**CATALOG
DESCRIPTION: **A study of
Groups, Rings and Fields, with an emphasis on the theoretical aspects
and proofs. Prerequisites: Math 415.

**Instructor: **Dr. Eric
Rowell. email: rowell@math.tamu.edu,
webpage: www.math.tamu.edu/~rowell. Office BLOC 510B

**Place and Time**: This course meets TR 9:35-10:50am

**Office hours**:
Wednesday 10-11am, Tuesday 2-3pm or by appointment (or drop in!)

**Course Objectives:** The objectives are to
learn advanced topics in modern algebra: ideals and quotients of rings,
field extensions, Sylow theory, and Galois theory.

**Text:** Fraleigh, A first course in Abstact Algebra, 7th
edition.

**Material Covered/Syllabus**: We will cover most of
Chapters V, VI, VII, and X, with additional topics from Chapter VIII or
IX if time permits.

**Grading**: Your grade will be based upon 2 Midterms
(28pts
each), Homework (15pts), and a Final (29pts) for a
total of 100 points. The grading scale is
the usual one: 90-100% A,
80-89 % B, 70-79% C,
60-69 % D, 0-59% F. Dates of exams/assignments
will be posted below.

**Homework**: Weekly homework sets will be turned in to
be
graded. Typically homework will be assigned on Thursdays and due the
following Thursday. As
writing proofs takes considerable
practice, the homework sets will
likely be quite time-consuming. Your lowest homework score will be
dropped.
Late homeworks count as a 0. Forming study
groups is encouraged, but
homework is to be done individually and be your own
work. Homework counts as 15pts, and will be posted below.
Some problems will be assigned only to students in the honors section and others to regular
section students only. Each honors section student will be asked
to present some material to the class.

Exams: There are three
exams. Calculators
are not allowed (or needed) on the exams. Honors students' exams will include
more challenging problems.

**Course Policies**: Make-ups for
missed
exams will only be guaranteed for a university approved excuse in writing,
other situtations (interviews etc.) will be considered on a
case-by-case basis, but must always
be supported with documentation.
Wherever possible, students should inform the instructor before an exam
or major assignment is
missed. Consistent with University Student Rules, students are required
to
notify an instructor by the end of the next working day after missing
an
exam. Otherwise, they forfeit the right to a make-up. Late homework is not accepted or graded. If a
homework cannot be completed due to a university approved excuse, that
homework will be dropped.

An Aggie does not lie, cheat, or steal or tolerate those who do. Copying work that was done by others is an act of scholastic dishonesty and any instance of it will be prosecuted according to University Student Rules.

The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services, currently located in the Disability Services building at the Student Services at White Creek complex on west campus or call 979-845-1637. For additional information visit http://disability.tamu.edu.

Copyright Policy: All printed materials disseminated in class or on the web are protected by Copyright laws. One photocopy (or printout from the web) is allowed for personal use. Multiple copies or sale of any of these materials is strictly prohibited.

**Important Announcements:**

** Key Dates (tentative):
**

- Exam I: February 21

- Q-drop Deadline: April 15

- Exam II: March 28

- Final Exam: Thursday May 2 12:30-2:30

**Homework Assignments/Syllabus (tentative)**

**Key: E **means** everyone, H **means**
honors (section 200), R **means** regular (section 500).
**

**HW 1 Due Jan. 24 (9:35am)**

- E: Read Fraleigh Sections 26 and 27. do: §26:
1,22,26,37; §27: 2,5,25,31,37

- R: §26: 18; §27: 18,19

- H: §26: 20; §27: 17,24

- E: Read Fraleigh Sections 26 and 27. do: §26:
1,22,26,37; §27: 2,5,25,31,37
**HW 2 Due Jan. 31 (9:35am)**- E: Read Fraleigh Sections 29,30. do: §29: 4,9,13,17; §30:
6,10

- R: §29: 1,6; §30: 26

- H: §29: 8, 32ab; §30: 27
**HW 3 Due Feb. 7 (9:35am)**

- E: Read Fraleigh Section 31. do: §31: 2,22,23,24

- R: §31: 3,5,6
- H: (read pg 288-291 again!) §31: 27,30,38

- E: Read Fraleigh Section 31. do: §31: 2,22,23,24
**HW 4 Due Feb. 14 (9:35am)**

- E: Read Fraleigh Section 33. do: §33: 3,4,9,10 also: X:
Determine the number of fields (up to isomorphism) E containing GF(2)
and contained in GF(64).

- R: §33:1,2,5
- H: §33: 11,13,14

- E: Read Fraleigh Section 33. do: §33: 3,4,9,10 also: X:
Determine the number of fields (up to isomorphism) E containing GF(2)
and contained in GF(64).
**HW 5 Due Feb. 21 (12:45pm)**

- E: Read Fraleigh Section 34. do: §34: 1abc,3abcd,7,9 and:

Let N< S_{4}be the (normal) subgroup: {e,(12)(34),(13)(24),(14)(23)} and H=<(1234)> the cyclic subgroup generated by (1234). Find |HN| using the second isomorphism theorem. Then try to write down all elements of HN.

- E: Read Fraleigh Section 34. do: §34: 1abc,3abcd,7,9 and:
**HW 6 Due Feb 28( 9:35am)**

- E: Read Fraleigh Section 16. do: §16: 9ab,12,13abc

- R: §16:1,2,3
- H: §16: 10,15

- E: Read Fraleigh Section 16. do: §16: 9ab,12,13abc
**HW 7 Due March 7 (9:35am)**

- E: Read Fraleigh Sections 36. do: §36:
5,6,11,13,17,18

- R: §36: 2,3,4
- H: §36: 16,19,20ab

- E: Read Fraleigh Sections 36. do: §36:
5,6,11,13,17,18
**HW 8 Due March 21 (9:35am)**

- E: Read Fraleigh Sections 37. do: §37:
2,4,5,6 also: do your best to classify groups of order 28, 30 or 231
(pick one).

- R: §37: 1,7
- H: §37: 8

- E: Read Fraleigh Sections 37. do: §37:
2,4,5,6 also: do your best to classify groups of order 28, 30 or 231
(pick one).
**HW 9 Due March 28(12:45pm)**

- E: Read Fraleigh Section 48. do: §48:
7,12,22abc,26,27,32,36abc,39

- R: §48: 3,11,16
- H: §48: 5,34,37

- E: Read Fraleigh Section 48. do: §48:
7,12,22abc,26,27,32,36abc,39
**HW 10 Due April 4(9:35pm)**

- E: Read Fraleigh Section 49 do: §49: 2,3,4,7a
- R: §49: 1,10
- H: §49: 6,13

**HW 11 Due April 11(9:35pm)**

- E: Read Fraleigh Section 50,51 do: §50:
2,4,5,10,18 §51: 15abc,16abc

- R: §50: 8,9
- H: §50: 17,24

- E: Read Fraleigh Section 50,51 do: §50:
2,4,5,10,18 §51: 15abc,16abc
**HW 12 Due April 18 (9:35am)**

- E: Read Fraleigh Section 51: Pick 5 problems to do (besides 15/16).

**HW 13 Due April 26 (9:35am)**

- E: Read Fraleigh Section 53,54 do: §53: 9,12,22ab §54:
4abcd,5,8

- R: §53: 1,2 §54: 1
- H: §53: 20 §54: 7

- E: Read Fraleigh Section 53,54 do: §53: 9,12,22ab §54:
4abcd,5,8