MATH-UA 343, Spring 2019: Algebra I

Basic information

Grading scheme

Final exam40%

Exam dates

About assignments

Assignments will usually be given on Tuesdays and handed in at class the next Tuesday. Collaboration is encouraged, but each student must write up and hand in their own solutions. If you work closely with someone else, please identify them on your assignment (e.g., "I worked with __________").

Late assignments will not be accepted except in the case of an emergency. If you expect to be absent on a day when an assignment is due, you can give your assignment to a classmate to turn in for you. At the end of the semester, your two lowest assignment grades will be dropped from your average. This is meant to accommodate non-emergency absences, so try not to use this unless you have to.

Solving problems is important! Doing exercises and understanding the assignments is the best way to master the material.

How to do well in this class

Problem sets

Course outline

1/29, 1/31 Sets and functions, what is a group? Ch. 1, 2, 3.1-3.2  
2/5, 2/7 Subgroups and cyclic groups Ch. 3.3, 4.1-4.2  
2/12, 2/14 Permutations and symmetries Ch. 5 Quiz 1
2/19, 2/21 Odd and even permutations, the alternating group Ch. 5  
2/26, 2/28 Cosets Ch. 6  
3/5, 3/7 Number theory, Euler and Fermat's Theorems, isomorphisms Ch. 6, 9.1 Quiz 2
3/12, 3/14 Cayley's theorem, products, homomorphisms Ch. 9.2, 11.1  
3/26, 3/28 Kernels and images, factor groups Ch. 10 Midterm
4/2, 4/4 Isomorphism theorems, finite abelian groups Ch. 11.2, Navarro  
4/9, 4/11 Rings    
4/16, 4/18 Polynomials and polynomial rings   Quiz 3
4/23, 4/25 Factorization    
4/30, 5/2 Vector spaces and fields   Quiz 4
5/7, 5/9 Vector spaces and fields