(Note the new time!)
Bent E. Petersen
The Mth 507 graduate seminar consists in part of talks given by OSU mathematics graduate students who are Summer GTAs and by invited speakers. The talks normally deal with the students' mathematics or mathematics education research, interesting byways, mathematics history, applications of mathematics, or recreational mathematics. Academic credit (3 hr) is normally available only to graduate mathematics students.
The title of each talk is a link to the corresponding abstract.
Nolan Mitchell
Title: RSA cryptosystem and a shorter Euclidean algorithm.
Abstract: The history of the RSA cryptosystem is explored and the encryption algorithm, with mathematical proof, is discussed. A novel variation of Euclid's algorithm by G. S. Glasby(1999 Mathematics Magazine), which requres only half of the normal hand calculations, is cited. An example of RSA message encryption with a RSA digital signature is given as well. Duration < 1hr.
Megan Powell
Title: Understanding the Underrepresentation of African-Americans in Math, Science,
Engineering, and Technology Fields.
Abstract: The purpose of this talk is to better understand the underrepresentation of minorities, mainly African-Americans in science, math, engineering, and technology (SMET) majors and what is actively been done to encourage more African-Americans to pursue SMET majors as undergraduates. I will discuss the factors that contribute to African-Americans success in SMET classes and their decision to choose a SMET major. I will also discuss various academic programs that aim to encourage more African-American student to pursue SMET majors.
John Ollis
Title: Penetration of a Projectile into a Saturated Sand Media
The impact of a projectile into any media at hypervelocities will produce enormous amounts of energy. How much velocity would it take to produce a shock wave that would travel a few feet or a few meters? To determine this one has to determine the material properties of the medium and the depth one can sink a projectile based on its impact velocity. The conservation equations and elastic/plastic constitutive relationships play a role in creating an algorithm that will provide a reasonable depth approximation. The talk will focus on analyzing the process used to determine such a numerical scheme.
Larry Pierce
Title: An introduction to Symbolic Dynamics
Dynamical systems are simply described as iterated maps on various surfaces. They arise from many physical systems. However, the maps themselves may be very complicated, and the action very hard to see.
Symbolic dynamics allows a means by which we can see the action of the map in a simple setting, allowing us to better view the dynamics of the system.
Kailash Ghimire
Title: Seifert-van Kampen Theorem and Its Applications
The Seifert-van Kampen theorem is used to find the fundamental groups of all covering spaces of figure 8 with special case such that each point inverse has cardinality 3 up to covering equivalence. This theorem is also useful to find the normality of these groups. (This talk is Part a of take home exam given for us in MTH632).
Diana Luca
Title: Random walks on trees
Abstract: Versions of the Strong Law of Large Numbers and Central Limit Theorem, two of the fundamental results of Probability Theory, can be obtained in the special case of Bernoulli random variables defined on a full binary tree. These results reflect the rich structure and dramatic fluctuation of partial sums on
trees.
Kyle Champley
Title: The mathematics of computed tomography
Abstract: Computed tomography wishes to determine the density of an object by shooting energy waves through the object. We model this mathematically by a density function, f. Then we try to reconstruct f from line integrals of f. This mathematical problem is used in diverse settings in medicine (CT scans, ultrasound, etc.), science, and technology (diagnostic radiology, quantum optics).
Jason Schmurr
Title: An Overview of Fermat's Last Theorem
Abstract: Fermat's last theorem was an open problem for 350 years, during which only incremental progress was made. The recent proof, stemming primarily from the Taniyama-Shimura-Weil conjecture and Frey curves, involves a surprising association of elliptic curves with modular forms.
Aaron Wangberg
Title: How you too can earn as much as a Portland CEO, or Math and the Art of Bicycle
Racing.
Abstract: In bicycle racing, there seems to be a very unique way to get faster: Buy better gear. One particularly expensive component racers buy is aerodynamic wheels. Different tests and experiments claim that buying these wheels can save up to 2 minutes over a 40 km time trial, while other tests say that the wheels only provide a 'placebo effect'.
I will present some of the mathematics behind these tests, and at the complexities of creating a good mathematical formula to create an accurate test. With this, I will show that everyone in the room is capable of making more money than any CEO at a Portland, or any other, corporation.
Jessica Strowbridge and Nicole Webb
Title: A Natural Generalization of the Win-Loss Rating System
Abstract: The NCAA Basketball tournament uses a system to rank participating teams based on win-loss ratios, difficulty of schedule, location of team and conference, and other factors. We will investigate a simplified mathematical model for ranking teams in a tournament using point spread, generational relationships, and a limiting process.
Corina Constantinescu
Title: Ruin Theory under Uncertain Investments
Abstract: An insurance company, having an initial capital u, receives premiums continuously and pays claims of random sizes at random times. A classical result states that if the rate of premium exceeds the average of the claims paid per unit time, then the ruin probability decays exponentially fast as u tends to infinity. However, if the insurance company invests in a risky asset whose price follows a geometric Brownian motion, it is known that the probability of ruin decays at best algebraically, under a specific model for claim size distribution. In this talk, the result is shown to be valid for claim size distributions having moment generating functions defined in a neighborhood of the origin.
Liam Finlay
Title: The regular value theorem and a proof that any k-dimensional subspace of Rn
is actually a n-dimensional submanifold of Rn
Abstract: This talk will be a basic introduction to manifolds and submanifolds, and to the regular value theorem. We will see that the regular value theorem allows us to prove that a space is a submanifold without referring to the charts and atlases of the original manifold. Specifically we will use the regular value theorem to show that any k-dimensional subspace of Rn is also a k-dimensional submanifold of Rn.
Kinga Farkas
Title: The Quartic Model of the Elliptic Curve and Certain Types of Isomorphisms
Abstract: Given a non-singular elliptic curve E in Weierstrass form, for each point of the curve, there is a corresponding quartic model of the elliptic curve, which is birationally isomorphic to E. This talk will show the existence of fractional linear transformations between these quartic elliptic curves and some consequences of these maps.
Anupan Netyanum
Title: Von Neumann alternating projections theorem
Abstract: My interest is in a theorem proven by Von Neumann. This theorem is called alternating projections theeorem in the case of two subspaces. Von Neuman proved that if we have 2 closed subspaces M1 and M2 in the Hilbert space X, then for any x in X, the limit of (PM2*PM1)^n(x) is actually PM1intersectsM2(x) where PM1 is the projection on to the space M1, PM2 is the projection on to the space M2, and PM1intersectsM2 is the projection on to the space M1 intersect M2
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