Kalyani Madhu, SUNY Brockport and University of Rochester
Periodic Points in Finite Fields: A Question in Arithmetic Dynamics
In Arithmetic Dynamics we study dynamical systems from a number theoretic point of view. This talk will introduce basic ideas in this relatively new branch of Mathematics that will enable us to understand an interesting question concerning the dynamics of ﬁnite ﬁelds.
Thursday, October 6, 4:00 - 4:50pm CANCELLED
Laurel Miller-Sims, Hobart & William Smith
When Not Knowing is Enough
It's impossible to do mathematics without running into things we don't know. We will look at logic puzzles where the key to the solution lies in a lack of knowledge. It's sometimes surprising where not knowing will get you!
Thursday, October 13, 2:30 - 3:20pm
Rebekah Yates, Houghton College
Numerical Range: Counting Necklaces and Looking for Symmetry
The numerical range of a matrix A is the set of all complex numbers resulting from mapping a vector in the unit sphere to the dot product of that vector with A. We will consider the question of when, under certain conditions, this set is symmetric about the origin. Along the way, we'll see several properties of the numerical range, encounter many familiar matrix characteristics, and find ourselves counting how many different necklaces can be made from a fixed number of beads of two different colors.
Pre-requisite Math 233 (Elementary Linear Algebra).
Thursday, October 20, 4:00 - 4:50pm
Elizabeth Wilcox, Colgate University
The Enormous Theorem
Have you ever thought about the work that goes into proving mathematical theorems? Take, for instance, the Fundamental Theorem of Calculus - who proved it? How did he (or she?) even come up with the idea to prove such a thing? And how long did that mathematician spend thinking before a proof materialized?
During the talk we'll learn about a theorem that was nearly eighty years in the making, taking mathematicians from 4 continents nearly 15,000 pages to prove - in a time before FaceTime, Skype, or even cell phones! I will introduce you to mathematical groups and show you that, even though you've been working with groups since grade school, these structures are so complex that after hundreds of years we are still learning new things about groups every day.
Wednesday, October 26, 2:30 - 3:20pm
Jim Matthews, Siena College
The Twenty Locker Problem
In many games, an important goal is to maximize your chances for success. This is true for the locker problem where teams of players attempt to maximize the chances of every team member being successful. We will describe the locker problem, invite participants to suggest solution strategies (possibly offering one or two of our own), and then using some basic probability (along with a bit of calculus and computer programming) to determine the chances of success for each.
This is a version of a search problem for succinct data structures that appeared in a paper written by Peter Bro Miltersen and Anna Gál which won the best paper award at the 30th International Colloquium on Automata, Languages and Programming in 2003. The main ideas for this exposition are accessible to the general public and the solutions that will be discussed can be carried out by average middle school level students. The applications of the college level material to this problem are delightful and probably surprising.
Wednesday, November 16, 2:30 - 3:20pm
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 7, 2:30 - 3:20pm
Adam Towsley, University of Rochester
Pythagoras, Fermat and Faltings – Using Curves to Learn About Triangles
We will look at a method for finding all Pythagorean triples, quickly leading us to questions about rational points on curves, a topic of much research over the last 100 years. These questions will be answered using Fermat's last theorem and Faltings' theorem.