Spring 2011 Archives

April 8, 2011: From dynamical systems to Coxeter groups

April 5th, 2011 by Dana Ernst

Title: From dynamical systems to Coxeter groups

Date: Friday, April 8, 2011

Location: Hyde 349

Time: 3:00-4:00PM (Pizza at 2:30PM in Hyde 349)

Speaker: Matthew Macauley (Clemson University)

Abstract: In this talk, I will describe how a scientist studying discrete dynamical systems in a bioinformatics institute stumbled into the field of Coxeter groups. Central to these diverse fields are involutions, and what has a group-theoretic interpretation on one hand may lead to insight to the dynamics on the other, and vice-versa. I will highlight some of the central themes and common structures, as well as discuss some novel approaches to some open and open-ended problems.

March 31, 2011: Breaking up is hard to do: Investigations in integer partitions

February 20th, 2011 by Dana Ernst

Title: Breaking up is hard to do: Investigations in integer partitions

Date: Thursday, March 31, 2011

Location: Hyde 349

Time: 4:00-5:00PM (Pizza at 3:30PM in Hyde 349)

Speaker: Andrew Schultz (Wellesley College)

Abstract: One of the early mathematical puzzles you might have been asked as a child is to think of all the ways you can add up numbers to get 4.  Of course 2+2=4 is famous, but most children familiar with addition will also be able to tell you that 4 can be expressed as 1+1+2,  1+1+1+1, or 1+3.  If we throw in the less-than-thrilling equality 4=4, this gives us a total of 5 ways to write 4 as a sum of positive numbers.  Listing the number of ways to write 100 as a sum of positive integers will take you a little longer: there are almost 200 million different possibilities.

The function p(n) is the function which keeps count of the number of ways of writing an integer n as a sum of positive integers, and mathematicians have long been interested in its properties.  In this talk we will discuss a number of very interesting results for this seemingly straightforward function, and along the way we will meet some of the greatest mathematical minds in history.

March 3, 2011: Mathematics, Mathematizing, and the Engineering of Mathematics Education

February 16th, 2011 by Dana Ernst

Title: Mathematics, Mathematizing, and the Engineering of Mathematics Education

Date: Thursday, March 3, 2011

Location: Hyde 349

Time: 4:00-5:00PM (Pizza at 3:30PM in Hyde 349)

Speaker: Jeffrey Taylor (Graduate Student, Plymouth State University)

Abstract: What historians do is not history; what biologists do is not biology – at least, it’s not the body of knowledge we put between textbook covers for our students. Similarly, a lot of what mathematicians actually do is not mathematics.

In this presentation, we will examine the distinction between mathematizing and mathematics, and use it to examine recent trends in the philosophy and psychology of mathematical learning, with the aim of critically articulating the 25 year old concept of “mathematical knowledge for teaching.”

Readings: Prior to the talk, it would be useful for people to take a look at the articles here and here, as well as the essay titled Those Who Understand by Lee Shulman, which you can access by logging in to myPlymouth, going to Library > Journals, searching for Educational Researcher, scrolling down to reveal the 1980’s, clicking on 1986, and then accessing  Issue 2.

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