Math 100B:  Abstract Algebra

  Instructor:  Prof. A. Wadsworth                                                                 Winter Quarter, 2008

  Lectures:   MWF, 2:00 - 2:50 PM in Center Hall 222.    

  Discussion section:  Thursday 3 - 3:50 PM in Center Hall 203.  

  Prerequisites:  Math 100A and Math 20F.  It is assumed that you have completed
Math 100A or the equivalent before beginning 100B.  If you have not taken 100A,
please consult with Prof. Wadsworth as soon as possible so that we can determine
whether you have sufficient background for 100B.  It is also assumed that you have
completed a first linear algebra course comparable to Math 20F.

  Grading:  35% homework;  20%  midterm test;  45% final exam.

  Final Exam:  Monday, March 17,  3 - 6 PM.    

  Current office hours and e-addresses: 

        Prof. Wadsworth, office:  7131 AP&M;  hours:  Wednesday, 3 - 4 PM  and
             Friday, 11 AM - 12 noon;  e-mail:  arwadsworth@ucsd.edu

        TA:  Neal Harris, office:  6341 AP&M;  hours: Wednesday 9:30 - 11:30 AM
             e-mail:  r nharris@math.ucsd.edu 

****UPDATE****(1/8/08):  Neal Harris's office hours for this week, on Wed., 1/9 are changed to
                      9 - 10:45 AM.
**** **** **** **** ****

   Texts:  J. A. Beachy and W. D. Blair, Abstract Algebra, Third Edition, Waveland Press.  
              K. Hoffman and R. Kunze, Linear Algebra, Second Edition, Prentice Hall.   Course
information handout:  Click here for a copy of the course information handout,
which will also be distributed in the first class meeting.  This handout and the homework
assignments will be pdf files, which are viewable using Adobe Acrobat Reader.  To
download a free copy of this, click on Adobe Acrobat Reader.
 
   Homework:  There will be weekly homework assignments due to be turned in by the
beginning of class on Friday.  The homework can be turned in at class or to the homework
drop box on the 6th floor of AP&M.  The homework must be turned in on time.  Late
homework will not be graded, except for very good cause (such as illness).   The first
homework assignment is due this Friday, January 11.  The homework assignments will
be posted here as pdf files. 

  The first homework assignment is due Friday, January 11.

  New office hours:  Beginning the second week of classes, Neal Harris's office hours
will be Wednesday, 9 - 10 AM and 12:15 - 1:15 PM.

  The second homework assignment is due Friday, January 18.

  The third homework assignment is due Friday, January 25.  Next Wednesday, Jan. 23,
we'll look at an example similar to the first part of the last added problem on this
assignment.  So, don't spend a lot of time on that problem before then if you don't see how
to do some parts of it.  Update (1/23/08):  Here are a few hints for Added Problem 3:
Part (c) uses part (a), but you don't need (b) for (c).  (You should still do part (b).)
For part (e), you can cut down the amount of trial and error in seaching for a if you use
properties of the norm map N: Z[i] --> Z given by N(a+bi) = (a+bi) (a-bi) = a2 + b2 = | a+bi |2
This map N is multiplicative, i.e., you can check that  N(rs) = N(r) N(s) for any r and s in Z[i].
Therefore since you want an a such that 5 is a multiple of a in Z[i], N(5) must be a multiple of
N(a) in Z.  Likewise N(3 +i) must be an integer multiple of N(a).  This leaves few possible
choices for a.

  The fourth homework assignment is due Friday, February 1.

  Midterm test:  The midterm test will be given in class on Monday, February 11.

  Here is a solution to Added Problem 2 on HW3.

  The fifth homework assignment is due Friday, February 8.

  Prof. Wadsworth will have extended office hours 11AM - 1 PM on Friday, Feb. 8.

  The sixth homework assignment is due Friday, February 15.

   In light of the midterm test on Monday, 2/11, Neal Harris will hold a review session Saturday, 2/9,
2 - 3 PM in the Calc Lab,  B402A in AP&M.  Also,  Prof. Wadsworth will have extra office hours
Monday, 2/11, 11:30 AM - 12:30 PM.

  Please bring a bluebook for the test.  For this midterm, the general nature of most of the problems
will be like the homework problems (but of course taking into account the time constraints of the
test).  But, in addition, you should know definitions of the basic concepts, and proofs of the important
theorems.  You are responsible for the topics covered in class (through the proof that PID's are UFD's)
and on your homework through hw 5 (due 2/8).  These are covered in the text in portions of Ch. 4, 5,
and 9, but you are not responsible for topics in the text not covered in class or in the homework.

  Starting this Friday, Feb. 15, Prof. Wadsworth has extended his Friday office hours to:  11 AM - 12:30 PM.

  The seventh homework assignment is due Friday, February 22.

  The eighth homework assignment is due Friday, February 29.

  The ninth homework assignment is due Friday, March 7.

  The tenth homework assignment is due Friday, March 14.

  Correction on hw 10:  In problem 1(e),  where it says  Bn  it should read  bn id. 

  In class on Friday, March 14 you'll be asked to fill out  a course evaluation form.  Here is the form, if you
would like to fill it out in advance and bring it to the class.

   Neal Harris' review session on Saturday at 10 AM will be in 7218 AP&M.  (This is the seminar
room opposite Prof. Wadsworth's office.)  Prof. Wadsworth's pre-exam office hours will be:
Sunday 12 noon - 2 PM,  and Monday 10:30 AM - 12:30 PM. 

  The final exam will be given Monday, March 17, 3 - 6 PM in the course classroom, Center 222.
Please bring a bluebook.  The exam is comprehensive of the entire course, though there might be
a slightly greater weight on what has been covered since the midterm test.  You are responsible for
what has been covered in class and in the homework, but not for topics in the text that were not
covered.