# Applied Math 106/206: Applied Algebra ## Lecture Notes, Handouts and Assignments Sort**Date****Title****Notes****Reading**2,9,14 Sep 09 Introduction, the Integers, and Algorithms [Notes #1](https://people.seas.harvard.edu/~salil/am106/fall09/lec1.pdf) Gallian Ch. 0 16 Sep 09 Primes & Factorization, Group Theory: Def & Examples [Notes #2](https://people.seas.harvard.edu/~salil/am106/fall09/lec2.pdf) Gallian Ch. 0,2 Problem Set 1 (due 9/23) [PS #1](https://people.seas.harvard.edu/~salil/am106/fall09/ps1.pdf) 21 Sep 09 More Groups [Notes #3](https://people.seas.harvard.edu/~salil/am106/fall09/lec3.pdf) Gallian Ch. 1,2 23 Sep 09 Subgroups and Cyclic Groups [Notes #4](https://people.seas.harvard.edu/~salil/am106/fall09/lec4.pdf) Gallian Ch. 3,4 Problem Set 2 (due 9/30) [PS #2](https://people.seas.harvard.edu/~salil/am106/fall09/ps2.pdf) 28 Sep 09 Cyclic Groups and Cryptographic Applications [Notes #5](https://people.seas.harvard.edu/~salil/am106/fall09/lec5.pdf) Gallian Ch. 4 30 Sep 09 Permutation Groups [Notes #6](https://people.seas.harvard.edu/~salil/am106/fall09/lec6.pdf) Gallian Ch. 5 5-7 Oct 09 Isomorphisms [Notes #7](https://people.seas.harvard.edu/~salil/am106/fall09/lec7.pdf) Gallian Ch. 6 7 Oct 09 Quiz I Until Notes #5, Gallian Ch. 4. Problem Set 3 (due 10/21) [PS #3](https://people.seas.harvard.edu/~salil/am106/fall09/ps3.pdf) 12 Oct 09 No class: Columbus Day 14 Oct 09 Automorphisms & Cosets [Notes #8](https://people.seas.harvard.edu/~salil/am106/fall09/lec8.pdf) Gallian Chs. 6-7 Midterm Feedback Responses [Feedback](https://people.seas.harvard.edu/~salil/am106/fall09/survey-responses09.pdf) 19 Oct 09 Orbits & Stabilizers, External Direct Products [Notes #9](https://people.seas.harvard.edu/~salil/am106/fall09/lec9.pdf) Gallian Chs. 7-8 21 Oct 09 Normal Subgroups and Factor Groups [Notes #10](https://people.seas.harvard.edu/~salil/am106/fall09/lec10.pdf) Gallian Ch. 9 Problem Set 4 (due 10/28) [PS #4](https://people.seas.harvard.edu/~salil/am106/fall09/ps4.pdf) 26 Oct 09 Homomorphisms [Notes #11](https://people.seas.harvard.edu/~salil/am106/fall09/lec11.pdf) Gallian Ch. 10 28 Oct 09 Computational Group Theory [Notes #12](https://people.seas.harvard.edu/~salil/am106/fall09/lec12.pdf) Gallian Ch. 11 Problem Set 5 (due 11/4) [PS #5](https://people.seas.harvard.edu/~salil/am106/fall09/ps5.pdf) 2 Nov 09 Rings [Notes #13](https://people.seas.harvard.edu/~salil/am106/fall09/lec13.pdf) Gallian Chs. 12-13 4 Nov 09 Ideals [Notes #14](https://people.seas.harvard.edu/~salil/am106/fall09/lec14.pdf) Gallian Ch. 14 Problem Set 6 (due THU 11/12) [PS #6](https://people.seas.harvard.edu/~salil/am106/fall09/ps6.pdf) 9 Nov 09 Homomorphisms [Notes #15](https://people.seas.harvard.edu/~salil/am106/fall09/lec15.pdf) Gallian Ch. 15 11 Nov 09 No class: Veteran's Day 16 Nov 09 Polynomial Rings [Notes #16](https://people.seas.harvard.edu/~salil/am106/fall09/lec16.pdf) Gallian Chs. 16-17 18 Nov 09 Quiz II Until Notes #14, Ch. 14 Problem Set 7 (due Wed 12/2) [PS #7](https://people.seas.harvard.edu/~salil/am106/fall09/ps7.pdf) 23 Nov 09 Ideals and Factors of Polynomial Rings [Notes #17](https://people.seas.harvard.edu/~salil/am106/fall09/lec17.pdf) Gallian Chs. 14,16,17 25 Nov 09 Vector Spaces [Notes #18](https://people.seas.harvard.edu/~salil/am106/fall09/lec18.pdf) Gallian Chs. 19,21 30 Nov 09 Extension Fields [Notes #19](https://people.seas.harvard.edu/~salil/am106/fall09/lec19.pdf) Gallian Chs. 20-21 2 Dec 09 Finite Fields, Error-Correcting Codes [Notes #20](https://people.seas.harvard.edu/~salil/am106/fall09/lec20.pdf) Gallian Ch. 22 Problem Set 8 (due Wed 12/9) [PS #8](https://people.seas.harvard.edu/~salil/am106/fall09/ps8.pdf)