Problem Sets 150C: Modern Algebra Spring 2009

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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 1: , due FRIDAY Apr 3, 2009
Solutions by Qiang Wang: HW1     Optional problems: 12.1.8     12.1.11     12.1.12

Homework 2: , due Apr 10
Solutions by Wang: HW2

Homework 3: , due Apr 15
Solutions by Wang: HW3


Homework 4: , due Apr 22
Solutions by Wang: HW4

By the way, for those of you interested in further recreational reading in Diaconis's book, here is the link.

And here are the .pdf and .tex source of the handout from Apr 14th section.

Homework 5: , due Apr 29
Solutions by Wang: HW5 and HW5 extra page (note, you didn't have to do 9.8.6b only 6a, and on the last problem you could also do it just w/ characters as in the Hint)         9.5.5.pdf

a handout to go w/ apr29 lecture

your MIDTERM was May 1st
For studying, here is a preliminary vocab list for the midterm
Solutions for midterm
Rough curve for midterm: 60-70 A     54-69 B     43-53 C     32-42 D


Homework 6:
Solutions by Wang: HW6         13.2.5.pdf

Homework 7: ,   due May 20
Solutions by Wang: HW7        

[Thanks for the super-cool hand-made compass! I also found out SOMEone/s nominated me for the 7th annual ASUCD Excellence in Education Awards. I'm not a finalist, but it's a GREAT honor to be nominated! Thanks for your hard work and thoughtfulness for submitting my name!!]

Homework 8: , (i clarified the last question)   due May 27
Solutions by Wang: HW8     [Note, an alternate TEDIOUS soln to 7e(iii) is that ψ(a2) = ψ(A +B a1 + C a12) = A +B ψ(a1)+ C ψ(a1)2 = A +B a2 + C a22     and then use (a) and (e)(i) to see after a lot of hard computation that this really IS a3.]
      ALSO, here is a handout on roots of unity showing how to use Galois theory to justify [Q(ζr) : Q ] = φ(r)     (not just ≤ as in the HW).
            13.4.2.pdf (note, that the construction really does give 2 pi/5 is not justified/verified)         13.4.5.pdf         13.4.6.pdf         13.4.7.pdf         13.4.8.pdf         13.4.9.pdf (note, Artin asks for a geometric solution, whereas the given one is algebraic.)         13.4.10.pdf

Homework 9: ,   due June 3
Solutions by Qiang Wang: HW9


See http://www.math.ucdavis.edu/~vazirani/S09/exams.html#exams for info on the final and a study guide