Mathematics 114, Spring 2003

Professor: Richard Borcherds

Office hours: Wednesday, Friday 1:00-2:30 927 Evans Hall
Office telephone: 642 8464

Our class meets in 85 Evans , TuTh 3:30-5:00 This is the course home page (address www.math.berkeley.edu/~reb/114).

Catalogue Description: Mathematics 114

Further topics on groups, rings and fields not covered in Math 113. Possible topics include: the Sylow Theorems and their applications to group theory; classical groups; abelian groups and modules over a principal ideal domain; algebraic field extensions; splitting fields and Galois theory; construction and classification of finite fields.

This section:

Math 114 will cover Galois theory, which is a tool for turning hard problems about polynomials and fields into (hopefully) easier problems about finite groups. The topics will include review of 113, field extensions, finite groups, the Galois correspondence, finite fields, solvability of equations by radicals.

Textbook:

Galois theory by Ian Stewart. Second edition. Published by Chapman and Hall.

Grading:

Homework will account for 40% of the grade.

Midterm 1 will account for 15% of the grade.

Midterm 2 will account for 15% of the grade.

The final will account for 30% of the grade.

Almost all the questions in the midterms or finals will be randomly selected questions from the book similar to homework questions, possibly with the constants in the questions changed. So if you understand how to do all the homework questions you will be able to do all the questions on the exams.

There will be no partial credit for incomplete answers of easy problems on the midterms or final exam. Marks for exams or quizzes will only be changed if there is a clear error on the part of the marker, such as adding up marks incorrectly or forgetting to mark a question. Marks for incomplete answers will never be increased, because this is unfair to students who do not ask for their marks to be increased.

The final homework grade will be computed from the grades for the 10 best homeworks, so it does not matter much if you forget one or two.

Examinations:

You may use a pocket calculator in the exams. You may also bring one (ordinary sized!) sheet of paper with writing on both sides to the exams. Apart from this one sheet, the exams are "closed book".

The first midterm is on ??

The second midterm is on ??

The final is on ?? It will be mostly on the material covered after the second midterm, though there will be some problems on earlier material.

Homework:

Homework is due by the end of the Tuesday lecture 1 week after it is assigned. Late homework will not be accepted. About half the marks for homework will be based on the number of questions that you made a serious attempt on, and about half will be based on more detailed marking of a few questions.

Reading and Homework Schedule
Lecture Date Reading Exercises (Due in class the next Tuesday)
01-02 1/21, 1/23 1.1-1.4 1.1,2,3,4,5,6,12,13,14,15
03-04 1/28, 1/30 1.5, 2.1-2.3 1.9,10,11; 2.1, 2, 5, 6, 8
05-06 2/04-2/06 2.4, 3.1-3.3 2.9, 2.11, 2.12, 2.14, 3.1, 3.2, 3.3, 3.8, 3.10, 3.15, 3.16, 3.17
07-08 2/11-2/13 3.4, 4.1-4.24.1, 2, 3, 5, 8, 11, 12, 14, 16, 17, 18
09 2/18
10 2/20 --- Midterm #1: Chaps 1-4.
11-12 2/25-2/27 7.1, 2, 4, 6, 7; 8.1, 2, 3, 4, 8.
13-14 3/04-3/06 8.6, 7, 11, 12; 9.2, 9.3, 9.7
15-16 3/11-3/13 11.1, 12: 1, 2, 3, 4, 5, 6
17 -18 3/18-3/20 10.1, 2, 3, 4, 6, 7
-- ---- ------------- (Spring Break 3/24-3/28)
19 4/01
20 4/03 --- Midterm2:
21-22 4/08-4/10 13. 13.1, 2, 4, 5, 9, 10, 11, 12, 14, 17
23-24 4/15-4/17 14. 3, 4, 5, 8, 10, 11, 12, 14
25-26 4/22-4/24 15. 5,6, 9a, 11, 14,15
27-28 4/29-5/1 16. 3, 4, 5, 6, 8 (first 4 cases), 9, 10 , 12
29-30 5/6-5/8 TBA TBA
-- 70 Evans Fri 5/23 12:30-3:30pm --- Final Exam:

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