#### Abstract Algebra, Fall 2020

##### Links & Materials

- Syllabus
- Textbook, Judson,
*Abstract Algebra: Theory and Applications* - Introduction to LaTeX on Overleaf (free online tool for typing and compiling LaTeX files)
- NYU classes webpage
- Lecture notes by Margaret Bilu, NYU, Fall 2019
- Sample midterm (Solutions), Fall 2019
- Sample midterm (Solutions), Spring 2020

##### Lecture Notes

- Lecture 1 (Sets, Quantifiers, Maps.)
- Lecture 2 (Inverse Maps. Equivalence relations.)
- Lecture 3 (Integers. Divisibilty. Eucledian Algorithm.)
- Lecture 4 (Congruence relations. Ring Z_n.)
- Lecture 5 (Units in Z_n. Laws of composition.)
- Lecture 6 (Groups. First examples.)
- Lecture 7 (Cayley tables. Subgroups.)
- Lecture 8 (Cyclic subgroups.)
- Lecture 9 (Order of an element.)
- Lecture 10 (Isomorphisms.)
- Lecture 11 (Cosets.)
- Lecture 12 (Lagrange's theorem .)
- Lecture 13 (Permutations. Cycles)
- Lecture 14 (Cycles factorizations.)
- Lecture 15 (Parity of permutations.)
- Lecture 16 (Homomorphisms & Kernels.)
- Lecture 17 (Cayley's theorem. Dihedral group)
- Lecture 18 (Cosets of Kernels.)
- Lecture 19 (Normal subgroups.)
- Lecture 20 (First isomorphism theorem.)

##### Homework Assignments

- Homework 1 (due Wednesday, September 16) LaTeX template for solutions
- Homework 2 (due Wednesday, September 23) LaTeX template for solutions
- Homework 3 (due Wednesday, September 30)
- Homework 4 (due Wednesday, October 7)
- Homework 5 (due Wednesday, October 14)
- Homework 6 (due Wednesday, October 28)
- Homework 7 (due Thursday, November 5)
- Homework 8 (due Wednesday, November 11)
- Homework 9 (due Wednesday, November 18)
- Homework 10 (due Wednesday, November 25)
- Homework 11 (due Wednesday, December 2)