Abstracts for George Andrews, Clanton Visiting
Mathematician, 2001-2002
AN OLD ALGORITHM IN A NEW ERA
(Major McMahon, you were born too soon!)
ABSTRACT: In the late 1890's, Major Percy Alexander MacMahon developed his Partition
Analysis with the object of proving his conjectures on plane partitions. While
writing at length on this topic and clearly indicating it's power, MacMahon
eventually admitted that he was unable to apply his new tool to solve any of his
conjectures on plane partitions.
In this talk, we shall examine MacMahon's method from a purely elementary point
of view and shall illustrate its power by considering questions of general
interest. First we turn to Question B3 from the 1999 Putnam exam (see the
October 2000 Monthly). Second we ask how many triangles are there with integer
sides and perimeter n. Our object will be to illustrate the utility of a
19th century idea that is only now coming into its own in the era of computer
algebra.
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RAMANUJAN, FIBONACCI NUMBERS AND CONTINUED FRACTIONS
(Or, Why I took Zeckendorf's Theorem along on my last trip to Canada.)
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ABSTRACT: This talk focuses on the famous Indian genius, Ramanujan. One object
will be to give some account of his meteoric rise and early death. We shall try
to lead gently from some simple problems involving Fibonacci numbers to a
discussion of some of Ramanujan's achievements. The talk should be
understandable for a general audience.
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