Math7752, Algebra II, Spring 2010

Tu Th 11am-12:15pm, Kerchof 317

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

• SYLLABUS

Some lecture notes:

• 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 assignments:

• 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).

Click here for the Math 7751 webpage from Fall 2009