This course gives an introduction to rigorous proofs and formal mathematical arguments in the context of elementary number theory. It is a more algebraic alternative to MAT215, our introduction to rigorous proofs in analysis (calculus). Topics covered include Pythagorean triples and sums of squares, unique factorization, Chinese remainder theorem, arithmetic of Gaussian integers, finite fields and cryptography, arithmetic functions and quadratic reciprocity. There will be a topic, chosen by the instructor, from more advanced or more applied number theory: possibilities include p-adic numbers, cryptography, and Fermat's Last Theorem.
Equal emphasis is given to learning new mathematics and to learning how to construct and write down a correct mathematical argument by dividing the question into logical steps where each step is explained and justified carefully, giving references if necessary. For most students this will be a completely new and very challenging way of doing mathematics, very far removed from the process of memorizing algorithms and working through concrete calculations typical of high school math.