Math-GA 2130: Algebra I, Thu. 7:10pm

Instructor: Yuri Tschinkel

Office hours:

• Thu 5pm-6pm or by appointment

Syllabus:

• Basic notions of algebra: groups, rings, and fields
• Symmetric groups, linear groups
• Structure theorems, Sylow subgroups
• Algebraic number fields, finite fields, field extensions
• Galois theory
• Polynomial rings, unique factorization
• Geometry of Numbers, ideals, ideal class groups, units
• Rings, algebraic integers, ideals

Grading:

• Homework: 20%
• Midterm October 17: 30%
• Final December 12: 50%

Recommended books:

• M. Artin, Algebra, Pearson Education
• A. Chambert-Loir, A Field guide to Algebra, Springer

Homework:

1. Elementary number theory: Euclidean algorithm, divisibility, primes, congruences, residues (due September 19)
2. Basic group theory (due September 26)
3. Group theory (due October 3)
4. Invariant theory (due October 10)
5. Galois theory (due October 31)
6. Galois theory (due November 7)
7. Rings (due November 14)
8. Units, Class groups (due December 5)