Workshops
There are three excellent short courses and an excellent workshop on Friday morning. These courses are:
Walking in the Mountains - The Steepest Descent Method, Ben Ntatin (Austin Peay State University)
The notion of linearity is fundamental for numerous considerations in mathematics and engineering science. In rough terms, if a problem is linear or can be well-approximated by a linear model, then there may very well be standard means of approaching it. It is well known that many physically significant problems under steady state conditions can be reduced to an equation of the form Ax= b where A is possibly a nonlinear operator. Typical examples of how such equations arise are found in models involving the heat, the wave or the Schrodinger equation. Solutions of such equations are in fact, the equilibrium points of the system they model. Consequently, considerable effort has been devoted to developing constructive techniques for the determination of solutions to such operator equations. Of course, one would think of the row reduction to echelon form method to solve such a system if A is linear. We will consider the case where A is a large matrix for which it becomes not only time consuming and laborious, but also expensive to solve such a system even with the help of technology. In this short course, we introduce the material necessary for the understanding of the steepest decent method and give a detail description of the related algorithm. Some practical applications are also provided. Participants are only expected to have a basic knowledge of multi-dimensional calculus. At the end, mention is made of the case when the case when A is non-linear.
RSA and Beyond: An Introduction to Cryptology, Jeffrey Ehme (Spelman College)
It has become very common for people to transmit highly confidential information over the public forum that is known as the internet. People routinely use credit cards to make online purchases and this is (relatively) safe. In this short course we will look at the mathematics of public key cryptography that makes this possible. More specifically, we will consider the Diffie-Hellman key exchange, RSA and ElGamal, the Miller-Rabin algorithm for finding large primes, and some elliptic curve versions of these topics. No previous experience with any of the mentioned topics is assumed. Participants will be provided with a complete set of notes and references.
Teaching with a Digital Text, Lang Moore and David Smith (Duke University)
The short course organizers, David Smith and Lang Moore, will present and demonstrate what they have learned in the preparation, testing, and publication of an interactive digital textbook for one-variable calculus. Issues to be investigated will include: student reading of an online text; classroom work with an online text; using activities, examples, and checkpoints; using an online homework system -- illustrated with WeBWorK; and using online instructor resources. Professors Smith and Moore have rewritten their one-variable calculus text, Calculus: Modeling and Application originally published on paper by D.C. Heath, as an online interactive text now published by the MAA. CDs containing the complete text will be available for each participant. Participants should bring their own laptop computers; wireless internet will be available.
Hands-On Activities To Encourage Student Engagement In Exploring Mathematics, Carroll Wells and Gary Hall (Lipscomb University)
This workshop is specifically intended for middle grades and high school mathematics teachers and for college teachers of math/education courses. Session 1: Hands-on activities to use in the study of trigonometry—Dr. Amy Nelson: Activities include using a battery operated Ferris wheel and spaghetti to generate graphs of trigonometric functions. Session 2: Hands-on activities to use in the study of problem solving techniques—Dr. Gary Hall: Activities include the use of a murder mystery and puzzles in teaching problem solving. Session 3: Hands-on activities to use in the study of geometry—Dr. Carroll Wells: Activities include the use of paper folding to create models of Platonic Solids and to study other geometry figures. Over 90 geometric terms can be discussed using these activities. All activities in the above have been used successfully for the past five years at Lipscomb University in summer institutes supported by a math/science partnership grant from the Tennessee Department of Education.
Travel Information
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