DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

Co-organizers:

Brian Nakamura, Rutgers University, bnaka {at} math [dot] rutgers [dot] edu

Doron Zeilberger, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: An ounce of Symbol-Crunching is worth a pound of Number-Crunching

Speaker: Doron Zeilberger, Rutgers University

Date: Thursday, September 15, 2011 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Suppose that you are dying to know the EXACT value of the number of partitions of a googol (10100) into at most 60 parts? Using the Maple package PARTITIONS you can get the 5738-digit answer in 0.028 seconds, after investing about 300 seconds in finding a symbolic expression for p60(n), the number of partitions of a symbolic n, into at most 60 parts. Having done that, you can find out in about two seconds, (for example), the EXACT value of p60(1010000), a certain 589838-digit integer.

(Joint work with Andrew V. Sills, see this masterpiece. Also very useful was the help of "joro" from the amazing mathoverflow forum. )

See: http://www.math.rutgers.edu/~bnaka/expmath/