Math 4010 & 5530 Section 101 Homepage

Syllabus
Schedule
Homework
asULearn (Online gradebook, chatroom, etc.)
News & Announcements

05/09 Introduction to GAP [source (.tex)]

05/08 Don't forget about our "final" meeting tomorrow. I'll grab some pizza at Little Caesar's, 
      some drinks, and cookies and head straight over to campus.

      Since Little Caesar's opens at 11am, I probably won't get here until about 11:20am. We'll 
      meet in WA 308 (not our usual room).

      I plan on showing off some of what GAP can do and we'll probably be done shortly after 12pm.

      I hope to see you there!

04/15 Test #2 and its source code are posted here.

      Please redo the entire test and turn it in by noon on Thursday. Don't feel that
      you have to type up your solutions. :)

04/12 Updated homework scores have been posted on AsULearn.
      Also, guess what? I gave out 2 homework "4's" so I guess Homework #4 (take 2) 
      was really Homework #5 and Homework #5 was really Homework #6. Oops!

04/01 Homework #5 #6: Due Tuesday, April 8^th

      Exercise 4.2
      Exercise 4.9
      Exercise 4.10
      Exercise 4.12

03/21 Homework #4 #5: Due Thursday, March 27^th unless Noah is giving his talk 
      that Friday and then it's due Tuesday, April 1^st.
      
      Exercise 2.7 (page 10)
      Exercise 3.1 (page 23) [Hint: Proposition 3.1.19]
      Exercise 3.3 (page 24)
      Exercise 3.6 (page 24) #1 [Hint: Exercise 3.3], #2 [Grad 1/2 Problem]

02/27 Test #1 (.pdf) [Source (.tex)] is due March 5^th.

      You may notice that the points do not add up to 100. Yes. That's on purpose.
      Do as much as you can do. Then hope that your classmates did far less...just
      kidding. In general, I expect the grad students to complete more than the 
      undergrads.

      You must work on problems yourself. You may ask me anything you want...I just
      might not give you a helpful answer. You can use notes and books freely. 
      You may also look up things online, but asking for help online is off limits.

      Ok. Let the pointing out of the typos and flawed questions commence!

02/10 Infinite Sadness - I messed up when typing up problem #4 on homework #4. I left 
      out the critical assumption that G = HK. Without assuming this it is impossible
      to show the relevant group is isomorphic to the direct product of quotients (in
      this case G is not HK, we have that G mod H intersect K is only isomorphic to
      a subgroup of G/H x G/K). Anyway, it's fixed now. Let's call that problem extra
      credit. 

02/04 Homework #4 (.pdf) [source (.tex)] is due Tuesday, February 11^th.

01/30 A handout for Tuesday's class (I'll bring copies)...
      The Alternating Group (.pdf) [source (.tex)]

01/28 Homework #3: Due Tuesday, February 4^th
                   1.7 #16
                   2.2 #5
                   2.3 #16
                   Grad Problem 2.5 #11
                   
      Homework #3 (.pdf) [source (.tex)]

01/21 Homework #2: Due Tuesday, January 28^th
                   1.3 #12, #19
                   1.4 #2, #3
                   1.6 #17

01/17 I've slightly adjusted my office hours. Here's the new info...
      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

01/14 Homework #1 (.pdf) [source (.tex)] is due Tuesday, January 21^st.

01/01 Syllabus [Syllabus for MAT 5530], schedule, and suggested homework to be posted.

      LaTeX Examples

      Some old 2240 handouts: 
      Gauss-Jordan Elimination & The Linear Correspondance
      Finding & Extending Bases Example
      Coordinate Matrix Example
      Kernel, Range, Composition of Linear Transformations Example
      Eigenhandout

      Course Data
      MAT 4010 Section 101 & MAT 5530 Section 101 
      REPRESENTATION THEORY
      Meeting Times TR 9:30am-10:45am 
      Room WA 106

      Course Title & Description:
      -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
      MAT 4010-101 & 5530-101 "Group Representation Theory" 3 credits
 
      Prerequisite: 3110

      Title: "Group Representation Theory"

      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.
      -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

      Any questions about this class? 
      Send me an email at cookwj@appstate.edu