- Instructor: Mikhail Ershov
- Office: Kerchof 302
- Office hours: TBA

- First midterm (due Monday, March 1st).
- Second midterm (due Thursday, April 8th).
- Final exam (due Tuesday, May 4th).

- Lecture 1. Modules
- Lecture 2. Generation of modules and free modules
- Lecture 3. Tensor products of modules
- Lecture 4. Tensor products and bilinear maps
- Lecture 5. Algebras over commutative rings
- Lecture 6. Tensor, symmetric and exterior algebras
- Lecture 7. Modules over PID. Part I
- Lecture 8. Modules over PID. Part II
- Lecture 9. Modules over PID. Part III
- Lecture 10. Canonical forms of linear transformations
- Lecture 11. Rational canonical form (continued)
- Lecture 12+. Jordan canonical form
- Lecture 14. Field extensions
- Lecture 15. Algebraic closures
- Lecture 16. Algebraic closures and splitting fields
- Lecture 17. Normal and separable extensions
- Lecture 18. Separable extensions (continued)
- Lecture 19. Galois groups and Galois extensions
- Lecture 20. Galois correspondence
- Lecture 21. Galois correspondence (continued)
- Lecture 22. Finite fields II
- Lecture 23. Cyclic extensions
- Lecture 24. Solvability by radicals and solvability of Galois groups
- Lecture 25. Some category theory
- Lecture 26. Direct and inverse limits

- Homework #1 (due on Thursday, January 28th).
- Homework #2 (due on Thursday, February 4th).
- Homework #3 (due on Thursday, February 11th).
- Homework #4 (due on Thursday, February 18th).
- Homework #5 (due on Thursday, March 4th).
- Homework #6 (due on Thursday, March 18th).
- Homework #7 (due on Thursday, March 25th).
- Homework #8 (due on Thursday, April 1st).
- Homework #9 (due on Thursday, April 15th).
- Homework #10 (due on Thursday, April 22nd).