3.1 Computational tools for number theorists | Andrew V. Sutherland, MIT
Channel: IAS | Park City Mathematics Institute | PCMI
Date: 2022-07-31

Abstract: In this lecture series I will survey a wide array of computational tools and platforms available to number theorists, including (1) computer algebra systems (Magma, Nemo/Hecke, PARI/GP, SageMath), (2) online databases (the LMFDB, databases included in GAP and Magma, and various tables and websites maintained by individual researchers), (3) software libraries (such as NTL and Pari, as well as specialized packages like ARb, Flint, GMP, MPFR, primesieve, Singular, smalljac), (4) algorithmic techniques (birthday-paradox methods, CRT-lifting, evaluation/interpolation, Groebner bases, LLL, Newton/p-adic iteration), and (5) implementation and deployment tools (Jupyter Notebooks, GitHub, Valgrind, parallelization/optimization methods, cloud computing). We will only scratch the surface of most of these topics; the primary goal is to give participants a broad perspective so they can make informed decisions when choosing computational tools to use in their own research, as well as some rules of thumb to help guide these decisions. There are no mathematical prerequisites, but I will assume students have some (possibly minimal) programming experience and that they are comfortable thinking algorithmically; familiarity with Python and/or C/C++ will be useful but is not required.

IAS | PCMI 2022
https://www.ias.edu/pcmi/2022-graduate-summer-school-course-descriptions