Prof. Friedhelm Schwarz , University of Toledo

Title: JAVA APPLETS AND COMPUTER-AIDED ASSESSMENT

Abstract:

The talk will illustrate how we are incorporating technology in our undergraduate courses.

In the first part we will look at some Maplets, these are java applets created with Maple. E.g., the Differentiation Maplet is an interactive learning object which can teach a student how to calculate all derivatives in his or her calculus course.   The second part will deal with compter-aided assessment without multiple choice. We will compare the commercial product MapleTA with the noncommercial product AiM (Assessment in Mathematics). In particular, we will look at the crucial issues of partial credit and data analysis.

September 23, 2005

Prof. Ivo Herzog , Ohio State University at Lima

Title: Pseudo-finite dimensional representations of sl(2,k)

Abstract:  A pseudo-finite dimensional representations of the Lie algebra L = sl(2,k) is a module over the universal enveloping algebra U(L) that satisfies the axioms of a finite dimensional representation. We will show how all such representations may be induced from a von Neumann regular epimorphic ring extension

October 7, 2005

Prof. John Spurrier, University of South Carolina at Columbia

Title: Comparing Two Regression Lines Over a Fixed Interval

Abstract:  Exact one-sided and two-sided simultaneous hyperbolic confidence bounds are developed for the difference of two simple linear regression lines over a finite interval for the predictor variable.  It is assumed that the errors are i.i.d. normal.  The dual problem of testing equality of two regression lines is also considered.  No restrictions are made on the values of the predictor variable in the training samples.  After making a suitable transformation, it is shown that the probability points used in these bounds is a function of the size of an angle.  These probability points are the root of an equation involving a one-dimensional integral and are evaluated numerically.  It is shown that these probability points come from the same distributions used by Wynn and Bloomfield (1971) and Bohrer and Francis (1972) to bound a single simple linear regression over a finite interval. 

Prof. Phong Q. Vu, Ohio University

Title:  Lyapunov-Sylvester equations, sums of commuting operators and theorems of Gearhart's type

Abstract:  The well known Gearhart's spectral mapping theorem relates the spectrum of the operator T(t) in a semigroup of operators on a Hilbert space to the spectrum of its generator A, as well as to the existence of periodic solutions of the differential equation u'(t)=Au(t) + f(t).

We present a new approach to the Gearhart's theorem which also enables us to obtain some essentially new generalizations.  The new approach is based, from one side, on the theory of almost periodic functions with values in Hilbert space, in particular on Parseval's equality for almost periodic functions, and from the other side, on results on sums of commuting operators (which are closely related to results on Lyapunov-Sylvester operator equations).  The generalizations are into two main directions; namely, (i) to more general classes of equations than the equation u'(t)=Au(t) + f(t) and (ii) to more general classes of functions than periodic functions.  The proposed general approach also sheds some new light to the original result of Gearhart.

No prior knowledge in semigroup of operators or in almost periodic functions is presumed.

Dr. Qin Shao, University of Toledo

Title: Periodic Time Series Data Analysis

Abstract:  Periodic time series have received extensive attention due to their broad application in climatology, hydrology, sociology, plant physiology, and economics. I will focus on several aspects of periodic time series data analysis. I will discuss in detail how to fit a parsimonious and adequate model for a given periodic time series, how to estimate the model parameters in the presence of outliers, and how to model a periodic time series with asymmetric or multi-model distribution. I will illustrate the proposed techniques by simulation study and real data analysis.

Thursday, November 17, 2005  

Emeritus Prof.  John Harvey, University of Wisconsin-Madison

Title: Mathematics Education: Reality or Fantasy?

Abstract:  This talk will discuss mathematics education in the present and future, especially collegiate mathematics education. Some of the topics will be reform efforts in mathematics curriculum and instruction, influences on mathematics education, and the need for increased research activity at the college level.

Panel Discussion:  The Future of Science and Mathematics at BGSU

Prof. G. Donald Allen, Texas A& M University

Title:  Two interesting problems: (a) What is a mean value, really? and (b) How to arrange exam question for optimum scores

Abstract:  Suppose we have n items to be placed on a test, and we can arrange the items in any order we wish. What is the best strategy for arranging problems on a test to achieve the highest possible test score average?    A number of possibilities come to mind.

    1.      Placing the easy items first followed by the more difficult ones.
    2.      Randomly placing items.
    3.      Difficult items alternately precede easy items, or vice versa.

To answer these questions additional assumptions are needed, the foremost being some mathematical model of the effect of one question upon succeeding ones.  Leading theories of testing, such as Item Response Theory, make the strict assumption of item independence.  For example, if the test begins with a very difficult item, one which most students will not solve, will this event affect their state of mind, or confidence, toward solving subsequent problems?  This is the influence of one question upon another, and thus the inter-dependency of test items. Even the simplest model for test item dependencies involves some considerable mathematics, but mathematics not generally requiring extensive prior course work.  Hence these problems are accessible to students in their early college careers.  We intend to explore, simulate, and hopefully find meaningful answers about this problem.