Number Theory I

Number Theory I is a first-quarter course introducing the fundamental ideas and methods of elementary number theory through problem solving and proof. Topics may include divisibility, prime numbers, modular arithmetic, greatest common divisors, and classical Diophantine equations.  Emphasis is placed on precise mathematical reasoning, clear proof writing, sustained engagement with advanced and challenging problems, and the development of long-term mathematical mentorship that supports continued growth in number theory.

Number Theory II

Number Theory II is the second quarter in a multi-quarter sequence in elementary number theory, continuing the development of rigorous proof techniques through sustained work on advanced and challenging problems. Building on Number Theory I, students engage more deeply with modular arithmetic, arithmetic functions, and Diophantine equations, with particular emphasis on foundational results such as Fermat’s Little Theorem, Euler’s Theorem, and related consequences. Additional topics may include primitive roots, quadratic residues, and classical applications of congruences. Throughout the course, students work extensively on olympiad-level problems, refine their written mathematical exposition, and develop conceptual connections across topics. The course supports long-term mathematical mentorship and prepares students for further theoretical study and independent work in number theory, including a subsequent course focused on research and advanced topics.

Number Theory III

Number Theory III is the third quarter in a multi-quarter sequence in elementary number theory, emphasizing deeper theoretical results and synthesis across topics. Building on Number Theory I and II, students investigate more advanced themes such as quadratic reciprocity, continued fractions, Pell-type equations, recurrence relations, and selected Diophantine problems. The course places strong emphasis on sustained engagement with advanced and olympiad-level problems, the development of elegant and efficient proofs, and the ability to connect ideas across different areas of number theory. Through seminar-style discussion and written work, students continue to develop mathematical maturity and prepare for independent inquiry and research in a subsequent advanced topics or research-focused course.

Interested in upcoming Number Theory or Research courses? Let us know.