Math 4107: Abstract Algebra I
Spring 2015, Georgia Tech
Instructor: Josephine Yu (jyu@math.gatech.edu)
Office hours: Mondays 10-11, Thursdays 2-3, and by appointment, in Skiles 250
Class: MWF 2-3pm in Clough 129
Course web page: http://people.math.gatech.edu/~jyu67/teaching/2015Spring4107/
Syllabus: syllabus
Tentative Schedule: Schedule with homework assignments and reading assignments
Piazza:https://piazza.com/gatech/spring2015/math4107/home
Homework Assignments:
See schedule
for tentative list of future assignments.
- HW1 (Due 1/14, Wed): Chapter 1: 1-8, 11, 14. Solution
- HW2 (Due 1/21, Wed): Chapter 1: 17-21. Chapter 2: 1,2,4,5,9. Solution
- HW3 (Due 1/28, Wed): Chapter 2: 7, 11-19. Solution
- HW4 (Due 2/6, Fri): Chapter 2: 20,21,22,24,26,27,28,31,33,34,35. Solution
- HW5 (Due 2/23, Mon): Chapter 2: 32, 36-40, 41 or 42, 43,44,45. Solution
- HW6 (Due 3/6, Fri): Chapter 2: 46-56. Solution
- HW7 (Due 3/27, Fri): Chapter 3: 2,8,11,13,15, 20,21,25,28,31. Solution
- HW8 (Due 4/6, Mon): Chapter 3: 33,38. Chapter 4: 1, 4-8. Solution
- HW9 (Due 4/17, Fri): Chapter 4: 11,12,26,28,29,34.
- HW10 (Due 4/24, Fri): Chapter 5: 2,6,8,11,13,18-22.
Reading Assignments:
Reading Quizzes
- Quiz 0 on equivalence relations
- Quiz 1 on the definition groups
- Quiz 2 on group homomorphisms
- Quiz 3 on cyclic groups and product groups
- Quiz 4 on symmetric and alternating groups
- Quiz 5 on group actions
- Quiz 6 on rings
- Quiz 7 on polynomial rings
- Quiz 8 on term orderings
In-class worksheets
Exams
Here are old exam problems from last time I taught this class: Old Problems.
- Exam 1 (Feb 11, Wed) On Friday you can bring in solutions to (your choice of) exam problems, and you can get back up to 1/3 of lost points. Solution
- Exam 2 (Mar 9, Mon) You can turn in corrected solutions by Friday, 3/13, at 2pm. Solution
- Exam 3 (Apr 8, Wed) Solution
- Final Exam (Apr 29, 11:30am - 2:20pm)
Resources and interesting/fun links about group theory and ring theory
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.
- How to study for a mathematics degree by Lara Alcock, free e-book available through GT library. The book offers practical tips on reading, writing, and study skills.
- 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
- Some puzzles you saw on quizzes were inspired by Peter Winkler's books Mathematical Puzzles: A Connoisseur's Collection and Mathematical Mind-Benders