MATH-GA 2210.001:
Number theory I
Number theory I
Contents
- Gaussian integers
- Integrability
- Theory of divisibility for ideals
- Lattices
- Minkowski theory
- The class number
- Dirichlet's unit theorem
- Extensions of Dedekind domains
- Hilbert's ramification theory
- Cyclotomic fields
- Localization
- Orders
Schedule:
W Only 7:10PM- 9:00PMLocation:
WWH 517Office hours:
Tuesdays 11-12h30am or by appointment.Grading:
- Homeworks: 20%
- Midterm 30%
- Final 50%
Recommended book:
[N] Neukirch. Algebraic number theoryHomeworks
- Problem set n°1 : Exercises 1, 3, 5, 6, 7 p 5 and Exercises 1 and 2 p 15 of [N] with solutions
- Problem set n°2 : Exercises 3, 4, 5 p 15 of [N] with solutions
- Problem set n°3 : Exercises 2, 3 ,4 p 23 of [N] with solutions
- Problem set n°4 : Exercises 7, 8 ,9 p 23 of [N] with solutions
- Problem set n°5 : Exercises 5, 6 p 23 and Exercise 3 p 28 of [N] with solutions
- Problem set n°6 : Exercise 10 p 23 and Exercises 6 and 7 p 38 of [N] with solutions
- Problem set n°7 : Exercises 1, 2, 4, 5 p 43-44 and Exercise 1 p 52 of [N] with solutions
- Problem set n°8 : Exercises 4, 5, 7, 9 p 52-53 of[N] with solutions
- Problem set n°9 : Exercises 1, 2, 3 p 58-59 of [N] with solutions
- Problem set n°10 : Exercises 1, 2, 3, 4, 5 p 64-65 of [N] with solutions
- Problem set n°11 : Exercises 1, 2, 3, 4, 5, 6 p 71-72 of [N] with solutions
- Problem set n°12 : Exercises 1, 2, 3, , 5 p 84 of [N] with solutions