[Note: For the MAT 5530 syllabus, please go here.]
Prerequisite: Math 3110 or permission of the instructor.
Texts: We will be using Dummit & Foote for the first part of the course and then transition to Steinberg for the remainder of the course.
Web Page: My webpage is located here:
https://mathsci.appstate.edu/~cookwj
and
our course webpage is located here: https://mathsci.appstate.edu/~cookwj/courses/math4010-spring2014.
Meeting times: We meet on Tuesdays and Thursdays from 9:30am until 10:45am in Walker 106.
Final Exam: Our final exam will be held in our regular classroom (Walker 106) on Friday, May 9th from 9:00am until 11:30am.
Lecturer:
| Name: | Dr. William (Bill) Cook | |
| Office: | Walker Hall 347 | |
| Office Hours: |
Monday 9:00am - 11:00am Tuesday 9:00am - 9:30am & 2:30pm - 4:00pm Wednesday 9:00am - 9:30am & 10:00am - 11:00am Thursday 9:00am - 9:30am (Other times by appointment) |
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| Phone: | (828) 262-2367 | |
| Email: | cookwj@appstate.edu | |
| Webpage: | https://mathsci.appstate.edu/~cookwj |
Technology: You are welcome to use any technology at your disposal to complete out of class assignments. We may spend some time in class exploring the (free) group computation software Groups, Algorithms, and Programming (GAP). No calculators or other computer technology will be allowed on exams or quizzes unless otherwise specified.
Course Topics:
This could also be called "intermediate group theory". We will
begin with a few topics not covered in 3110 (such as free groups)
and then discuss group actions (and permutation representations).
Studying how a group acts on a set will lead us to class
equations, Cauchy's theorem, & the Sylow theorems.
Then we'll move over to the world of linear algebra and have our
groups act on vector spaces. Specifically, we'll study modules
and (linear) representations. After reviewing some linear algebra,
we'll cover the "basics" such as submodules (subrepresentations),
simple modules (irreducible representations), module maps
(intertwining operators). Then we'll prove Maschke's theorem,
Schur's lemma and then get into character theory. Once we've
developed some fundamental results about characters (such as
the orthogonality relations), we'll prove Burnside's theorem
(groups of order p^k q^l are never nonabelian simple).
Time permitting we'll look at some other topics such as the
representation theory of the symmetric group and Young tableaux,
tensor products and Frobenius reciprocity, Jordan form, etc.
So basically the semester will break up into 2 major parts:
Your term grade will be based on the results of your tests and final exam as well as your scores on quizzes and homework. Here is more information about the individual components of your grade:
Tests & Final Exam: There will be two tests. The first test will (most likely) primarily cover group actions and the second will (most likely) cover group representation and group character basics. Each test will make up 25%. The dates of the tests listed in the tentative course schedule may change. The actual dates will be announced in class. We will have a cumulative final exam covering the whole course. It will make up 25% of your course grade. Both tests and the final may have a take home portion.
Homework & Quizzes: I will post a list of suggested homework problems from our texts – these will not be collected. Even though these homework problems will be not collected, working out all of the suggested problems is strongly recommended. Please ask questions about problems with which you have had difficulty. 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 copy your collaborators work and turn it in as your own. The homeworks and quizzes will make up 25% of your term grade.
Here are the components of the term grade with their weights:
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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/syllabi.