Introduction to number theory (Berkeley Math 115) - Introduction to number theory lecture 15. Numerical calculation

This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We discuss some methods for speeding up number theory calcuations on a computer. Correction: the "modular" method to speed up multiplication mentioned in the lecture is only faster if one does many calculations with these numbers (as in computing determinants) because the initial cost of reducing the input modulo many spall primes is still high. The textbook is "An introduction to the theory of numbers" by Niven, Zuckerman, and Montgomery (5th edition).