Math B4900, Spring 2018
Modern Algebra II
Logistics
Professor: Zajj DaughertyOffice hours: Wed 12:45–1:45 or by appointment in NAC 6/301.
Class: MoWe 4:00–5:40 in NAC 4/156
Textbook: Abstract Algebra, 3rd Edition (pdf), by David S. Dummit and Richard M. Foote. [Errata]
Grades and course expectations: (Click to expand.)
Schedule
Week 1 |
Review of linear algebra. Read 11.1—3. Vector spaces, linear maps, matrices, change of basis, duals, forms, trace. Notes: [Monday (slides) (printout)] [Wednesday (slides) (printout)] Rough notes on vector spaces (last updated 2/13) |
Due 2/7: Homework 1 (pdf) (tex) (solutions) | |
Quiz Wednesday 2/7 in class. (solutions) | |
Week 2 |
More review of linear algebra. Read 11.4, 12.2, 12.3, vector spaces notes. Notes: [Monday (slides) (printout)] [Wednesday (slides) (printout)] |
Due 2/14: Homework 2 (pdf) (tex) (solutions) | |
Week 3 |
More review of linear algebra. Read 12.3, vector spaces notes. Notes: [Wednesday (slides) (printout)] |
Due 2/21: Homework 3 (pdf) (tex) (solutions) | |
Week 4 |
Algebras, modules, and representations. Read 7.2, 10.1, 18.1, and alegebras, modules, and representations notes. Notes: [Tuesday (slides) (printout)] [Wednesday (slides) (printout)] |
Due 2/28: Homework 4 (pdf) (tex) (solutions) | |
Quiz Wednesday 2/28 in class. (solutions) | |
Week 5 |
Algebras, modules, and representations. Left regular representation of S_3. Read 10.1, 18.1, and alegebras, modules, and representations notes. Notes: [Monday (slides) (printout)] (No slides for Wednesday.) |
Due 3/7: Homework 5 (pdf) (tex) (solutions) | |
Week 6 |
Quotients, isomorphism theorems, direct sums, Schur's lemma. Read 10.2, 10.3, and 10.5. See also notes Notes: [Monday (slides) (printout)] |
Due 3/14: Homework 6 (pdf) (tex) (solutions) | |
Week 7 |
Free modules, exact sequences. Read 10.2, 10.3, and 10.5. See also notes Notes: [Wednesday (slides) (printout)] |
Due 3/21: Homework 7 (pdf) (tex) (solutions) | |
Week 8 |
Projective and injective modules. Read 10.5. See also notes Notes: [Monday (slides) (printout)] |
Due 3/28: Homework 8 (pdf) (tex) (solutions) | |
Week 9 |
Projective and injective modules - big picture. Maschke's theorem, 18.1. See also notes on algebras, representations, and modules and on representations of group algebras. Notes: [Monday (slides) (printout)] [Wednesday (slides) (printout)] |
Due 4/18: Homework 9 (pdf) (tex), and "Make-up" assignment (pdf) (Chapter 1 of Character Theory). (Solutions to HW 9) | |
Exam 1: (solutions) | |
Week 10 |
Artin-Wedderburn Theorem. Read 18.2. Notes: [Monday (slides) (printout)] |
Week 11 |
Artin-Wedderburn Theorem. Read 18.2. Notes: [Monday (slides) (printout)] |
Due 4/25: Homework 10 (pdf) (tex). (Solutions to HW 10) | |
Week 12 |
Tensor products. Read 10.4. Notes: [Monday (slides) (printout)] [Wednesday (worksheet)] |
Due 5/2: Homework 11: worksheet (pdf) (tex). (Solutions to HW 11) | |
Week 13 |
Tensor products and representations of S_n. Read 10.4. Notes: [Monday (slides) (printout)] [Wednesday (worksheet)] |
Due 5/9: Homework 12: worksheet (pdf) (tex) (solutions). | |
Week 14 |
Lie algebras. Read notes on Lie algebras. Notes: [Monday (slides) (printout)] [Wednesday (slides) (printout)] |
Due 5/16: Homework 13 (pdf) (tex). | |
Week 15 |
Lie algebras. Read notes on Lie algebras or course notes on "Combinatorial representation theory of complex Lie algebras and related topics". Notes: [Monday (slides) (printout)] [Wednesday (slides) (printout)] |
Due 5/21: Make a notes sheet for the exam, and review all concrete computations from Monday and Wednesday (like computing the roots of sl_3). | |
Exam 2 Monday 5/12 at 3:30pm. Covereing everything but projective and injective modules and short exact sequences, up through computing the roots of sl_3. One problem will come directly off the first exam. |
Extra details for special homework assignments
Research paper summaries: Hand these in any time, but the first is due no later than 4/9, and the second is due no later than 5/16. (Click for assignment details.)Writing guide
For the basic requirements of homework write-ups, see writing tips.Also see Francis Su's Guidelines for Good Mathematical Writing.
I also highly recommend learning to type up your homework using LaTeX. There are lots of great resources out there. To see my code, the LaTeX files for notes and handouts can be found by replacing .pdf with .tex for most of the files above. You'll also need preamble.tex (occasionally updated). You can find another sample on my teaching page, and lots of sample code at TeXample.net. The Not So Short guide to LaTeX is linked from my resources page. You can obtain LaTeX via LaTeXproject.org.