Math 6121: Algebra I (Graduate level)
Fall 2015, Georgia Tech
Instructor: Josephine Yu (jyu@math.gatech.edu)
Office: Skiles 250
Email: jyu@math.gatech.edu
You are encouraged to contact me (and your classmates) through Piazza.
Class: Tuesdays and Thursdays, 9:35 am - 10:55 am, in Skiles 257
Office hours: Mondays 1-3pm and by appointment, in Skiles 250.
You are also welcome to talk to me after class (unless I have a meeting to go to).
Syllabus: here
Course web page: https://people.math.gatech.edu/~jyu67/teaching/2015Fall6121/
Schedule: Tentative Schedule. I will be updating this throughout the semester.
Piazza: Sign-up link
Course Description
Textbook: Abstract Algebra (3d edition) by Dummit and Foote.
Other recommended references:
We will follow the official topic outline fairly closely.
One of the goals of this course to prepare students for the Algebra Comprehensive Exam. We will learn most of the material listed in items 2-6.
Homework Assignments:
On every homework due date, there will be a quiz at the beginning of the class.
Exams
- Exam 1: Sep 24
- Exam 2: Nov 5
- Final Exam (Apr 29, 11:30am - 2:20pm)
Resources and interesting/fun links about groups, rings, and fields
If you find an interesting page, please send me an email and I will add it to the list.
- How many perfect shuffles are required to put a deck of 2n cards into its original position? See how it depends on n.
- Why is group theory important?
- Multiplicative group of integers modulo n
- Groups of small order
- Dihedral groups
- Symmetric groups
- The classification of finite simple groups, List of finite simple groups
- Applications to physics: Noether's theorem, Higgs Boson
- Applications to computer science: RSA cryposystem, RSA Factoring Challenge(no longer active), Elliptic curve cryptography, coding theory, e.g. Verhoeff algorithm which uses the dihedral group of order 10, automata theory
- Applications to chemistry.
- Applications to molecular systems biology.
- History of group theory. Lagrange (1736-1813), Abel (1802-1829), Galois (1811-1832), Klein (1849-1925), Noether (1882-1935)
- Finite simple group of order two
- Solving Rubik's Cube in 20 moves