This course provides a proof-based introduction to elementary number theory and discrete mathematics. Topics from number theory include the Euclidean algorithm and prime factorization, congruences and modular arithmetic, Fermat’s and Wilson’s theorems, as well as quadratic residues, Gaussian integers, and cryptography. Discrete topics include sets and induction, recurrence relations, probability, graph theory, and combinatorial geometry. Depending on student experience, the course may integrate the knowledge of calculus to provide a limit-based analytic approach to number theory. This is a fast-paced class. This course appeals to those students intending to major in a field involving significant post-calculus mathematics, though any student with an interest in mathematics for its own sake will be well-served. This course will be offered in alternate years, beginning in the 2020-2021 school year. Students will need to have demonstrated significant mathematical maturity and a willingness to confront abstraction.
Students are required to complete a summer assignment in preparation for this class, which may vary depending on their background. In particular, senior IB Diploma Candidates taking this class in lieu of HL Mathematics Analysis and Approaches will need to complete an assignment particular to that content.
Open to Seniors.
This course is offered 2020-2021 and alternate years.