In Fall 2016 we will meet every Thursday from 11:30 AM-12:15 PM in RT 1516.
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NOTE: WE WILL MEET IN RT 1402 rather than RT 1516 this week!
Incredible Sums and How To Evaluate Them
Speaker: Dr. Felipe Martins
Thursday, September 23, 2016
11:30 AM - 12:15 PM, RT 1402
|Abstract: Calculus gives us many remarkable formulas. Two of those are:|
pi^2/6 = the sum from n=1 to infinity of 1/n^2
gamma = the limit as n goes to infinity of the sum from k=1 to n of (1/k- ln(n)).
The first is the famous Basel problem. Euler solved the problem when he was 27 years old, and became instantly famous for the achievement. The second is the definition of the Euler-Mascheroni constant, which appears in topics as disparate as the Riemann zeta function in number theory and Feynman diagrams in quantum field theory.
However, the formulas above, by themselves, are pretty useless from the point of view of computations. In this talk we will present the Euler-Maclaurin formula, which is a remarkable identity relating sums to integrals that can be used in concrete computations with both series and finite sums.
Finally, how could a mathematics student not be interested in a presentation that has the name Euler appearing four times in its abstract?
Pizza and beverages will be provided
Everyone is welcome!