While a math book club may at first sound oxymoronic, it is not only possible; it is generating an enthusiastic response among math department faculty and students. The club is fresh out of the planning stage, but it already has nearly ten members and its first book lined up. The book? P-adic Numbers: An Introduction, by Fernando Q. Gouvêa. Assistant Professor of Mathematics Pedro Teixeira decided to found the club in order to encourage more talk about mathematics within the department. Several participants echoed this sentiment. Senior math major Katherine Williams said she is excited.
“I get to learn new math and talk to people about it, and it’s a really cool branch of math I’ve wanted to learn about,” Williams said. Visiting Assistant Professor of Mathematics Mercredi Chasman added that she hopes to “have fun talking math with my fellow faculty and students.”
Teixeira envisions the club meeting weekly to talk about the current book, as most book clubs do. The main difference will be that the discussions are more likely to center on proofs, problems, and mathematical concepts than character development, motifs, or themes.
P-adic Numbers is an undergraduate math textbook, so the club meetings will be similar to class discussions — although no one will be teaching. The goal of the book club is for students and faculty to learn together and to discuss math outside of class. P-adic numbers are a relatively new concept for most of the participants, but they are not far afield from the specialties of Teixeira (who focuses on algebra), Associate Professor of Mathematics Mary Armon (who focuses on number theory) and Professor of Mathematics Dennis Schneider (who focuses on analysis).
So what are p-adic numbers? Usually, we look at numbers greater than one as getting larger and larger as they are raised to higher powers. P-adic numbers change the way size and distance work. A prime number is selected to be p, and its powers are designated as getting smaller and smaller as their degree increases. If we let the number two, for example, be p, then two squared is larger than two cubed, and much larger than two to the 100th power. According to Teixeira, this allows you to “introduce notions of what it means to be small and large that are completely different.”
The current topic requires a background in algebra and analysis, but students and faculty with the relevant knowledge are welcome to join. For more information, those who are interested should contact Teixeira.