| Colby Math/Stats Colloquium |
| Fall 2008 |
| Talks (unless otherwise indicated) are in Mudd 405 from 4 - 5 PM on Mondays. |
| Refreshments begin at 3:30. |
Abstract |
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| September 29 |
Noah Kieserman Colby College |
In this talk I will tie up a Math professor in such a way that they will provably not be able to escape. |
| October 13 |
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October 16 Thursday |
Anne Crumlish Hewitt Associates LLC |
I'll talk about the actuarial profession and share my experiences (career opportunities, etc.) as an actuary. |
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October 20 Olin 1 |
Barry Mazur Harvard University |
Jakob Bernoulli wrote in his treatise Ars Conjectandi (published posthumously in 1713) that his aim was to correct "our most frequent error" (counting things incorrectly) and to offer an art "most useful," because it "teaches how to enumerate all possible ways in which several things can be combined, transposed, or joined with another." This treatise stands -- in my mind -- for the unity inherent in mathematics, for it deals with the simplest of mathematical questions and by pursuing these questions is led to major foundational ideas for many of our modern scientific interests. I aim to start with one elementary and beautiful theme in Bernoulli's treatise and show how it connects to broad developments in modern mathematics. |
| October 27 |
Chrissy Maher Colby College |
In the first part of my talk, I'll discuss a few games I've encountered such as 24, Set, Tic Tac Toe, and Dots and Boxes, all of which either have mathematical content, or promote mathematical/logical reasoning. Tic Tac Toe and Dots and Boxes will serve as the transition into the second part of the talk, as they are games between two people in which each is trying to play in order to maximize their chance of winning. A (possibly eternal) game between two opponents, with one having a winning strategy is a method of proof in mathematical logic. |
| November 3 |
Scott Taylor Colby College |
In 2006, Science Magazine declared the proof of the Poincare Conjecture to be the scientific breakthrough of the year. From 1900, when Poincare posed the problem, until 2003, when Perelman cracked the conjecture, many mathematicians had unsuccessfully attempted an answer. I will explain what the conjecture says and explore the first major attempt to prove it. The talk will serve as an introduction to the mathematical field of low-dimensional topology and should be accessible to anyone who enjoys geometry. |
| November 10 |
Scott Lambert Colby College |
A common theme in analysis is to discover when it is possible to approximate a function by simpler functions with ``nice'' properties. The Weierstrass Approximation Theorem tells us that we can approximate any function which is continuous on a closed, finite interval by polynomials. We will discuss what it means for a sequence of polynomials to be a good approximation of a given function and why such approximations are desired. We will show how to construct such approximations with convolutions -- an operation involving integrals. |
| November 17 |
Ivan Balbuzanov Colby College |
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| November 24 |
Brian Kim University of Northern Colorado |
Monte Carlo simulations have been used extensively in studying the performance of control charts. Researchers have used various numbers of replications in their studies with none providing justification for the number chosen. This research examined six recently published studies to develop recommendations for the minimum number of replications necessary to reproduce the reported results within a specified degree of accuracy. The results of this study indicated that small number of replications could be used to reproduce the target ARLs within the 2 percent error bands satisying the modified Mundfromis criteria. In general, the number of replications required to rproduce the target ARL decreased as the shift size increased. |
| December 1 |
Jim Scott St. Olaf College |
Contact between individuals is an important factor for transmission of infectious diseases. Social networks represent potential pathways through which transmission may occur. Using data obtained from my collaborators, I examine social networks in 21 villages in rural Ecuador to identify characteristics that are associated with having social connections. These data may be used to inform potential public health intervention strategies. |
| December 4 |
Janelle Charles Texas Tech |
In this talk, the relationship between optimal control and statistics is examined. We explore the use of control theoretic smoothing splines in the estimation of continuous probability distribution functions defined on a nite interval [0; T], where the data is summarized by empirical probability distributions. In particular, we consider the estimation of distributions of the form e f ( t ) , where there is no restriction on the sign of f ( t ). The construction of the optimal smoothed curve, y ( t ), is based on the minimization of an integral cost function done through the application of the Hilbert Projection Theorem, which guarantees that a unique minimum exists. |
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