Dr. Alissa S. Crans - A Surreptitious Sequence: The Catalan Numbers
This lecture was filmed at the 2017 National Math Festival in Washington, D.C. and features Dr. Alissa S. Crans of Loyola Marymount University.
Many of us are familiar with famous sequences of numbers such as the odd numbers 1, 3, 5, 7, …, perfect squares 1, 4, 9, 16, 25, …, Fibonacci sequence 1, 1, 2, 3, 5, 8, … ,or the triangular numbers 1, 3, 6, 10, 15, … But what about the sequence 1, 1, 2, 5, 14, …? First described by Euler in the 1700s and made famous by Belgian mathematician Eugene Catalan 100 years later, these “Catalan numbers” take on a variety of different guises as they provide the solution to numerous problems throughout mathematics.
Dr. Alissa S. Crans has been recognized nationally for her enthusiastic ability to share and communicate mathematics, having been honored with the Hasse Prize for expository writing on mathematics, as well as with the 2011 Henry L. Alder Award for distinguished teaching by a beginning college or university mathematics faculty member. A presenter at the first National Math Festival in 2015, Crans has also been invited to speak at MoMath and in various lecture series including the MAA Distinguished Lecture and George Kitchen Memorial Lecture, as well as at numerous mathematical days for undergraduates. She is known for her active mentoring and support of women and underrepresented students and is dedicated to helping all students increase their appreciation and enthusiasm for the discipline. She proselytizes about math in settings that range from the public library to “Nerd Night” to public school classrooms. She is Professor of Mathematics at Loyola Marymount University, where her research interests lie in the field of higher-dimensional algebra and are currently supported by a Simons Foundation Collaboration Grant.
The National Math Festival thanks the Department of Mathematics at Loyola Marymount University for their support of this program.