MATH-UA 344.001:
Algebra II
Algebra II
Contents
- Rings theory
- Generality about rings
- Important classes of rings
- Polynomials rings
- Vector spaces
- Definitions and first examples
- Homomorphisms of vector spaces
- Quotient spaces
- Linear independence and bases
- Fields
- Extension Fields
- Roots of polynomials
- Algebraic elements
- Splitting field
- Construction with straightedge and compass
- Finite field
- Galois theory
- Galois basics
- Examples
- Normal Extensions
- Fields to Groups and back again
- Cyclotomic fields
- Galois basic
Schedule:
Mon/Wed 9:30 to 10:45Location:
CIWW 317Office hours:
Tuesday 9:30-11am or by appointment.Grading:
- Homeworks: 10%
- Quizes: 10%
- Midterm (October 16th): 30%
- Final (December 16th): 50%
Recommended book:
I.N. Herstein- Topics in Algebra, 2nd edition, 1975Notes of the course
Homeworks
- Problem set n°1 with solutions.
- Problem set n°2 with solutions.
- Problem set n°3 with solutions.
- Problem set n°4 with solutions.
- Problem set n°5 with solutions.
- Problem set n°6 with solutions.
- Problem set n°7 with solutions.
- Problem set n°8 with solutions.
- Problem set n°9 with solutions.
- Problem set n°10 with solutions.
- Problem set n°11 with solutions.
- Problem set n°12 with solutions.
Quizzes
Midterm
- Practice for midterm with solutions.
- Midterm with solutions.
Final
- Practice for the final with solutions.
- Final with solutions.