Problem Sets 150A: Modern Algebra Fall 2008

Info | Online resources | Homework | Exams | Syllabus
Click here for current announcements in plain text.
Click here for the study list you put your contact info, to find collaborators on HW. (updated Sept 27) Also, on MyUCDavis, we have a discussion page. Feel free to post questions and answers.

Problem sets

Homework 0: , a handout from class, due ??       (we will mostly work on it together in class--complete the multiplication table, and think about the "painting" by Monday Sept 29)

Homework 1: , due October 3
Solutions by Jeff: pdf
    Optional problems: 1.1.19   1.2.10

Homework 2: , due October 13
Solutions by Jeff: pdf
    Optional problems:   2.2.16 what is written is correct, but (c) requires justification;     2.2.4 the math is correct, and now the exposition of the proof had been re-written     2.2.8    


Homework 3: , due October 20
Solutions by Jeff: pdf
        Solutions to Optional Problems 2.2.17     2.2.20b

Quiz 1 was Oct 16
Here are solutions

Homework 4: , due Oct 27

Solutions by Jeff: pdf
        Solutions to Optional Problems 2.3.1
Quiz 2 was Oct 23
Here are solutions

Note, your midterm is Oct 29 in class.         Here is a study guide of vocabulary of sorts to focus you. (It was also on the back of your Quiz2.) Remember, one of the main page links actually makes flash cards for you!
Expect material on permutation matrices and determinants from Ch1, and all of Sections 1,2,3,4,5,6 from Chapter 2. Since we have not yet done Cor 2.6.15, you won't be directly responsible for it. But we do know enough to understand Cor 2.6.13, and Jeff has talked about Cor 2.6.11 in section. See hw5 for a better idea of what you need to know by Weds.

In addition to some definitions, a proof or two, and some computations, there will also be TRUE/FALSE questions, requiring you justify the true statements and provide a counter-example for the false ones.
Barring typos or errors, here is a draft of your midterm solutions .
 

Homework 5: , due Nov 3
Solutions by Jeff: pdf  
  Optional problems:   2.6.2   2.6.6   (actually, I was hoping for a proof from scratch, like one proves the Counting Formula, not a fleshing out of Artin's proof at the bottom of pg 58).     2.6.8   2.7.3   2.7.4   2.7.5

Homework 6: , due November 10
Solutions by Jeff: pdf    
        Optional problems:   2.7.3 (oops, was listed in hw5 too!)     2.7.9   2.8.7 (please note, only the backwards direction is done; not the forward direction. i.e. this is incomplete)     2.8.9   2.10.9 (the H should be G', and it was not shown that phi is a homomorphism)   2.misc.10

Homework 7: , due November 17
Solutions by Jeff: pdf  
      Optional problems: 5.2.8

Homework 8: , due Nov 24
Solutions by Jeff: pdf  
      Optional problems: 5.4.7

This handout explaining pg 173, annotated may help. Or this version colored pg 173 that has red dots for some of the rotation points and red lines for some of the glide/reflection lines. Except g/7 is not the glide reflection line, just an easy line to see you reflect around but then translate some OTHER direction.) See hw8.html for more linked handouts and scanned pages. (The old abridged version is here.)

Homework 9: , due Dec 3
Solutions by Jeff: pdf  
        Optional problems: 5.7.6         Optional problems: 5.8.4        

   

Homework 10: , due Dec 8 (many helpful study tools/info for final; refresh often in case of updates)
Here are the final's solutions

NEW Many XC opportunities for those who know/learn LaTeX: (I guess I'll accept other typsettings like Word or MathXML, but TeX is best) Over the course of 150A, there have been several handwritten handouts. By turning them into TeX documents, including graphics (in x-fig or possibly even scanned in and included pdf or in picture format (bonus for adding color appropriately) ) , earn XC proportional to how many handwritten pages are converted. Something like 1-2pts per page. Update: All such XC is due in lecture Dec 5, or before then. I expect you to turn into me (1) a hard copy, (2) to email me the .tex file (preferably laTeX) and other relevant graphics if you included figures, and (3) I may ask you to edit it if I see errors.
It is posted to Discussion for organizing it.