Monday, April 10
MSCS Colloquium – Writing Numbers as the Sum of Factorials
Suzanne Doree, Professor of Mathematics Augsburg College
In standard decimal notation, we write each integer as the linear combination of powers of 10. In binary, we use powers of 2. What if we used factorials instead of exponentials? How can we express each integer as the sum of factorials in a minimal way? This talk will explore the factorial representation of integers, including historical connections to permutations, a fast algorithm for conversion, and the secret of the “third proof by mathematical induction.” Next we’ll extend this representation to rational and then real numbers, ending with some remaining open questions.
3:30 pm, RNS 310
Chemistry Seminar: The evolution of the hexadehydro-Diels-Alder (HDDA) reaction
Thomas Hoye, Ph.D., University of Minnesota
7:00 pm, RNS 150
Biology Distinction Poster Session
4th floor atrium, 4:00PM
Tuesday, April 11
Wednesday, April 12
MSCS Colloquium – A Universal Taylor Series
You perhaps learned in Calc II that the Taylor polynomials of a function can do a very good job of approximating the original function. For example, the Taylor polynomials of y = sin x are quite well-behaved.
In this talk, we will discuss the existence of a function whose Taylor polynomials behave in the worst possible way – its Taylor polynomials can approximate any continuous function whose graph passes through the origin! In other words, the Taylor series of such a function is as divergent as imaginable; its partial sums “travel everywhere.” Such a badly behaved Taylor series is called a universal Taylor series.
Time permitting, we will also discuss a function whose successive derivatives behave just as wildly, some new research on what such a function can look like, and how you can get involved in this research.
3:30 pm, RNS 310 – Everyone Welcome!
Thursday, April 13
Friday, April 14