This course develops in the theme of "Arithmetic congruence, and abstract algebraic structures." There will be a very strong emphasis on theory and proofs.
Primes and unique factorization, congruences, Chinese remainder theorem, Diophantine equations, Diophantine approximations, quadratic reciprocity. Applications such as fast multiplication, factorization and encryption.
This course includes topics on professional development and responsible conduct of research. The course satisfies the GT RCR Academic Policy for Doctoral Students to complete in-person RCR training.
Introduction to quantum computing and quantum information theory, formalism of quantum mechanics, quantum gates, algorithms, measurements, coding, and information. Physical realizations and experiments. Crosslisted with PHYS 4782
Introduction to numerical algorithms for some basic problems in computational mathematics. Discussion of both implementation issues and error analysis. Crosslisted with CX 4640 (formerly CS 4642).