. Dave Bayer
From: 6:30PM-7:30PM
Room: Philips 120

This talk will relate anecdotes from the speaker's experiences as math consultant, hand double, and one-line actor in the 2001 film "A Beautiful Mind."

Tue, October 02, 2012: Trailing the Dovetail Shuffle to its Lair

Speaker: Dr. Dave Bayer
From: 11:30AM-12:30PM
Room: Philips 120

This talk will describe the mathematical analysis of riffle shuffling a deck of cards, joint work with Persi Diaconis. The conclusion of this work, widely circulated, is that "Seven shuffles suffice". We will consider various models and analogies to shuffling (e.g. running a several lap race, kneading bread dough), and explore a classic card trick, in order to understand how shuffling actually works.

Fri, September 28, 2012: Undergraduate Research Experiences

From: 12:00PM-1:00PM
Room: Norton 101

Three of our majors will speak about their summer research experiences. Mr. Thomas Langford will speak on the REU he attended at Texas State University, where he studied mobile cyber-physical systems. Mr. Kevin Sanders will speak on the REU he attended at the Colorado School of Mines, where he studied at the Renewable Energy Materials Research Science and Engineering Center. Mr. Christian Weigandt will speak on the REU he attended at University of Maryland - Baltimore County, where he worked with the Interdisciplinary Program on High Performance Computing. This is a great opportunity to learn more about summer research opportunities!

Fri, September 14, 2012: Patterns and Integer Valued Polynomials

Speaker: Dr. Jenny Fuselier
From: 12:00PM-1:00PM
Room: Norton 101

In second semester calculus, students learn how to find Taylor series expansions for basic functions. They look for patterns in successive derivatives and use these patterns to generate coefficients. For example, when considering f(x)=sin(x) about x=π/4, a pattern of signs + + - - + + - - ... arises, and (-1)^(n(n-1)/2) is included in the expansion to achieve these signs. Students (and teachers!) may wonder how one determines the polynomial n(n-1)/2 as the right choice. Is there a way other than trial and error? In this talk, we explore what patterns of +’s and −’s are generated by integer valued polynomials and see how to build the “right” polynomial for a predetermined pattern.

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Wed, September 05, 2012: Stories from the Real World. How Python Made My Life Easier (and Maybe Yours Too!)

Speaker: Dr. Zach Jones
From: 3:45PM-5:00PM
Room: Congdon Hall - 127

Abstract: The day-to-day work of a performance analyst can be simplified into two categories: analyzing data and producing data from various testing. At first glance, these two tasks seem orthogonal to one another. To my surprise, I found a common building block which has transformed the way I do my work, using the Python programming language. First, I will introduce IPython, which I recently discovered and forced me to take a second look at Python for day-to-day data analysis. IPython is an interactive interface to Python, which when combined with several Python libraries creates a powerful interactive graphical environment with capabilities comparable to the "3 Ms" Maple, MATLAB and Mathematica. Afterwards, l will talk about how I created a new workload generator with my new found interest in Python. Using mostly Python, I was able to rapidly build the generator from scratch. While the generator is in Python, before I wrote a single line of Python code, I utilized knowledge gained from probability and abstract algebra to model the behavior of the generator to match the desired workload.

Bio: Dr. Zachary H. Jones is a Member of Technical Staff at NetApp where he works as a Performance Analyst. He received his B.S. In Computer Science and Mathematics from High Point University in 2006. He received his Ph.D. in Computer Science from Clemson University in 2010. His research interests are quite broad and include operating systems, HPC, computer architectures, virtualization, graphics, and appreciation of algorithms.

Thu, February 23, 2012: An introduction to mathematical modeling of chemotaxis

Speaker: Ms. Erica Zuhr
From: 3:15PM-4:15PM
Room: Congdon 128

Chemotaxis is a common biological phenomenon which occurs when the movement of an organism or cell is influence by a chemical in the environment. Chemotaxis arises naturally in a wide range of biological processes including immune system function, egg fertilization, and tumor growth and metastasis. The most well-known and commonly studied model for chemotaxis is the Keller-Segel model. In this talk I will derive the system of equations known as the Keller-Segel model for chemotaxis from basic principles and go over some results on solutions of the system.

Thu, February 16, 2012: Practical Posets

Speaker: Ms. Katie Johnson
From: 3:15PM-4:15PM
Room: Congdon 128

A partially ordered set, or poset, is simply a collection of objects where some of the objects are comparable and some are not. Naturally, we want this relation, <, to have some nice properties such as A less than B means B should not be less than A, or A<B and B<C should mean that A<C. Posets model many real-life situations, such as little league rankings, employees in a company, and patients in an ER waiting room, all of which we will discuss. Because we all have some experience working with real world posets like these, we possess a good intuition for how things should work. Sometimes our intuition helps us develop conjectures and prove theorems. Occasionally our intuition may mislead us and we must rely on the mathematics to tell us what is really going on. We will see examples of each of these while we try to answer practical questions such as: what is the most fair way to assign salaries to employees? How does ER triage scheduling change when we have multiple doctors?

Thu, January 19, 2012: The mathematics of the impossible

Speaker: Dr. Andrew Schultz
From: 3:30PM-4:30PM
Room: Qubein 206

Some mathematical problems have existed for thousands of years without known solutions. While occasionally a brilliant new perspective will answer one of these outstanding questions, in the modern era mathematicians have also discovered that some of these problems simply cannot be solved. In this talk we will discuss some of these unknowable problems as well as the mathematical revolutions that proved their impossibility.

Tue, January 17, 2012: The Euler Characteristic

Speaker: Dr. Keir Lockridge
From: 4:00PM-5:00PM
Room: Phillips 120

In the mid-18th century, Euler noticed an amazing fact concerning the number of vertices v, edges e, and faces f of any convex polyhedron: v - e + f = 2. (If you have a soccer ball, you can verify this identity!) This observation was foundational for the discipline of topology, and it underlies a topological proof of the classification of Platonic solids. In this talk, I will introduce a few simple surfaces (e.g., the sphere, torus, and Möbius strip) and discuss the role played by the Euler characteristic in their classification.

Fri, November 18, 2011: Applications of Young Diagrams and Young Tableaux

Speaker: Dr. Laurie Zack
From: 12:00PM-1:00PM
Room: Norton 101

Young diagrams and Young tableaux have been studied over the past 100 years when they were first applied to the study of representations of the symmetric group. They have since been used to study different classical groups as well as the areas of graph theory, combinatorics, and even physics. Typically they are introduced in a representation theory class, however, with some minimal definitions this talk will present a few elementary applications suitable for early introduction.

Fri, November 04, 2011: Actuarial Science Internships

Speaker: Lincoln Financial Group
From: 12:00PM-1:00PM
Room: Congdon hall 138

Actuaries from Lincoln Financial Group will be visiting the department discussing the internship program at LFG. If you are interested (or curious) about a career in actuarial science, please plan to attend.

Fri, October 28, 2011: Combinatorial and topological methods in studying free resolutions of monomial ideals

Speaker: Dr. Sonja Mapes
From: 12:00PM-1:00PM
Room: Norton 101

The goal of this talk is to give a description of minimal free resolutions of "rigid" monomial ideals. The talk will begin by defining what a minimal free resolution of an ideal is and will quickly focus on the special case of monomial ideals. Along the way I will give descriptions of various combinatorial and topological tools that one can use to find free resolutions of monomial ideals. In particular for rigid monomial ideals we will heavily use the structure of the lattice of least common multiples of the generators of the monomial ideal to describe the minimal resolutions. The new results in this talk are joint work with Tim Clark.

Fri, October 07, 2011: Summer Experiences

Speaker: Ms. Samantha Allen and Ms. Lisa DeVince
From: 12:00PM-1:00PM
Room: Norton 101

Samantha and Lisa are two of our department's graduating seniors. They will be speaking to us on their summer experiences. Samantha participated in an REU on high performance computing, and Lisa did an internship with Lincoln Financial.

Fri, September 16, 2011: Fractals and Their Dimensions

Speaker: Ms. Melissa Glass
From: 12:00PM-1:00PM
Room: Norton 101

Abstract: Fractals are well known for their interesting and beautiful pictures. But mathematically, fractals are known for their strange dimensions. Usually we think of an object being one-dimensional or two-dimensional and so on. Roughly speaking, fractals are objects that have fractional dimension. Besides producing some really awesome images, fractals have many applications in our world. Just look around. Things in nature are not perfect squares or circles. We can actually represent many things in our environment with fractals instead of using classical geometry. In this presentation, we will define some well known examples of fractals. Next, we will discuss different notions of dimension and compute some dimensions for the examples introduced in the beginning. We will end with some surprising applications of fractals.