Preliminary Arizona Winter School 2025: Mathematical cryptography and algorithms in number theory
The Preliminary Arizona Winter School (PAWS) is a virtual program on topics related to the upcoming AWS, with an intended audience of advanced undergraduate students and junior graduate students.
Format: The program will run for 9 weeks, alternating between 5 weeks of lectures and 4 weeks of problem sets (with a TA session)
Each lecturer will be accompanied by graduate student assistants, who will be in charge of writing weekly problem sets and facilitating weekly, hour-long problem solving and discussion meetings with groups of students.
Introduction to mathematical cryptography will assume only a first undergraduate course in abstract algebra as a prerequisite. Analysis and implementation of algorithms in number theory will assume fluency with algebra at a beginning graduate level and familiarity with the basic objects of algebraic number theory (such as number fields and their rings of integers), but will not assume any prior experience with analysis of algorithms.
The school will feature an online (Zulip) discussion board where students can ask questions and interact with the speakers and assistants outside of scheduled meeting times.
We will facilitate additional virtual events, some purely social to build a community, and some more structured sessions on timely and pertinent topics like "What is graduate school in Math like?", "Tips for applying to graduate school this Fall," "How do I navigate the first year of graduate school?" "How do I look for an thesis advisor?", "How to get the most out of the upcoming AWS."
We encourage undergraduate students to take their PAWS course as an independent study with a faculty member at their home institution.
- Organizers: Renee Bell, Brandon Levin and Padmavathi Srinivasan (main organizers) with Anthony Várilly-Alvarado, Isabel Vogt and Hang Xue
- Please contact aws@swcmath.org with any questions.
- Funded by the National Science Foundation.
September 22nd — November 21st, 2025
PAWS 2025 consists of two concurrent lecture series.-
Sabrina Kunzweiler: Introduction to mathematical cryptography
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Juanita Duque-Rosero: Analysis and implementation of algorithms in number theory
This course will assume only a first undergraduate course in abstract algebra as a prerequisite.
This course will assume fluency with algebra at a beginning graduate level and familiarity with the basic objects of algebraic number theory (such as number fields and their rings of integers), but will not assume any prior experience with analysis of algorithms.