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Colloquium, Spring 2006

Day: Thursday, May 4th Time: 4:00pm Place: BH 112 Title: Formal Power Series Speaker: Erin Beyerstedt Abstract: Formal power series have useful applications in many branches of mathematics. In combinatorics, they occur as generating functions, facilitate solving different counting problems, and are helpful in finding closed forms for recurrence relations. In number theory, they have applications to partitions and the sum of divisors function. Prior to the publication of the paper Formal Power Series by Ivan Niven in 1969, a theory of formal power series was simply assumed by many mathematicians. However, no single paper had rigorous mathematical justification for the manipulations commonly performed on these series. Ivan Niven provided such justification and, in fact, revealed the absence of the convergence question. During my talk, I will present and explain his approach and then look at some of the aforementioned applications.