Math 2210: Number Theory

Course Information

Syllabus

Official description in the NYU Catalog

Class meets: T 7:10-9pm at WWH 517.

Instructor: Benjamin Bakker

email: (last name)-at-cims-dot-nyu-dot-edu

Office Hours: M 4-5pm in Warren Weaver Hall 619

Homework

• • Homework 1.

  • Homework 2.

  • Homework 3.

  • Homework 4.

  • Homework 5.

  • Homework 6.

  • Homework 7.

  • Homework 8.

  • Homework 9.

  • Final.

Lecture Topics and References

Lecture 1: Review of fields. Basic properties of number fields and rings. Lecture Notes. (For a review of field theory, see either M. Artin's Algebra, E. Artin's Galois Theory, or the appendix of Marcus.)

Lecture 2: The trace, norm, and discriminant. Lecture Notes.

Lecture 3: Dedekind domains. Lecture Notes.

Lecture 4: Prime decomposition. Lecture Notes.

Lecture 5: Decomposition groups i. Lecture Notes.

Lecture 6: Decomposition groups ii. Lecture Notes.

Lecture 7: 'Geometry of numbers'; the Minkowski bound. Lecture Notes.

Lecture 8: The unit theorem. Lecture Notes.

Lecture 9: Distribution of ideals i. Lecture Notes.

Lecture 10: Distribution of ideals ii. Kummer's special case of Fermat's last theorem. Lecture Notes.

Lecture 11: Zeta functions and the class number formula. Lecture Notes.

Lecture 12: Distribution of primes. Lecture Notes.

Lecture 13: Dirichlet's theorem on primes in progressions. Lecture Notes.

Lecture 14: Analytic continuation of L-functions and zeta functions. Lecture Notes.