PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Svetlana Katok, Becky Halpenny.

Title:Grouping and rearranging terms in infinite series
Seminar:PMASS Colloquium
Speaker:Joe Roberts, Penn State
Abstract:
When studying infinite series of real numbers, it is tempting to expect the familiar properties of addition to hold, and in some cases they do. Series that converge absolutely are as well behaved as finite series --- they are associative and commutative. However, series that are not absolutely convergent have very different properties. The Riemann Rearrangement Theorem states that any conditionally convergent series can be reordered to sum to any real number or to diverge (illustrating a failure of commutativity), and there are divergent series for which one can choose a subsequence of partial sums that converge to any arbitrary real number (a failure of associativity). I will give examples of these kinds of unexpected outcomes, eventually building to a construction due to Sierpinski of a single power series whose terms can be grouped to converge uniformly to any continuous function on [0,1] vanishing at 0 --- a "universal Taylor series".

Room Reservation Information

Room Number:MB113
Date:04 / 03 / 2014
Time:02:30pm - 03:20pm