MATERIAL for the course: representation theory of finite groups and Galois theory in characteristic zero

Miki's last office hours:
Monday May 9: Miki will be available at 6pm  today to answer any last questions you have about the grading.
For finals week: Miki will go over the practice final on Monday (5/16) at 6pm, and also be around Tuesday if
you want to come and ask more questions.

Test final on the web page. To download just point your browser to the files test_final.* where *\in \{tex,dvi,ps,pdf\}
Links: tex test_final.tex dvi test_final.dvi ps pdf test_final.pdf
Don't forget to hit reload button!!!!!!!!!!!!!!!!
MATH      18.702   Algebra   Assignments
 Number and date of assignment Actual assignment -- Numbers refer to exercises given in Artin's book (see below) Deadline (see algorithm below)
 Exercises I, Wednesday, Feb 2.  7.1.5, 7.2.5, 7.2.15, 7.2.16, 7.3.10, 7.7.9, 7.7.10, 7.7.11, 7.7.12 Wednesday, Feb 9, in class.
 Exercises II, Wednesday, Feb 9.  9.1.1, 9.1.8, 9.4.6, 9.5.7, 9.5.10, 9.5.12, 9.5.13(2x) Note: When finding character tables use the results of the book,  especially Theorem 5.9. (This won't have been completely proved in the lectures yet...)
Wednesday, Feb 16, in class.
 Exercises III, Wednesday, Feb 16 .  9.6.3, 9.6.9, 9.m.8, 9.m.9, and: Determine the character table of the permutation group S_5. Hint: Use that S_5 acts on a set with 10 elements (namely the set of pairs of elements of {1,2,3,4,5}) to produce an additional charater.  (2x)
Wednesday, Feb 23, in class.
 Exercises IV, Wednesday, Feb 23. 13.1.3, 13.2.1, 13.2.5, 13.3.1, 13.3.2, 13.3.3, 13.3.8, 13.3.11
Wednesday, March 2, in class.
 Exercises V, Wednesday, March 1.  13.3.13, 13.5.1, 13.5.4, 13.6.5, 13.6.7, 13.6.15, 13.m.1, 13.m.3 Wednesday, March 9, in class.
 Exercises VI, Wednesday, March 8.  13.8.1, 13.8.3, 13.9.2, and: (1) Give a good estimate for the number of irreducible monic polynomials of degree d over the field with p elements. (2) Let K be an extension of degree 4 of Q(= rational numbers). How many distinct subfields can K have? Give examples. (3) Let F be a field of characteristic p and let a be an element of F which is not a pth power of an element of F. Show that X^p-a is irreducible in F[X]. Wednesday, March 16, in class.
 Exercises VII, Wednesday, March 15.   Plain TeX file: exVII.tex  dvi file: exVII.dvi  ps file:  pdf file: exVII.pdf
Wednesday, March 30, in class.
 Exercises VIII, Wednesday, March 29.  Plain TeX file: exVIII.tex  dvi file:  exVIII.dvi ps file: pdf file: exVIII.pdf
Wednesday, April 6, in class.
 Exercises IX, Wednesday, April 5.  14.1.17, 14.1.18, 14.5.2, 14.5.9, 14.5.11, 14.6.3 Wednesday, April 13,  in class.
 Exercises X, Wednesday, April 12.   13.4.1, 13.4.4, 14.3.3, 14.3.4 Optional , 14.5.8, 14.8.3 Wednesday, April 20, in class.
 Exercises XI, Wednesday, April 19.  14.8.5, 14.8.9, 14.m.1, 14.m.12, and (1) Let K \subset L be an extension of fields of characteristic zero. Let n be an integer prime to [L:K]. Let a be an element of K. Show that if a is an nth power in L then a is an nth power in K.
Wednesday, April 27, in class.
 Exercises XII, Wednesday, April 26 Plain TeX file: XII.tex dvi file: XII.dvi ps file: pdf file: XII.pdf
Wednesday, May 4, in class.

(2x) This exercise is worth 8 points in stead of 4. (Generally exercises are worth 4 points.)
         This exercise is optional!

Some information on this course:

1. BOOK: Michael Artin, Algebra, Prentice-Hall, Inc.
    The edition I'm using is May 1991, which is the only one available as far as I know.

2. Notation used in listing the exercises: The expression a.b.c signifies:
    Chapter a, Section b, Exercise c.
    It can happen that b=M; this refers to the miscellaneous problems section.

3. Lectures are on MWF, 10-11 in 4-105.
    Attendance is strongly encouraged. In particular, you won't know the material covered if you don't show up!

4. Homeworks assigned: Usually in the Wednesday lecture.

5. Homeworks due:  STRICT DEADLINE: Give your work to me in class on wednesday.
    Any late homework that makes its way to the grader Miki (see below) on Wednesday will
    be graded and 50% of the grade will count.

6. Names of grader(s):
    Miki Havlickova.  E-mail:
    Office: 2-229.  Office hours: Monday 4:30-5:30, 4th floor, building 2, stairwell accross from 2-290.

7. GRADING: There will be a final exam but no midterm.
    The final exam will make up roughly 40% of the final grade.

8. Office hours: 11-12 on Friday.

9. The above is subject to change. Bug reports are welcomed!