# Geneseo Mathematics Colloquium Schedule

## Fall 2009

Thursday, September 24, 3:30 - 4:20 pm
Newton 203
Paul Seeburger, Monroe Community College

### Making Multivariable Calculus Come Alive using Dynamic Visualization Tools

A tour of an NSF-funded project that seeks to develop geometric intuition in students of multivariable calculus. This online exploration environment allows students to create and freely rotate graphs of functions of two variables, contour plots, parametric surfaces, vectors, space curves generated by vector-valued functions, regions of integration, vector fields, etc. This tool is designed to improve student understanding of the geometric nature of many of the concepts from multivariable calculus. A series of assessment/exploration activities has also been designed to help students "play" with the 3D concepts themselves, and to assess improvements in geometric understanding gained from these activities. 3D glasses will be provided.

Wednesday, October 7, 2:00 - 2:50 pm
Newton 203
Phong Le, University of California at Irvine

### Using Modulo Arithmetic to Find New Solutions to Old Polynomials

In this talk we will rebuild the integers using arithmetic modulo prime numbers. This will allow us to find solutions to polynomial equations such as x2+1=0 in an entirely new setting: the finite field. This new algebraic construction will raise many interesting questions with some surprising answers.

Thursday, October 29, 3:30 - 4:20 pm
Newton 203
Kristin Comenga, Houghton College

### Polytopes: Generalizing Polyhedra to Higher Dimensions

Most people remember working with polyhedra in elementary and high school: cubes, prisms, tetrahedra, pyramids, etc. Euler's relation states that if V is the number of vertices, E the number of edges and F the number of faces, V + F = E + 2. In this talk we will survey variations on this result for generalizations of polyhedra called polytopes. The polyhedra most of us have experience with are three-dimensional. Polytopes can be any non-negative dimension, with the simplest example beyond polygons and polyhedra being the four-dimensional hypercube. How can Euler's relation generalize to polytopes in any dimension? How can we generalize this to look at angles of polytopes instead of the number of faces? We will look at a number of examples of polytopes as we explore some of the answers mathematicians have found to these questions. We will end with a brief glimpse of open questions about angles in polytopes. No specific math background will be assumed, but curiosity is expected!

Thursday, November 12, 3:30 - 4:20 pm
Newton 203
Emilie Wiesner, Ithaca College

### Clever Counting Strategies in Sudoku

Have you ever played Sudoku? Have you wondered what makes one puzzle harder than another? what the minimum number of clues could be? how many puzzles there are? So have other mathematicians! I'll talk about these questions and, in particular, how mathematicians have tried to count the number of puzzles. This turns out to be a tough count to make, and mathematicians have used clever counting strategies from Combinatorics and Abstract Algebra to do it.

Wednesday, November 18, 2:00 - 3:15 pm
Newton 202
Jeff Johannes & Gary Towsley, SUNY Geneseo

### A Concise History of Calculus

A lively overview of over two thousand years of calculus history. Not only who-did-what along the way, but the cultural and sociological causes and effects of the calculus. Strongly recommended for anyone who has taken or is taking calculus.

Wednesday, December 2, 2:00 - 2:50 pm
Newton 201
Olympia Nicocdemi, SUNY Geneseo

### Wavelets and Elementary Linear Algebra

Wavelets are in use everywhere, from deep inside a little digital camera to big telescopes that help us find out what's out there. The name wavelets sounds so user friendly. And they are, but the theory behind them is not always accessible to undergraduates in their early studies. In this talk, we will make that theory a little friendlier by linking what we learn in elementary linear algebra to the theory and practice of wavelets.