| 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: exVII.ps 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: exVIII.ps 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: XII.ps 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: mikihavl@mit.edu
Office: 2-229. Office hours: Monday 4:30-5:30,
4th floor, building 2, stairwell accross from 2-290.
9. The above is subject to change. Bug reports are welcomed!