Prerequisite: Math 3110 or permission of the instructor.
Texts: We will have two primary texts for this course:
Web Page: My webpage is located here:
https://BillCookMath.com
and
our course webpage is located here: https://BillCookMath.com/index.html?page=./courses/math4010-spring2023.
Meeting times: We meet Mondays, Wednesdays, & Fridays from 10:00am until 10:50am in Walker 314.
Final Exam: Our final exam will be held in our regular classroom (Walker 314) on Wednesday, May 10th from 8:00am until 10:30am.
Lecturer:
| Name: | Dr. William (Bill) Cook | |
| Office: | Walker Hall 347 | |
| Office Hours: |
Monday, Wednesday, & Friday 9-10am & 11am-12ish Tuesday 9am-10am & 11am-12pm (Other times by appointment) |
|
| Phone: | (828) 262-2367 | |
| Email: | cookwj@appstate.edu | |
| Webpage: | https://BillCookMath.com |
Technology: You are welcome to use any technology at your disposal to complete out of class assignments. No calculators or other computer technology will be allowed on exams or quizzes unless otherwise specified.
Course Topics:
After some intermediate linear algebra background, we will look at the basic theory of Lie algebras including the definition,
examples, subalgebras, homomorphisms, and quotients. Then we will transition to some representation theory, discussing the
definition of a representation/module, module maps, Schur's lemma, sl2 representation theory, Weyl's theorem, the root space
decomposition of simple Lie algebras, root systems, Weyl groups, Cartan matrices, Dynkin diagrams, and the classification of
simple Lie algebras. Time permitting, we will also look at irreducible representations of simple Lie algebras, the weight
space decomposition, and the classification of irreducible representations of finite dimensional simple Lie algebras.
A tentative (albeit very very inaccurate) course schedule can be found at:
https://billcookmath.com/index.html?page=./courses/math4010-spring2023/schedule.html.
Your term grade will be based on the results of your tests and final presentation as well as your scores on quizzes and homework and class participation. Here is more information about the individual components of your grade:
Tests: There will be two tests. Each test will make up 25% of your term grade. I have not attempted to fix dates for these tests presently. The actual dates will be negotiated/announced in class. Both tests will likely have a take home portion.
Homework & Quizzes:
I will regularly assign sets of homework problems to be turned in for a grade. We may have a few quizzes (if needed).
I encourage you to work on your homework with your classmates. However, you must write up your solutions yourself.
Do NOT merely copy your collaborators work and turn it in as your own. The homeworks and quizzes will make up 30% of your term grade.
Participation & Final Presentations:
Instead of having a final exam we will have final presentations. Everyone will pick a topic to present (this topic
will have to be approved and should be something related to what we covered in class). I will require that you create
a nice handout to go with your presentation. We will have presentations during the final exam period.
Also, I except you to come to class and participate in discussions. I may periodically ask (especially grad students) to present a homework problem.
Participation as well as your final presentation and handout will make up 20% of your term grade.
Here are the components of the term grade with their weights:
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Differences between 5530 and 4010: This course is dual listed with Mat 4010. We have the same meeting times. However, your exams will include extra problems (most likely given as a take-home portion of the exam) and most homework assignments will include additional problems just for 5530 students. In addition, I will hold your presentations and presentation handouts to a higher standard. (Don't you feel special?)
Attendance: Don't miss class. If you miss class, you are responsible for the material covered during your absence. If you miss a quiz, test/exam, or workshop, you must bring in documentation proving that your absence is excusable or otherwise receive a zero. If a make-up quiz/test/exam is granted, it must be made up before the next quiz/test/exam.
Help! If you need help, please come to my office hours. If you are in Walker Hall and my office door is open, please feel free to stop by and ask questions – even if it's not during my posted office hours.
Fine Print: Copies of the academic integrity code, disability services information, religious observance policies can be found at https://academicaffairs.appstate.edu/resources/syllabi-policy-and-statement-information.