William Gryc
Education
- Ph.D., M.S., Cornell University
- B.A., Amherst College
Teaching Interests
Students often see mathematics as a quest for the “right answer.” My goal as a teacher is to have students shift their focus to the process of finding the answer instead of the answer itself, as the justification is more important (and often more interesting) than the answer. In particular, I want my students to develop the ability to create a precise and logical argument as well as to effectively communicate that argument. While these skills are vital to doing mathematics, they are also vital to navigating and understanding the world in which we live.
Research and Scholarship
My training is in functional analysis, a field that at its core uses tools of linear algebra to solve and analyze solutions to differential equations. My latest publications involve looking at properties of spaces of so-called holomorphic functions. However, I am also interested in applying mathematics to theory of auctions, and my research projects with students usually involve auctions. In auction theory there are two basic questions: Given an auction, what is the best strategy for bidders to adopt, and how much revenue can a seller expect to generate from that auction? I have led multiple student projects in auction theory, ranging from analyzing making “best offers” on eBay to strategies for so-called penny auctions. I’ve also mentored projects on baseball and neuroscience. Generally, I am interested in most projects involving both mathematics and economics.
- Calculus I
- Calculus III
- CUE: Directed Research - Segal-Bargmann Spaces
- Mathematics Independent Study/Research: Functional Analysis
- Operations Research
- Real Analysis
- Special Topic: Pre-Calculus
William E. Gryc. Boundary traces of holomorphic functions on the unit ball in C^n. Computational Methods and Function Theory (2024). https://doi.org/10.1007/s40315-024-00549-0
William E. Gryc. Revenue in first-price auctions with a buy-out price and risk-averse bidders. Journal of Economics, 129:2 (2020), pp. 103--142, DOI 10.1007/s00712-019-00674-8.
William J. Britt*, William E. Gryc, Jamie A. Oliva*, Brittney N. Tuff*, and Charli E. White*. Strategies for making best offers on eBay. American Journal of Undergraduate Research, 14:3 (2017), pp. 5--35.
Lindsey D. Nagy, Don J. Dale, and William E. Gryc. Refinements to the MLB-NPB Posting System: A Clear Win for Japanese Players and Loss for Japanese Teams, Journal of Sports Economics, 19:1 (2018), pp. 113--152. doi: 10.1177/1527002515609961.
William E. Gryc and Todd Kemp. On sharp constants for dual Segal-Bargmann L^p spaces. Journal of Mathematical Analysis and Applications 424 (2015), pp. 1198--1222.
William E. Gryc and Todd Kemp. Duality in Segal-Bargmann spaces. Journal of Functional Analysis, 261 (2011), pp. 1591--1623.}
William E. Gryc. On the holonomy of the Coulomb connection over manifolds with boundary. Journal of Mathematical Physics, 49, 062904 (2008) 19 pp.
Will Britt: Nash Equilibrium for eBay Best Offer Auctions. EPaDel Sectional Meeting of the MAA, Kutztown University, Kutztown PA, April 1, 2017.
Jamie Oliva, Brittney Tuff, and Charli White: Best Offers on eBay. CURM Student Research Conference, Loyola Marymount University, Los Angeles CA, April 1, 2016.
Macauley Breault: Mathematics of Neuroscience. Garden State Undergraduate Mathematics Conference, Monmouth University, West Long Branch NJ, April 11, 2015.
Jarrett Felix: Penny Auctions, Decision Weights, and Revenue. EPaDel Sectional Meeting of the MAA, University of Scranton, Scranton PA, April 26, 2014.
Courtney Hunsberger: Baseball and Loss Aversion. Garden State Mathematics Conference, Felician College, Rutherford NJ, April 13, 2013.
Melanie Panosian: Penny Auctions and Prospect Theory. Garden State Mathematics Conference, Felician College, Rutherford NJ, April 13, 2013.
Lauren Spirko: Strategies for Penny Auctions. Garden State Mathematics Conference, Essex County College, Newark NJ, April 2, 2011.
- Robert C. Williams Award, 2016
- Bridge Builder Award, 2010, 2011, 2014, 2015, 2017
Mathematics
Mathematics, Computer Science & Statistics
Contact: williamgryc@muhlenberg.edu