# Colloquia

## Professor Moseley 9/6/2012

Date: 9/6/2012

Time: 4:30 PM

Place: 315 Armstrong Hall

I will be giving an undergraduate colloquium on Thursday

September 6, 2012 in Armstrong 315 at 4:30 to help everyone to

understand the "Linear Operator Theory" approach to Math 251 and Math

261. See attached. Not all in Math 251 and Math 261 is Linear Theory,

but enough is to make this approach reasonable, especially for the

engineers. About 90-99% of the students in Math 251 and Math 261 are

engineers. They need to know what a Linear System is from a mathematical

perspective. This begins with the definition of a vector space as an

abstract algebraic structure. Students (engineering and others) find

this hard, but math avoidance is not the answer. In my classes I am

trying to keep them from getting stuck in 3 space. (Please help me.

I'm stuck in 3 space and I can't get out.) The sooner they are exposed

to the Euclidean view of mathematics, the better. This does not

necessarily mean a lot of proofs. I do very few proofs. You and all

of your students are invited. I have enough overheads for 2-3 hours. However, I have cut

it down to a 10-20 minute talk plus questions. Hope to see you there.

PDF for colloquium can be downloaded here

## Mr. Yezhou Wu 7/10/2012

On the inversion of the Vandermonde matrix

Date: 7/10/2012

Time: 2:00 PM

Place: 112 Armstrong Hall

The inversion of the Vandermonde matrix plays important role in the

solution of many problems. For a general n by n matrix it costs

O(n^3) time to calculate the inversion. In this talk we will give an

algorithms in O(n^2) for Vandermonde matrix and show some

applications of linear codes.

## Mr. Dong Ye 7/5/2012

An algebraic proof of

Erdos-Ko-Rado Theorem

Date: 7/5/2012

Time: 2:00 PM

Place: 315 Armstrong Hall

A family of subsets F of some sets is intersecting if any two members of

F have at least one point in common. Erdos-Ko-Rado Theorem says a

intersecting family of $k$-subsets of an $n$-set where $n\ge 2k$ has size

at most ${n-1} \choose {k-1}$. In this talk, I will present an algebraic

proof of Erdos-Ko-Rado Theorem.

## Dr. Jennifer Bruce 5/22/2012

Date: 5/22/2012

Time: 3:00PM

Place: 315 Armstrong Hall

The talk will be on two topics, first about her experiences working with

high school and middle school teachers on the East Tennessee Math and

Science Partnership, and then on a Quantitative Literacy Research Study,

which was a first year seminar course project that will be used for

future development of Maryville's core curriculum.

## Mr. Amsaad Mohamed 5/7/2012

Well-posedness Theory of the Transport Equation

Date: 5/7/2012

Time: 11:30AM-12:30 PM

Place: 315 Armstrong Hall

In this talk, first we

will try to introduce the connection between the ordinary differential

equation(ODE) and the transport equation under some regularity assumptions

on the vector field. We will start by recalling the classical results of

the Cauchy-Lipschitz theory (in which Lipschitz regularity of the vector

field is assumed) and then will present some ideas of the theory of

characteristics and the connection between the ODE and the transport and

the continuity equations in the smooth case. Next, we will begin to

investigate the well-posedness of the transport equation out of the smooth

setting and then we will illustrate the importance of the notion of

renormalization property and how this property implies well-posedness of

the transport equation.

## Professor Matt Pascal 4/20/2012

Homeschooling and Mathematics Education: Results, Trends, and Trajectories

Date: 4/20/2012

Time: 2:30-3:30 PM

Place: 422 Armstrong Hall

Beginning the 1970s, homeschooling gainedmomentum as an option for parents who want more control over the education oftheir children than public or private schools can offer and it is legally confirmedto be an acceptable format for education in all 50 states. Research on homeschoolingis unfortunately difficult and, thus, uncommon, primarily because of broad diversityin the regulatory control that states have over home schools. Using a top-down (orobjective-oriented) approach, this project investigated several groups of collegestudents who had been homeschooled prior to college admissions to compare theirperformance in mathematics and their academic trajectories in comparison totheir traditionally educated peers.

## Professor Elizabeth A. Burroughs 4/5/2012

Research in Professional Development for Grades K-8 Mathematics Classroom

Coaches

Date: 4/5/2012

Time: 2:30-3:30 PM

Place: 422 Armstrong Hall

This talk will provide a description of the design, implementation, and evaluation of a professional development course for grades K-8 mathematics classroom coaches in seven states across the western United States. The course is one component of a larger research project studying the knowledge held by effective mathematics coaches. The professional development is centered upon standards-based mathematics practice and eight themes aboutknowledge held by coaches. The course is a 45-hour summer residential course attended by approximately 60 coaches across two summers. The coaches are randomly assigned to attend one of two summers to allow for an experimental design with a treatment and a control group. The results document a significant change in coaching knowledge held by participants. The results from this project provide a research-based model for a professional development course for mathematics classroom coaches.

## Dr. Minchul Kang 3/19/2012

Mathematical modeling of fluorescence microscopy and its applications to

cancer systems biology

Date: 3/19/2012

Time: 4:30-5:30 PM

Place: 422 Armstrong Hall

*Refreshments will be served at 3:00PM in 310 Armstrong Hall.

All living cells sense, integrate and respond to their environment by a complex system of communication known as cell signaling, which is mostly mediated by protein-protein interactions. Therefore, to determine proteins’ binding partners and binding rate constants are crucial steps to understand cell signaling. While high-throughput methods to screen binary protein binding pairs are now well-established, still no genomic scale kinetic rate calibration tools are available. To this end, simple, accessible yet accurate methods to measure kinetic constants under physiological condition were sought by a combination of mathematical modeling and fluorescence microscopy techniques such as Fluorescence Recovery After Photobleaching (FRAP) and Förster resonance energy transfer (FRET). In addition, a further application of this research to cancer systems biology will be discussed.

## Professor Mikhail Feldman 3/16/2012

University of Wisconsin Madison Professor, Mikhail Feldman, will host a

colloquium on Lagrangian Solutions of Semigeostrophic

System and all are invited to attend.

Date: 3/16/2012

Time: 3:30-4:30 PM

Place: 315 Armstrong Hall

*Refreshments will be served at 3:00PM in 310 Armstrong Hall.

Semigeostrophic system is a model of large-scale

atmospheric/ocean flows. I will discuss some

results on existence and properties of weak Lagrangian solutions in

physical space. The approach is based

on Monge-Kantorovich mass transport theory, and on theory of transport

equations for BV vector fields.

Open problems will be also discussed.

## Dr. Yan Hao 3/8/2012

A tale of two stochastic models

Date: 3/8/2012

Time: 3:30-4:30 PM

Place: 315 Armstrong Hall

*Refreshments will be served at 3:00PM in 310 Armstrong Hall.

Modeling and analysis of biological phenomena require techniques and tools from various disciplines. Though deterministic models have been broadly used and proved to be a powerful tool in the study of mathematical biology, stochastic models often compliment them on capturing individual behavior and effects of noise, molecular fluctuations and random environmental changes for example. In this talk, I will present two examples to show when and how stochastic models can be applied to study biological problems. In the first example, an agent based model is used to study resource sharing rules among human populations under realistic ecological conditions and revealed that simple sharing is an effective risk reducing strategy that plays an important role in maintaining human populations. In the second example, Markov chains and stochastic differential equations are applied to model the cardiac calcium dynamics which is crucial for cardiac rhythm regulation and is known to be the key to understanding many cardiac diseases.

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