Syllabus 150A: Modern Algebra
Fall 2006

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Grades will be posted on MyUCDavis. Check regularly for errors. You have 2 weeks after the posting (so essentially 3 weeks after a HW is due) to catch errors and bring them to our attention.
Lectures: MWF 10:00-10:50am, WELLMN 230   crn: 30338
Discussion section: T 10:00-10:50am, WELLMN 230  
Instructor: Monica Vazirani, MSB 3224, phone: 752-2218, mjvazirani@ucdavis.edu OR (but only if it is really really urgent, otherwise please use the first address) vazirani@math.ucdavis.edu
In ALL emails, please put "Subject: 150A" or I will delete your email as suspected spam.
Office hours: this week, i had some pre-exam hours Mon (Dec 11) 1-3pm.
I'll add another office hour on Friday, Dec 15, 1-2:30pm. If overflowing, we may go to a room nearby my office.

T.A.: Alexander Papazoglou, MSB 3110 papazoga@math.ucdavis.edu
Office hours: Tuesdays 11am-1pm
Text: Michael Artin, Algebra, published by Prentice Hall, 1991. This is on reserve in Shield library.
Problem Sets: There will be weekly homework assignments, generally handed out on Wednesday, due the following Wednesday IN CLASS.Or at worst to your TA by noon.
You are encouraged to discuss the homework problems with other students. However, the homeworks that you hand in should reflect your own understanding of the material. You are NOT allowed to copy solutions from other students or other sources. If you do collaborate with students on a problem, please write their names at the end of your homework (collaborators: Alice, Bob, Carol, etc.). No late homeworks will be accepted. Solutions to the problems will be discussed in the discussion section. This is also a good forum to get help with problems and to ask questions!
Exams: Midterm -- November 3, Friday.

Final exam: Saturday, December 16 at 1:30 pm in ?? ? Wellman
There will be no make-up exams!
Grading: The final grade will be based on: Problem sets (and occasional quizzes) 25%, Midterm 25%, Final 50%
Prerequisites: A proof-writing class (such as 108), and a good linear algebra class (such as 22A, 67, or 167).
Web: http://www.math.ucdavis.edu/~vazirani/F06/150A.html

Online resources

Peter Scott's group theory tutorial. (revised link) Each subsection has a quiz at the bottom of the page.

Introduction to permutations, a pdf file, especially the first 10 pages. (this link seems to be inactive!)
There's a brief wikipedia entry on permutations, till I relocate this file.

Introduction to group theory

Other textbooks.

I REALLY like Artin's book, as do most professors. Many students find it a bit terse or lacking in computation and like wordier books or books with more pictures. So I'm listing a few to browse through.
1. I like Contemporary Abstract Algebra by Joseph A. Gallian . See also a related website.
2. This book has MANY examples and applications. It has come highly recommended to me. Algebra: Pure and Applied by Aigli Papantonopoulou
3. Students tend to like (but instructors not so much!): A First Course in Abstract Algebra, by John B. Fraleigh
NEW Worksheet for Burnside's Formula to be discussed/used in class Nov 20.
OLDer An annotated and colored copy of 173 from Artin.
A description of the point groups from 173 Artin.
A copy of page 173 from Artin. Printing it will help you determine point groups, since you can draw on it, draw on the back (flip), etc.
OLD
Handout on rigid motions and drawing them (Oct 30).
Handout on conjugation and relations among the rigid motions (Oct 30).
Longer (8page) handout on rigid motions (Oct 30).
Handout on conjugation and cycle notation (Oct 23).
Random other .pdf files available: hw0--symmetries of square and hexagon , handout on basis notation like [T]_B^B , a second handout on change of basis , handout on Z/nZ , extra practice problems , (note, R[x]_3 is another notation for P_3(R), polynomials of degree less than or equal to 3) more practice problems ,

Problem sets ,


Midterm!!! is Nov 3

Final Exam: Saturday, December 16 at 1:30 pm ? Wellman

Content of the lectures:

The class is based on Chapters 2,5, 6 of Artin's book. Topics to be discussed include:

Week 1
Permutations and permutation matrices
(optional--Determinants ; determinants are covered in 67)
The definition of a group
(option-- finite fields from Ch3 and GLn(Fp) ,  SLn(Fp) as examples of groups)
Week 2
Subgroups
Homomorphisms
Isomorphisms  (might review diagonalization)
Week 3
Focus on examples (Dn, Sn, An, in particular for n= 3,4,   the groups of order 8, cycle notation and conjugation in Sn )
Cosets
Week 4
Products of groups
Quotient groups
Modular arithmetic
Week 5 
Orthogonal matrices and rotation
Symmetry of plane figures
The group of motions of the plane
Midterm
Week 6
Finite groups of motions
Discrete groups of motions / the wallpaper patterns
Week 7
Group operations (focus on examples)
Operation on cosets
The Counting Formula (focus on examples)
Applications of Burnside's Formula (optional; Papantonopoulou is a good reference)
Week 8
Finite Subgroups of the rotation group (Tetrahedral group)
Operations of a group on itself
Class equation
Week 9
Operations on subsets
Sylow Theorems
The Groups of order 12
Week 10
Computations in the Symmetric Group
The free group
Generators and relations

If there is time, one may cover select parts of Chapters 9.