Speaker Name: Derek Habermas (habermds at potsdam dot edu)
Speaker Afiliation: SUNY-Potsdam
Abstract: Take a natural number, like 7. How many ways can you write that number as the sum of positive numbers? For example, 7 = 6+1 = 5+2 = 5+1+1 = ... What if you require that the numbers be distinct? Or odd? Or congruent to 2 or 3 mod 4? These sums are called partitions, and partition theory has been around for almost 300 years attracting the attention of great minds such as Euler and Ramanujan. We will explore common questions and research tools used in this area, including Ferrers graphs and generating functions, culminating in a proof of Euler's beautiful Pentagonal Number Theorem. We will also survey a brief history of the subject, and state some recent (announced in January 2011) significant progress of someone who was almost my Mathematical grandfather.
Target Audience: We use the formula for the sum of an infinite geometric series, and we introduce generating functions. All other material is elementary.
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