d Math 5c

Math 5c

 

Introduction to Abstract Algebra

Spring 2011-12

 

 

MWF 9:00 AM // 151 Sloan

 

Course Description | Policies | Textbooks | Lectures | Handouts | Homework | Math Courses

 

Instructor: Susama Agarwala, 176 Sloan, 395-4347, susama@caltech.edu
Office Hours: Monday 1-3 pm
Graders:
Jingjing Huang, 385 Sloan jingjing@caltech.edu
Office Hours: Tuesda 7-8 pm
Liubomir Chiriac, 260 Sloan lchiriac@caltech.edu
Office Hours: Monday 4-5 pm

 

 

Feedback Form

 

Announcements

 

15 April Update to homework 2.
23 April Clarification on homework 3.

COMMENTS ON THE FINAL The final exam is 4 hours long. Not 3. I originally wrote it as a 3 hour exam. The fourth hour is for peace of mind. Also, note that it is due on Thursday, not Wednessday.

 

 

Course Description

 

 

The third term of Ma 5 will cover Galois theory and some representation theory. These topics are found in Dummit and Foote, parts IV and VI. Not all the material in the chapters will be covered. In addition, there will be supplemental material pulled from other textbooks, such at Lang that the students will be responsible for.

 

Policies

 

 

Grading: There will be a Midterm and a Final examination; each will be a timed (3 hour) take-home exam. The homework will count towards 40% of the final grade, while the midterm and Final will each count towards 30%.

Homework Policy: The solutions for the homework problems must be turned in every Wednesday by 12 PM (noon) in the marked box outside room 253 Sloan. Under regular circumstances, each students will be granted only one extension on homework, but arrangements have to be made 24 hours in advance with the instructor.

Students may, and are encouraged to, collaborate together on homework as long as each student writes up solutions individually in his or her own words. In solving homework problems, you should quote theorems and lemmas from class and the text. Results from the text in sections not yet covered or from other texts will not receive credit unless the proof is supplied. Students may always cite results proved in class or earlier in the book, or results from previously assigned problems. If the problem refers to another problem in the book, students may use results from the referred to problem, unless otherwise indicated. Any other results must be proven to be used on homeworks or exams. There is no collaboration allowed on the exams.

I reserve the right to change certain topics covered in the course if there is popular demand to do so.

 

Textbooks

 

 

Abstract Algebra by D. S. Dummit and R.M. Foote, third edition, John Wiley 2004.
ISBN: 0-471-43334-9

Class lectures will sometimes cover slightly different material and may cover material from a different point of view. In particular, exams and homework may involve material covered in lectures but not in Dummit-Foote.

Texts I will be taking material and problems from include

Algebra by S. Lang, third edition, Springer 2002

 

Lectures

 

                                                 

The following detailed syllabus may chance without notice.

 

Date

Description

Week 1

Fields, algebraic extensions, D&F 13.1 -2, Lang V.1

Week 2

Algebraic Closure, Straightedge compass construction, Splitting field D&F 13.2-3 Lang V.2-3

Week 3

Seperable and Inseperable Extensions. Finite fields. D&F 13.5 Lang V.4-6

Week 4

Galois Theory D&F 14.1-2 Lang VI.1-2

Week 5

 

Week 6

 

Week 7

 

Week 8

 

Week 9

 

Week 10

 

 

Handouts

 

 

Date

Description

 

 

 

Homework

 

 

 

  California Institute of Technology | Questions? kaubry@ caltech.edu