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Keynote Mathematics Colloquium on Friday, March 4th

On Friday, March 4th starting at 3:10pm in RSS 102, Keith Promislow of Michigan State University will give a fascinating talk about deep connections between mathematics and polymer physics in a talk about Amphiphilic Polymer Membranes.

Title: Network Formation in Amphiphilic Polymer Membranes

Abstract: Polymer chains are typically hydrophobic, the addition of functional groups to the backbone adds regions of hydrophilicity. The amphiphilic material (both hydrophobic and hydrophilic) has a strong affinity for solvent, imbibing it to self assemble charge-lined networks which serve as charge-selective ion conductors in a host of energy conversion applications. We present a continuum model for the free energy of an amphiphilic mixture. The associated gradient flows admit dynamic competition between network morphologies of distinct co-dimension.  We present the competitive geometric evolution for co-dimension 1 bilayers and co-dimension two pore morphologies, present an analysis of the associated spectral problems, and describe rigorous existence results.

The talk will be aimed at a general scientific audience and everyone is welcome to join Dr. Promislow and the faculty of the Department of Mathematics for tea prior to the talk at 2:45pm in RSS 346.

C of C Math Students Sweep Conference Paper Awards

Three students from the Department of Mathematics at the College of Charleston recently presented papers that won awards at the 2014 SEINFORMS Conference in Myrtle Beach, SC on October 14-15, 2014. SEINFORMS is the Southeastern Chapter of the international INFORMS (Institute for Operations Research and the Management Sciences) organization. SEINFORMS hosts a multi-disciplinary annual meeting every October where both academic and practitioner papers are peer-reviewed and presented in tracks representing business, economics, and the allied fields.

Graduate students Drew Passarello and Bryce Pruitt presented a paper entitled “Ranking Methods for Olympic Sports: A Case Study by the U.S Olympic Committee and the College of Charleston” which was co-authored with C of C Math undergraduate students Stephen Gorman and John Sussingham, former C of C Math graduate student Peter Greene, Professor Amy Langville, and Dr. Peter Vint of the U.S. Olympic Committee. Their paper develops a method to determine if the U.S. Olympic sports program is improving on a sport-by-sport basis. In the current work, the method was applied to the U.S. Men’s Ice Hockey and Women’s Alpine Skiing programs. The paper won the best Graduate Student Paper Award at the conference! Their paper will be published in the conference proceedings – a preprint of the paper is available here.

Undergraduate student Tyler Perini presented a paper entitled “The Humility Project: Text Analysis for Characteristic Linguistic Patterns” which was co-authored with Professor Amy Langville. The Humility Project is a study that blends Mathematics with Psychology and Philosophy in an effort to empirically quantify ‘humility.’ Their research focuses on analyzing the words people use when answering certain questions that target this elusive virtue. Using word counting tools, they represent a training set as a set of document vectors, which can be partitioned with matrix decompositions to find underlying similarities between kinds of answers. The ultimate goal is to use the training set to classify an incoming ‘query’ document as more-humble or more-not-humble in its word usage. Tyler’s presentation won the Undergraduate Student Paper competition!

Congratulations to all authors!

Math Students Discuss Modeling Contest Experience


Clay Gardner, Mike Lis, and Tyler Perini recently participated in the 2014 COMAP (the Consortium for Mathematics and Its Applications) Mathematical Contest in Modeling.  They formed one of several teams of students from the College of Charleston, and their solution of the contest problem earned them a “meritorius” rating reserved for the top 9% of contest entrants.

Clay, Mike, and Tyler were asked to share some thoughts on what it was like to work together and solve the problem.

Why did you participate in the COMAP MCM?

Mike had this to say:

I participated in COMAP because it sounded like the coolest math contest I have heard of. I think all three of us wanted to challenge ourselves to see what we were capable of producing in such a small time frame. I’ve always kind of glorified the archetype of the isolated mathematician and COMAP was a perfect opportunity to try it out.

Clay agreed that the experience sounded like fun:

I participated in COMAP mostly for fun, and because I was interested in working with Mike and Tyler. Also, I wanted to see how well we could preform when going against schools from around the world.

What was it like to work on this problem?

Clay responded with:

Working on a team made me realize how communication and getting along with each other is by far the most important aspect of creating good models and writing a paper. Having a breadth of skills is far much more important than a depth of skills, this goes for the individual as well as having three people with problem solving abilities that overlap as little as possible.

Mike added:

The time restriction definitely made the weekend interesting, I think we managed the clock very well. Working with Tyler and Clay was far and away the best part of the project. Bouncing ideas around was definitely fun, but it was also extremely insightful seeing how they approached the problem on their own.

Tyler, now a seasoned COMAP veteran, had this to add:

It’s always surprising how much fun COMAP is… I always go in nervous about the problem. After the first day, though, we got in the groove of working on the problem, and I loved hanging out with my team! There’s definitely some intense bonding over the weekend – hours of sweat, tears, frustration, and tons and tons of junk food will do that to you! You never get the true COMAP experience until you reach the stressful cramming of that last half hour before the paper is due, but we survived and learned a lot in the process!

On that note, the teammates were asked about what they learned throughout the process:

What did you learn (about math, modeling, new ideas and concepts, etc.) throughout the contest?


I learned a lot about how to communicate, since we had two completely different models doing the same thing we had to make sure that we could effectively communicate our models back and forth to make sure that we still were solving the same problem.

Mike indicated how important it is to collaborate with others when working on a complicated problem:

Clay and Tyler are two of the most diligent people I’ve met. I learned a lot by working alongside them, seeing how much thought they each put into their work. I also learned the importance of communicating ideas well. We really made sure to understand why we were approaching the problem a certain way, to ensure that our ideas were worth the time investment of following through. I think if I had worked alone I would have wasted far more time chasing unfruitful ideas.

Overall, it was a great experience and a chance for the team to apply some of the abstract concepts they learn in their coursework.  Next year’s teams will be challenged to do even better.

CofC Mathematics Major uses Math to Predict NCAA Tournament Winners

Stephen Gorman, a junior mathematics major at the College of Charleston, spent last summer in a Research Experience for Undergraduates at Davidson College researching the mathematics of ranking methods.  Recently he spoke with the College on How to Become a Billionaire in 5 Easy Steps by employing mathematical strategies to pick a winning NCAA Tournament bracket.  You can learn more about Stephen’s approach here and even see how his bracket is fairing here.

Want to find out how math is used to predict winners?  Check out Professor Amy Langville’s book “Who’s #1?  The Science of Rating and Ranking” for more information!  Professor Langville’s work on ranking  and rating methods is just one example of how mathematics can be applied to solve interesting real-world problems.

CofC Math Student Solves Math Horizons Problem

Lauren Tubbs, a junior Mathematics Major at the College of Charleston, recently worked on solving a multi-part problem that was posed in the Playground section of the September 2013 issue of Math Horizons, a journal published by the Mathematical Association of America.  Lauren successfully solved Problem 295 on “Counting Divisors” and submitted her solution to the journal.  The problem statement is:

(a) Show that, if n is an odd number, then n^2+19 has at least six divisors, and that n^2+119 has at least eight divisors.
(b) Are 19 and 119 the best possible numbers we could have chosen for part a?  For this part, (still assuming n is an odd number), find the smallest positive integers a and b such that n^2+a has at least six divisors, and n^2+b has at least eight divisors.

Lauren’s solution is here for anyone who would like to read it.  A common challenge for undergraduate math students is simply: How do I get started on mathematical research?  Professor Dinesh Sarvate, who has directed many undergraduate research projects here at CofC, describes one way to get students started:

In general,  when a student approaches me for research or when I see that a student is  capable of some research,  I ask them to do such problems from Math Horizons, the American Mathematical Monthly, or the College Mathematics Journal before giving a more time consuming research problem. So I hope to get students involved for years to come.

Lauren describes her experience in getting started below:

Prof. Sarvate is my advisor and at my advising appointment he gave me some very good advice about which classes to take and about math in general. He also said that once I’d had discrete structures or abstract algebra, we could do a research project together. I was happy to take discrete structures I from him that summer, which I really liked, and in the fall as I was taking discrete structures II, I asked him if we could do a project. He gave me the Math Horizons problem to start with, making sure I understood exactly what the problem was asking. I was rather nervous at first and thought I wouldn’t be able to solve it as I’d never seen a similar problem before and had no idea how to tackle it. But it was an excellently chosen first problem because within an hour I had gotten the first two parts of the question and by that evening I had roughly figured out why the last two parts were true, though it took me a week to get a good proof and two weeks to write it up properly. The problem was also a great choice because it required almost no background: if it had been a geometry or calculus problem I would have first had to learn or relearn a lot of material, whereas with this number theory problem I was able to concentrate on the fairly new processes of problem-solving and proof-writing.

Lauren also describes how Professor Sarvate helped her in refining her solution to a manuscript she could submit to the journal:

I sent Prof. Sarvate my handwritten solution and he asked me to type it up formally in LaTeX. The first draft was something like four pages long. Prof. Sarvate went through the draft with a red pen and marked it up very carefully, crossing out whole paragraphs of unnecessary explanation and replacing clumsy phrases with more professional ones. This was extremely valuable since I had only ever written proofs for class before, and I was unsure what to include and how to phrase a solution for a journal. I really like this mathematics editing, trying to make things as elegant and concise as possible while remaining clear. With Prof. Sarvate’s help I eventually got the solution down to a single page. He also showed me how to format my solution and cover letter. It was submitted in October.

Overall, it was a great way to get introduced to problem solving and the research process, and Lauren also says that she hopes to work on a “real” research project in discrete mathematics when her course schedule allows for it.