Algebraic Number Theory

Math W4043, Fall 2011
Instructor: Maksym Fedorchuk

Lectures: Tue-Thu 9:10-10:25 in Math 307
Office hours: 7th floor of Math Building, Tue-Thu 11-noon
Textbook: Algebraic theory of numbers by Pierre Samuel
TA: Xuanyu Pan <pan@math>
TA holds office hours in the Help Room

Syllabus

An excellent reference for extra reading material is James Milne's lecture notes on algebraic number theory

Week 1: Rings and ideals
Week 2: Modules. Integrality.
Week 3: Integers in quadratic fields. Rings of integers in number fields. (Notes courtesy of Rankeya Datta)
Week 4: Norm, trace, and discriminant. (Notes courtesy of Rankeya)
Week 5: Structure theorem on algebraic integers. Dedekind domains. (Notes courtesy of Rankeya)
Week 6: Factorization in Dedekind domains. The ideal class group. (Notes courtesy of Rankeya)
Week 7: Splitting of primes in extensions. (Notes courtesy of Rankeya and Miriam Melnick)
Week 8: Ramification in quadratic field extensions. (Notes courtesy of Rankeya). The midterm (October 27)
Practice midterm (courtesy of Jarod Alper)
Midterm (October 27) Midterm solutions
Week 9: Quadratic reciprocity. Galois extensions of number fields. (Notes courtesy of Rankeya Datta)
Week 10: Galois extensions of number fields. Finiteness of the ideal class group.
Week 11: Finiteness of the ideal class group (continued).
Week 12: The unit theorem.
Week 13: Fermat's Last Theorem (for regular primes).
Review Session I: Tuesday (December 13) 1-2pm in math 622.
Review Session II: Tuesday (December 20) 1-2pm in math 622.

Final Exam, Thursday, December 22

Assignment 1 due Thu, 9/15 (solutions)
Assignment 2 due Thu, 9/22 (solutions)
Assignment 3 due Tue, 10/04 (solutions)
Assignment 4 due Thu, 10/13 (solutions)
Assignment 5 due Thu, 10/27
Assignment 6 due Thu, 11/3 (solutions)
Assignment 7 due Thu, 11/10
Assignment 8 due Tue, 11/22 (solutions)
Assignment 9 due Tue, 12/06 (solutions)