Math-GA 2130.001: Algebra I, Thu. 7:10pm, WWH 202

Instructor: Yuri Tschinkel

Office hours:

• Thu 4:30-5:30pm 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 19: 30%
• Final December 14: 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, Euler function, residues (due September 14)
2. Legendre symbol, quadratic reciprocity, (due September 21)
3. Basic group theory, (due September 28)
4. Sylow's theorems, (due October 5)
5. Basic invariant theory, (due October 12)
6. Galois theory, (due November 2)
7. Galois theory, algebraic integers, (due November 9)
8. Algebraic integers, (due November 16)