Ma 005c:  Introduction to Abstract Algebra (Spring 2016-17)

ANNOUNCEMENTS

Registration for Spring term opens Thursday, February 23, 2016.

This page was last updated:  .


First Midterm

The mid term will be handed out in class on Wednesday 5/3/2017. It will be due in class on Monday 5/8/2017. You are allowed to use class notes, and parts of the textbook as you do for homework. You are not allowed to collaborate!


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Tensor Products!

Keith Conrad has very good notes on tensor products that address a lot of the common confusions people have when first learning about them. I highly recommend them. Part 1 and Part 2.


COURSE DESCRIPTION

The third term of Ma 5 will cover the theory of field extensions, Galois theory and representation theory. The lecture material will be taken from Parts IV and VI of Dummit and Foote. Some but not all of the homework will come from the textbook. Other texts you may wish to consult: Michael Artin's algebra book and Serge Lang's Algebra text. , as will the exercises, with some additional supplementary material provided.


PREREQUISITES

The only prerequisites are Ma 5ab


SCHEDULE

MWF 09:00 - 09:55, 151 Sloan.


INSTRUCTORS

Pablo Solis
OLGA TAUSSKY AND JOHN TODD INSTRUCTOR IN MATHEMATICS
360 Sloan
626-395-4336


TA's

Jize Yu


OFFICE HOURS

My office hours: Thursdays 4-5
360 Sloan

Jize: Fridays 4-5
158 Sloan


POLICIES

Grades

The assessment will include homework every week, which will count towards 50% of the grade, a Midterm and a Final examination; each worth 25% and will be a timed (4 hour) take-home exam. Extensions of one day will most likely be granted IF REQUESTED AT LEAST 2 DAYS PRIOR TO DUE DATE. Extensions of two days or longer may be granted in some circumstances. Late assignments are only accepted in extreme circumstances.


TOPICS COVERED

The first few weeks are didicated to the construction of field extensions. This usually is an extension of a field by the solution of an irreducible polynomial over that field. After extensions are covered, we then define the Galois group and applications of the main theorem of Galois theory which outlines a correspondence between subgroups and subfields. We end the course with some representation theory of finite groups.


TEXTBOOKS

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

Other texts you may wish to consult: Michael Artin's algebra book and Serge Lang's Algebra text


LECTURE NOTES

Date Description
    Notes
   
   

HOMEWORK

For the homework you are allowed to draw upon your knowledge from 5a,5b and use results in the text upto and including section 13.6. (This marker will be updated as the course progresses)

Please turn in homework into Jize's mail box directly and NOT into the math 5c homework box.
All the problems are in THIS pdf file; you may have to download the file and open with adobe for the file to display correctly.

Here are optional problems for additional practice; they will not be graded.

Due Date Homework Solutions
 4/10/2017, 5pm  Probems #1-#3  
  4/18/2017, 5pm   Probems #4-#7  
  4/26/2017, 5pm   Problems #8 - #10  
  5/2/2017, 5pm   Problems #11 - #13  
     
     
     
     

EXAMS

 


READING