Algebra I

Math 653-600

Fall 1997




Instructor: Peter F. Stiller
Office: Milner Hall 215 or Blocker Bldg. 634B
Office Phone: 5-5727 or 2-2905
E-mail: stiller@math.tamu.edu
Office Hours: Fall Schedule



Course Information

Time: TR 2:20 to 3:35
Place: BLOC 105
Text: Algebra 3rd Edition by Serge Lang, Addison Wesley (1993).
Supplementary Material: See the bibliography below
Prerequisites: The equivalent of Math 415-416. The student should also be familiar with concepts from linear algebra.
Grades: Mid-term Exam (25%), Final Exam (25%), Research Project (25%), Problem Sets (25%). The Mid-term Exam, as well as the Final Exam, will be given in class. Homework problems will be assigned on a regular basis. This will include five special Problem Sets which will be turned in for a grade. The Research Project will involve outside reading and an oral report (below) .
Overview: This course will introduce the students to the basic objects of algebra: groups, rings, modules, fields. We will study a number of important topics including the theory of groups, Galois theory, and avanced concepts in linear algebra and representation theory.



Syllabus

Detailed Description: We will cover a substantial portion of the text. Chapters 1-4 will be covered this semester, along with topics from Part Two.

Topics



Bibliography:




Week #1 September 1-5

Read Chapter 1, pgs. 1-13. Try the following exercises:

Note: Exercises marked with an asterisk are especially recommended.


Week #2 September 8-12

Continue reading Chapter 1, pgs. 13-20. Try the following exercises:

Note: Exercises marked with an asterisk are especially recommended.


Week #3 September 15-19

Continue reading Chapter 1, pgs. 20-25. Try the following exercises:



Week #4 September 22-26

Continue reading Chapter 1, pgs. 36-42.

Note: Exercises marked with an asterisk are especially recommended.


Week #5 September 29 - October 3

Continue reading Chapter 1, pgs. 42-46.

Note: Exercises marked with an asterisk are especially recommended.


Week #6 October 6 - 10

Continue reading Chapter 1, pgs. 25-33.

Note: Exercises marked with an asterisk are especially recommended.


Week #7 October 13 - 17

Continue reading Chapter 1, pgs. 33-36.

Note: Exercises marked with an asterisk are especially recommended.


Week #8 October 20 - 24

Continue reading Chapter 1, pgs. 49-53.

Note: Exercises marked with an asterisk are especially recommended.


Week #9 October 27 - 31

Continue reading Chapter 1, pgs. 66-74.

Note: Exercises marked with an asterisk are especially recommended.


Week #10 November 3 - 7

Read Chapter 2, pgs. 83-91.

Note: Exercises marked with an asterisk are especially recommended.


Week #11 November 10 - 14

Continue reading Chapter 2, pgs. 92-97.

Note: Exercises marked with an asterisk are especially recommended.


Week #12 November 17 - 21

Continue reading Chapter 1, pgs. 97-107.

Note: Exercises marked with an asterisk are especially recommended.


Week #13 November 24 - 26 Thanksgiving Holiday

Continue reading Chapter 2, pgs. 107-114.

Note: Exercises marked with an asterisk are especially recommended.


Week #14 November 31 - December 4

Read Chapter 4, pgs. 173-194.

Note: Exercises marked with an asterisk are especially recommended.


Assignment #1

Do the following exercises ......




Assignment #2

Do the following exercises:




Assignment #3

Do the following exercises ......




Assignment #4

Do the following exercises ......




Assignment #5

Do the following exercises ......






Project Information

The major project consists of reading a paper (or other source) for information on one of the topics below and writing a brief synopsis of the key result(s). A 20 minute oral presentation will be given during the last week of the course.



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