Harvey Mudd College
"The Mathemagic Show"
Time: 1 hour
Art Benjamin will demonstrate and explain how to perform rapid mental calculations and other feats of mind.
"Optimization Models in Financial Mathematics"
Time: 1 hour
Advances in computation and analysis have led to significant interest in the mathematics of financial markets. The models in this area often derive from some form of optimization problem such as maximizing expected utility or minimizing expected loss. We will describe a variety of these optimization models and results that derive from duality, optimality conditions, and convexity properties. We will also discuss issues that arise when regularity and convexity conditions do not apply.
"Definition by Recursion"
Time: 30 minutes
Recursively defined objects pervade practically every field of mathematics. Here, we investigate recursively defined sets of integers. Motivated by the so-called fixed-point logics (useful in finite model theory and computer science), we describe a generalized theory encompassing all possible types of recursive definitions, and pose some open questions.
Hei-Chi Chan Illinois University Springfield "Some Amazing Formulas for Pi" Time: 30 minutes Abstract:
In 1996, David Bailey, Peter Borwein and Simon Plouffe discovered some stunning formulas for Pi (and for other constants). Since then, numerous formulas of this type were discovered. In this talk, we review some of these results and present in some detail a group of formulas for Pi that are expressed in terms of the Golden Ratio.
Paul Coe Dominican University "HORSEing around with Mathematics" Time: 20 minutes Abstract:
I have often wondered where the best place to stand is when shooting a basketball and playing HORSE. Using elementary probability theory and the formula for the sum of a geometric series, I have been able to find a close-form expression for the probability of giving a letter in the game of HORSE. Under certain assumptions, the expression yields a simple rule for where to shoot.
Timothy Comar (speaker) Jesica M. Tyrus Benedictine University "Regular and Almost Regular Stick Numbers of Knots" Time: 30 minutes Abstract:
We introduce variations of the concept of the stick number of a knot K. We define the alpha-regular stick number of K to be the minimal number of equal-length sticks needed to form K as a polygonal knot in space assuming that adjacent sticks meet at an angle of alpha, where alpha is in (0, pi) and the almost regular stick number of K, which allows for small variations in the stick lengths and in the angles between adjacent sticks. We provide general lower-bound formulas for the regular and almost regular stick numbers and give coordinates for several almost regular representations of knots and links for particular values of the angle alpha between two adjacent sticks. The coordinates provided for the trefoil knot give an almost regular representation with alpha = arccos(-1/3) realizing the lower-bound of 11 sticks.
Subsequential Tauberian theory, a brand new branch of Tauberian theory, is introduced. Consequently, some related Tauberian theorems are proved.
Mehmet Dik Rockford College "Necessary and Sufficient Tauberian Conditions for Convergence Recovery of a Sequence out of its Abel Summability" Time: 30 minutes Abstract:
We introduce some necessary and sufficient classical and neoclassical Tauberian conditions for convergence retrieval of a real sequence out of Abel summability or generalized Abel summability. Consequently, we prove some Tauberian-like theorems and corollaries.
Howard Dwyer Monmouth College "A Demonstration of Conformal Mapping Using a Graphing Calculator" Time: 30 minutes Abstract:
Using the parametric graphing capabilities of the Texas Instruments TI-83, it is possible to demonstrate some of the basic features of conformal mapping. By comparing the display of a simple region to the display of its image under the mapping, we can see that angles and orientation is preserved, that interior points are mapped to interior points, and that the local magnification does indeed correspond to the modulus of the mapping's derivative. This is possible without any programming, simply by using the calculators graphing capabilities in ways that were probably never intended by the folks at TI.
Roger Eggleton Illinois State University "Jigsaw Puzzles and Mathematics" Time: 30 minutes Abstract:
When we use mathematics to quantify and "simplify" the shapes of jigsaw puzzle pieces, some interesting combinatorial facts emerge. In this application, mathematics makes several interesting contributions: it reveals some beautiful combinatorial identities, it models innovative ways in which we can quantify novel contexts and deduce interesting facts about them, and it gives a focus that makes it easy to invent new variations.
DePaul UniversityHerbert Kasube
Bradley University (panelists) "CUPM Curriculum Guide 2004 : An Overview of the Recommendations and What They Mean for Mathematics Departments" Time: 1 hour Abstract:
Approximately every ten years the Committee on the Undergraduate Program in Mathematics (CUPM) produces a guide for mathematics departments. The latest edition has just been released and is the result of a input from a great many constituencies. This panel will discuss the Recommendations and how departments can benefit from them.
Kari E. Fowler Northern Illinois University "Interaction Between Coefficient Conditions and Solution Conditions of Differential Equations" Time: 20 minutes Abstract:
Consider the differential equation f'' + A(z)f = 0. My dissertation involves investigation into the influence of the normality of the coefficient A(z) on the solution f and also the influence of the normality of the solution f on A(z). I will discuss this influence within the context of some Peter Lappan-related results.
Steve Hinthorne Principia College "Teaching Future Elementary Teachers the History of Arithmetic and Geometry" Time: 1 hour Abstract:
The history of mathematics enlivens its teaching and enhances its understanding. Therefore, future teachers of arithmetic and geometry in the early grades need to be aware of this history. This talk shares some of the history of arithmetic and how to incorporate it in math content courses for elementary education majors.
Andrew Leahy Knox College "Distributed Computing in the Numerical Analysis Curriculum" Time: 30 minutes Abstract:
Distributed computing, which uses networks of computers to solve computationally intensive mathematics problems, is becoming an increasingly important technological tool in client disciplines. In this talk, we will describe how we have been working to develop a revised undergraduate numerical analysis curriculum which incorporates these techniques and which also exposes students to ideas from numerical analysis much earlier in their undergraduate mathematics career.
Ming Jeng Lin Roosevelt University "Using various software programs to solve linear programming problems." Time: 30 minutes Abstract:
At Roosevelt University, we have developed a course on Operations Research for our senior and graduate students. In the course, students use a variety of software packages to solve various types of mathematical models. This talk will focus on how software such as Microsoft Excel, LINDO/LINGO, and MPL/CPLEX are used to teach the basic concepts, algorithms, and mathematical procedures, formulate the mathematical model, and explain and interpret the results.
Mercedes McGowen William Rainey Harper College "Meeting the needs of ALL our students: How well are we doing?" Time: 1 hour Abstract:
What classroom experiences foster the development of mathematical thinking-pattern recognition, generalization, abstraction, problem solving, careful analysis, rigorous argument and flexible thinking? Designing a curriculum based on the CUPM Guide 2004 and CBMS MET recommendations to develop these skills effectively and at appropriate levels for all students is one of the biggest and most important challenges we face. To address these questions, we will look at student data and analyze some mathematical tasks that illustrate ways in which mathematical knowledge for teaching differs from knowledge of mathematics.
Sherry Meier Illinois State University Todd Oberg Illinois College Cynthia Stecher Northern Illinois University "Panel Discussion on Issues and concerns related to mathematics teacher education programs" Time: 1 hour Abstract:
In this panel we will look at basic questions about how schools are preparing prospective mathematics teachers. Is there a disconnect between the mathematics students study in preparation programs and the knowledge they need to teach K-12 mathematics? Should we have more specialized courses for K-12 teachers? Are our preparation programs living up to the expectations of school administrators? What is the theoretical basis for our current requirements?
Todd Oberg Illinois College "Matrices, ISBE, and NCATE - What have I learned over the past 12 months?" Time: 1 hour Abstract:
This talk will start out with my observations and learnings over the last twelve months in working with the accreditation report and matrices from ISBE. I will also talk about the new mathematics standards adopted by NCATE last fall.
Mark Pinsky Northwestern University "Stirling's formula from the Poisson distribution" Time: 20 minutes Abstract:
Many "elementary" proofs of Stirling's approximation for n! have been produced in recent times, including proofs that depend on ideas from probability theory. We review some of these and present a streamlined approach which requires only the simplest ideas from calculus and analysis.
Don Porzio (organizer) IMSA Ilene Hamilton Adlai Stevenson HS Natalie Jakucyn Glenbrook South HS Ray Klein Glenbard West HS Michelle Kolet Schaumburg HS "Computer Algebra Systems in Secondary School Mathematics - Their Usage and Their Impact on Undergraduate Mathematics" Time: 1 hour Abstract:
Computer algebra systems (CAS) have become more readily available to students and teachers over the past several years. This panel discussion will focus on: 1) current usage of CAS in the secondary school mathematics classroom, 2) key questions that CAS raises for the secondary school teacher, and 3) key issues that CAS raises for the undergraduate mathematics instructor who must work with students who have been taught in a classroom where CAS played an integral role in the learning process.
Paul Sally University of Chicago "Problems in Mathematics from Zero to Infinity" Time: 1 hour Abstract:
In this talk I will discuss several problems which begin at a very elementary level and escalate rapidly into serious mathematics.
Heidi Staebler Illinois State University "Students' Perceptions of Learning in an Inquiry-Based University Level Mathematics Course" Time: 30 minutes Abstract:
This talk will report on a case study investigation involving classroom observation, instructor interviews, and student interviews that sought to address the question: What are students' reactions to, and perceptions of, inquiry-based instruction, particularly in regard to their own learning?
Michael Starbird University of Texas--Austin "Circles, Pyramids, Spheres, and Archimedes" Time: 1 hour Abstract:
How do we discover the formulas for the areas of objects such as circles and triangles and the volumes of solids such as cones, pyramids, and spheres? In each case, an effective strategy involves dividing the object into small pieces and seeing how the small pieces can be re-assembled to produce an object whose volume or area is easier to compute. One of the most impressive of these triumphs occurred in the third century B.C., when Archimedes devised an ingenious method using levers to deduce the formula for the volume of a sphere. All these methods foreshadowed the concept of the integral.
Bernard Turner Texas Instruments "What's New at TI?" Time: 1 hour Abstract:
Participants will learn about new and emerging technologies and products that will help energize mathematics teaching and learning, including a new generation of graphing devices and their integration into the wireless classroom.
Nader Vakil Western Illinois University "Simplifying the Syntax of Mathematical Analysis" Time: 1 hour Abstract:
The goal of this paper is to motivate and facilitate a more widespread adoption of the methods of non-standard analysis in the teaching of an introductory course in real analysis. After a brief discussion of some of the issues concerning the foundations of mathematical analysis, we present a version of Edward Nelson's "Internal Set Theory" that can be used to simplify the syntax of mathematical analysis.
Yao Wang Roosevelt University "Survival Bounds for Monotone Log-odds Rate Distributions" Time: 30 minutes Abstract:
This paper proposes the log odds rate to characterize distribution of failure and further proposes the log odds rate as a new way of viewing and modeling the failure process in the region of aging. It will be shown that the model of increasing log odds rate (ILOR) is less stringent than the model of increasing failure rate (IFR). The ILOR bounds on the reliability are more useful than the IFR bounds.
Sarah Ziesler Dominican University "The Fourier transform, restriction theorems and decay estimates" Time: 30 minutes Abstract:
I will discuss restriction theorems for the Fourier transform on hypersurfaces, when the affine curvature is introduced as a mitigating factor. In particular I will discuss the connection with decay of oscillatory integrals and an approach for proving such theorems without oscillatory integrals. This is work in progress with A.Carbery and C.Kenig.