MA4310: Abstract Algebra

Printable version

Course description

Detailed study of abstract algebra: elementary number theory (congruences, quadratic residues, arithmetic functions), group theory (monoids, permutation groups, homomorphisms, quotients, Lagrange's theorem, finite Abelian groups, Sylow's theorems), ring theory (domains, prime and maximal ideals, quotients, PID's), splitting fields, finite fields.
Credits: 3.0
Lec-Rec-Lab: (0-3-0)
Semesters Offered: Spring
Pre-Requisite(s): MA 3310

Text

Here are my lecture notes for Group Theory: GTN.pdf . We will likely follow these notes until they run out. They cover the same essential material as Chapters 3 through 15 of the back-up text, but are a little dense. I will probably add material as I go and send you updates.
After surveying the class I may alter what we actually cover, depending on what you have learned in MA 3310, what your future plans are and what you would like me to cover.
I was originally trained in group theory and much of my early focus was the applications of group theory to combinatorics.
If I understand correctly what was covered in MA3310 Fall 2019. We may just begin with group action,

Backup Text

T.W. Judson, Abstract Algebra, (Version 2.22)

Second backup Text

J. Gallian, Contemporary Abstract Algebra.
I think many of you have this text, so we may use it.

Grading

Your grade will be based on homework assignments and midterm examinations.

Homework

Don't panic I may rethink how we do homework, but below is what I did in 2013.
All home work and take-home examinations are to be typeset in LaTeX and stored in a single file, that will be handed in periodically. You are expected to have correctly solved all assigned problems by the end of the semester. The file name must be: MA4310DLKreher.pdf, except "D" is your first initial, "L" is your middle initial and "Kreher" is your last name. Here are the home work exercises

Using LaTex

LaTeX is available from the mathlab computers. You can also download your own personal version for your PC or Laptop. Here are some instructions I found on the Internet: http://www.ling.upenn.edu/advice/latex/pc-setup.html .

Sample Exercise solution

A sample LaTeX file can be found at MA4310DLKreher.tex. Open it as if it were a .txt file. .
After running pdflatex on this file it produced the pdf file which is shown on the next page. MA4310DLKreher.pdf .