Math apps

Langlands program tools

Computational laboratories in number theory

In Winter 2024 I taught MATH 476 at the University of Michigan. We followed Hugh Montgomery’s wonderful book Computational Laboratories in Number Theory. I implemeted many (variants) of these programs in HTML/JavaScript. They are available on this page. I would like to thank Hugh for designing these labs, and for sharing the code of his original DOS programs with me.


Laboratory 1 : GCDs and the Euclidean algorithm

Laboratory 2 : Factorization and prime numbers

Laboratory 3 : Congruences

Laboratory 5 : Solutions of congruences and binomial coefficients

Laboratory 6 : Linear congruences and the Chinese remainder theorem

Laboratory 9 : RSA public key cryptography

Laboratory 10 : Hensel’s lemma

Laboratory 11 : Power residues and primitive roots

Laboratory 15 : Quadratic residues

Laboratory 16 : Binary quadratic forms