The Rose Mathematics Seminar

Overview

The Rose-Hulman Mathematics Seminar meets on a regular basis throughout the year per the schedule below. The seminar is quite informal and so the topics are likely to vary from week to week .  Anyone --- student, faculty, or visitor --- is encouraged to give a talk or series of talks on any topic of interest.  We're especially happy to have students attend or better yet, give talks! Students can get credit for attending and giving talks, by signing up for MA450. For seminars in past years go to the seminar history page. Here is a printable campus map if needed by our off-campus visitors.

Also of interest: Here is the seminar page for our sister institution Indiana State University.

• Regular Day and Time (Winter 2009-10): Wednesday, period 7 - 1:35
• Place: G221
• Organizer: Kurt Bryan bryan@rose-hulman.edu   (812) 877-8485

Current and Upcoming Schedule (latest first)

• Topic:  Modeling Complex Fluids - A Primer on Continuum Mechanics
• Speaker:  David Finn
• Date:  10 Feb 2010
• Abstract:  To mathematically describe a complex fluid, a fluid that exhibits properties of both a solid and a liquid, we need mathematics capable of modeling deformation, continuous changes of the shape of an object, and the interaction of the fluid with its boundary. We also need to be able to model the forces acting on the material through the surface of the material, and how the material's deformation influences the forces and possibly exert forces on the material, and even how material properties can be incorporated into the description of the forces. This is done through the subject of continuum mechanics, which is part mathematics and part physics, and heavily used in certain areas of engineering. This talk will be an introduction to continuum mechanics and its application in describing complex fluids. Only knowledge of vectors and partial derivatives are required to understand the mathematical methods of continuum mechanics in this talk, plus enough physics to understand F=ma.

• Topic:  Oobleck, Silly Putty, Shampoo, Syrups and Other Complex Fluids
• Speaker:  David Finn
• Date:  03 Feb 2010
• Abstract:  In this first of a series of two talks on complex fluids from my sabbatical at the Institute of Mathematics and its Application, I will give examples and motivation of complex fluids or non-Newtonian fluids, and how they differ from usual fluids or Newtonian fluids. This talk will be more demonstrations and experiments to give some of the phenomenological differences between non-Newtonian fluids and Newtonian fluids. The mathematical descriptions of the phenomenon given in this talk will be given in the next talk.

• Topic:  THE WORLD’S HARDEST EASY GEOMETRY PROBLEM
• Speaker:  Herb Bailey
• Date:  18 Jan 2010
• Abstract:  If you Google the title you will find the problem and many solutions -‘some short, some long, some right, some wrong’. It is easy to solve with trig, but hard if you use only high school geometry. There is also a second hardest problem of the same type that has been published. The common theme is that all angles must be an integer multiple of 10 degrees. Using trig, I have shown that there are only four more problems of this type. I can solve three of them using geometry and have tried for many hours, without success, to find a geometric solution of the fourth. As a prize, if you can help me solve the fourth, we can coauthor a paper describing our results and propose a problem that is harder than 'The World’s Hardest'.

• Topic:  Deciding Complex Feasibility by Reducing to Finite Fields
• Speaker:  Arnold Yim, Rose Student
• Date:  17 Dec 2009
• Abstract:  Last summer, I participated in an REU program at Texas A&M University where I worked with Dr. Rojas and a couple of other students on deciding complex feasibility. This problem was to determine whether a system of polynomials has a complex root or not. Our approach was to reduce the polynomial to different finite fields and determine whether the system had roots in those finite fields. If enough of those fields had a root, then we can conclude with some certainty that the system had complex roots. We coded up an algorithm outlined by Koiran, then looked at how different families of polynomials behaved in different finite fields in attempt to improve the algorithm. In particular, we looked at polynomials whose Galois groups are dihedral groups and symmetric groups. After running some tests, we were able to find certain patterns in the density of prime numbers for which the polynomials had a solution, which we later used to generalize specific formulas for the prime density based on the Galois group of the polynomial. Although a little background would be in algebra would be helpful, this talk should be accessible to all audiences.

• Topic:  Deciding Complex Feasibility by Reducing to Finite Fields
• Speaker:  Arnold Yim, Rose Student
• Date:  16 Dec 2009
• Abstract:  Last summer, I participated in an REU program at Texas A&M University where I worked with Dr. Rojas and a couple of other students on deciding complex feasibility. This problem was to determine whether a system of polynomials has a complex root or not. Our approach was to reduce the polynomial to different finite fields and determine whether the system had roots in those finite fields. If enough of those fields had a root, then we can conclude with some certainty that the system had complex roots. We coded up an algorithm outlined by Koiran, then looked at how different families of polynomials behaved in different finite fields in attempt to improve the algorithm. In particular, we looked at polynomials whose Galois groups are dihedral groups and symmetric groups. After running some tests, we were able to find certain patterns in the density of prime numbers for which the polynomials had a solution, which we later used to generalize specific formulas for the prime density based on the Galois group of the polynomial. Although a little background would be in algebra would be helpful, this talk should be accessible to all audiences.

• Topic:  Using Mathematical Models and Operations Research to Tackle the Risky Business of Aviation Security
• Speaker:  Sheldon H. Jacobson, Professor and Director, Simulation and Optimization Laboratory, Department of Computer Science University of Illinois
• Date:  09 Dec 2009
• Abstract:  Aviation security has become a topic of intense national interest, as the risk of terrorism and of other hazardous threats to the nation's air system increase. Recent events have hastened changes to improve the security of the air traffic industry. This includes multi-million dollar investments in new security technologies and equipment. Passenger screening is a critical component of such aviation security systems. This paper introduces the sequential stochastic security design problem (SSSDP), which models passenger and carry-on baggage-screening operations in an aviation security system. SSSDP is formulated as a two-stage model, where in the first stage security devices are purchased subject to budget and space constraints, and in the second stage a policy determines how passengers that arrive at a security station are screened. Passengers are assumed to check in sequentially, with passenger risk levels determined by a prescreening system. The objective of SSSDP is to maximize the total security of all passenger-screening decisions over a fixed time period, given passenger risk levels and security device parameters. SSSDP is transformed into a deterministic integer program, and an optimal policy for screening passengers is obtained. Examples are provided to illustrate these results, using data extracted from the Official Airline Guide.

• Topic:  Actuary: The Best Job in the World
• Speaker:  Phil Banet, Allstate - Rose math alumnus
• Date:  04 Nov 2009
• Abstract:  Ever wanted to know more about being an actuary? Not sure what it is? It’s only one of the highest rated jobs in the country. Please join us Wednesday, November 4, at the Mathematics Colloquium to hear more from a practicing actuary with Allstate Insurance Company who just happens to also be a graduate of Rose-Hulman. Phil Banet has been an actuary since he graduated from Rose in 1991. He’ll be discussing his experiences as well as how Rose helped prepare him for this fascinating career.

• Topic:  Classical Markov Logic and Network Analysis
• Speaker:  Ralph Wojtowicz and Geoff Ulman,, Metron Inc
• Date:  07 Oct 2009
• Abstract:  Markov logic is a set of techniques for estimating the probabilities of truth values of formulae written in first-order languages. In network analysis applications, the formulae describe properties of and relationships or links among entities. The truth values tell if an entity has a property or whether or not a link exists. The networks may involve many different sorts of entities and types of links. Estimates are based on the values specified in training and test data. We refer to the special case involving two truth values as classical Markov logic. Data in this case must assign either ‘false’ or ‘true’ to all (closed) formulae. In practical applications, however, we may have limited confidence in some information sources or data values. To model such uncertainties, we generalize Markov logic in order to allow non-classical sets of truth values. The concepts and methods of category theory give precise guidelines for selecting sets of truth values based on the form of a network model. We plan to give an overview of Markov logic; discuss applications to alias detection, cargo shipping, insurgency analysis, and social network analysis; and describe open problems.

• Topic:  Moment Convergence Rates and Method of Moments Central Limit Theorems via Induction
• Speaker:  Mark Inlow
• Date:  30 Sep 2009
• Abstract:  In 1965 von Bahr proved that the difference between each finite moment of the sample mean and the corresponding normal moment is O(n^{-1/2}) by appealing to results by Esseen, Loeve, and Cramer. We present two proofs of his result using only elementary properties of expectation plus mathematical induction. Since the normal distribution is determined by its moments, if all moments of the sample mean exist then, by a converse of the second limit theorem, it is asymptotically normal. Thus our results also provide simple versions of Markov's 1898 method of moments central limit theorem.

• Topic:  Roll-ups and Differential Geometry
• Speaker:  S. Allen Broughton
• Date:  16 Sep 2009
• Abstract:  We all know that cylinders and (frustums of) right cones can be formed by rolling up a flat strip of paper, metal, plastic, or other flexible material. In fact there are pictures of such "roll-ups" in Calculus books. However, what happens when we do not have such a standard cone shape? What region do we cut out of the paper or metal to achieve a desired cone shape? The problem started as a phone call from a local manufacturing design company who had to solve this problem. They wanted to build a specific shape but did not know what the flattened out shape would be. Since their plan was to build the part from a flattened sheet of metal, the answer to the roll-up problem was crucial. In this talk we discuss the geometry problem and show a solution using the techniques of differential geometry. The techniques are not advanced, in fact everything can be done with multi-variable Calculus and the simple separation of variables in Differential Equations. The time for the talk does not allow for a complete discussion of the "ghastly derivations" but we will discuss the formulas that allow us to solve the practical problem. The formulas can be evaluated using numerical integration (Calculus II) and we show the flattened out shape form the given problem. For those interested in full details see the technical report at http://www.rose-hulman.edu/math/MSTR/MSTRpubs/2009/RHIT-MSTR-2009-01.pdf