Number theory
Graduate · Math
Syllabus focus
Theoretical / proof-based
Pricing calculator
Choose materials, tutoring, or both — or book a single session as needed. Customize your plan on the subscribe page.
$1,162 · Number theory · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle or Venmo.
Topics typically covered
Theoretical / proof-based
Algebraic number theory
- Dedekind domains and fractional ideals
- Class groups and finiteness of the class number
- Ramification and splitting of primes in extensions
- Discriminant and integral bases
- Minkowski's lattice point theorem and applications
Local fields and adeles (introduction)
- p-adic numbers and valuations
- Completion of Q with respect to the p-adic valuation
- Local class field theory (overview)
- Adeles and ideles (introduction)
- Chevalley's product formula (statement)
Analytic methods
- Dirichlet series and the Riemann zeta function
- Prime number theorem (proof outline)
- L-functions and Dirichlet's theorem on primes in arithmetic progressions
- Modular forms (introduction)
- Elliptic curves: Mordell–Weil theorem (statement)
Notes
Topics reflect common graduate number theory syllabi at US universities. Courses may focus on algebraic or analytic tracks; this list spans typical first-year graduate coverage.