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

Coming Soon: Merrill Place Residence Hall and Conference Center

Starting fall 2017, Plymouth State students will have a new residence hall to call home. To accommodate its growing enrollment, the University recently began construction on Merrill Place Residence Hall and Conference Center, a seven-story building that will house up to 350 students. “Merrill Place’s design is in line with the evolving housing preferences of […]

Example Image

A New Day, A New Way of Giving

Thanks to life in the digital age, when information is as close as a swipe and a tap away, old-school philanthropy has been turned on its head. Donors want—and can find—more information about the causes and organizations they support. They want to feel confident that their gift is going to make a difference; and with […]

Example Image

Building a First-Year Class

PSU’s overwhelming success with enrollment for the 2015–16 academic year was the result of focused multi-year investments in admissions, marketing, academic and co-curricular programs, and new and repurposed facilities.