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.

Featured in Plymouth Magazine

Example Image

And Justice for All

Alisha Medeiros ’15 wants to help troubled youth make better choices and live fulfilling lives. This desire, influenced by a family tragedy, led her to pursue a career in criminal justice.

Example Image

Honoring the Past with a Gift for the Future

Together, Kappa brothers celebrate the good times and help each other in times of need. “The friendships with Brothers of Kappa have stayed with me and so many others for all these years,” says Dana Nelson ’69, one of the fraternity’s founding brothers. “This relationship will stay with us the rest of our lives.” To […]

Example Image

First in the (New) Nation

A Young Man’s Journey from a Nepalese Refugee Camp to the New Hampshire Polls » Southern Bhutan. Early 1990s. Members of an ethnic minority population, the Hindu Lhotshampas, began fleeing rising levels of persecution by the Bhutanese government. Denied their citizenship rights because of religious and cultural differences, the group—more than 100,000 strong—eventually sought protection […]