AM106: (Advanced) Applied Algebra (Fall 2016)

Madhu Sudan: AM106 (AM206): (Advanced) Applied Algebra (Fall 2016)

This course may have add additional information including problem sets and solutions. If you need these for teaching a course of your own, please write to Madhu.

General Info

Lecturer: Madhu Sudan; MD 339; email: first name at cs dot harvard dot edu; Office Hours: MW 4-5pm
TF: Jaroslaw Blasiok; MD 138; email: jblasiok at g dot harvard dot edu ; Office Hours: M 4-6pm (location MD 138).
Staff email: am106-f16-staff@seas.harvard.edu
Lecture Time and Location: MW2:30 in MD G115.
Sections: Thursdays 1pm – 2pm in Pierce 320
Thursdays 4pm – 5pm in MD221

Announcements

Final exam is from 9am-12pm on 12/12/2016 in Emerson 104. Final is closed book, but you are allowed two letter-paper-sized, handwritten, double-sided cheat-sheets. Practice final here.

Calendar and Handouts (Lecture Notes, Problem Sets)

08/31/16: Lecture 1 – Introduction, Induction. [Notes. Madhu’s Notes. Reading: Gallian, Chapter 0.]
08/31/16: PS 0 Out (pdf). Due 09/02/16 (submission links: AM 106, AM 206).
09/05/16: Labor Day – No classes.
09/07/16: Lecture 2 – Integers: Basic Properties: Division, Remainder, Prime numbers, Factorization, Modular Arithmetic. [Notes, Madhu’s Notes. Reading: Gallian, Chapter 0.]
09/07/16: PS 1 Out (pdf). Due 09/13/16.
09/12/16: Lecture 3 – Algorithms [Notes. Madhu’s Notes. Reading: Gallian, Chapter 0. For algorithms and big-Oh notation, any text on algorithms will cover basics. See, e.g., Cormen-Leiserson-Rivest-Stein, Chapter 3.]
09/14/16: Lecture 4 – Groups. [Notes. Reading: Gallian, Chapter 2.]
09/14/16: PS 2 Out (pdf). Due 09/20/16.
09/19/16: Lecture 5 – Subgroups. [Notes. (Updated 9/20/2016). Reading: Gallian, Chapter 3.]
09/21/16: Lecture 6 – Cyclic groups. Application: Diffie-Hellman Cryptosystem. [Notes. Reading: Gallian, Chapter 4.]
09/21/16: PS 3 Out (pdf). Due 09/27/16.
09/26/16: Lecture 7 – Permutation Groups. [Notes. Reading: Gallian, Chapter 5.]
09/28/16: Lecture 8 – Isomorphisms and Cosets.[Notes. Reading: Gallian, Chapters 6 and 7.]
09/28/16: PS 4 Out (pdf). Due 10/04/16.
10/03/16: Lecture 9 – Membership in Permutation Groups in Polynomial Time. [Notes.]
10/05/16: Quiz 1
10/10/16: Columbus Day – no classes
10/12/16: Lecture 10 – Cosets (contd.). Direct Products of Groups. Classifying Abelian groups. [Notes. Reading: Gallian, Chapters 7, 8, 11.]
10/12/16: PS 5 Out (pdf). Due 10/18/16.
10/17/16: Lecture 11 – Normal Groups and Homomorphisms.[Notes. Reading: Gallian, Chapters 9, 10.]
10/19/16: Lecture 12 – Symmetry Groups and Crystallography [Notes. Handout. Reading: Gallian, Chapter 27, 28.]
10/19/16: PS 6 Out (pdf). Due 10/25/16.
10/24/16: Lecture 13 – Rings [Notes. Reading: Gallian, Chapters 12, 13.]
10/26/16: Lecture 14 – More Rings [Notes. May also touch on this. Reading: Gallian, Chapters 12, 13.]
10/26/16: PS 7 Out (pdf). Due 11/01/16.
10/31/16: Lecture 15 – Ideals and Ideal Homomorphisms. [Notes. Reading: Gallian, Chapter 14.]
11/02/16: Lecture 16 – Polynomial Rings.[Notes. Reading: Gallian, Chapter 16.]
11/02/16: PS 8 Out (pdf). Due 11/08/16.
11/07/16: Lecture 17 – Error-Correcting Codes. [Notes.]
11/09/16: Lecture 18 – Decoding Reed-Solomon Codes.
11/14/16: Quiz 2
11/16/16: Lecture 19 – Fields and Extensions. [Notes. Reading: Gallian, Chapters 20 and 21.]
11/16/16: PS 9 Out (pdf). Due 11/22/16.
11/21/16: Lecture 20 – Vector spaces and Finite Fields. [Notes. Reading: Gallian, Chapters 19 and 22.]
11/21/16: PS 10 Out (pdf). Due 11/29/16.
11/23/16: Thanksgiving holidays – no classes
11/28/16: Lecture 21 – Fast Algorithms: Polynomial multiplication, FFT, and Root-finding. [No notes. For reference see this and this.]
11/30/16: Lecture 22 – Wrap-up root-finding algorithm. Wrap-up course. [No notes.]
12/12/16: Final 9am-12noon in Emerson 104.

Madhu Sudan: AM106 (AM206): (Advanced) Applied Algebra (Fall 2016)

General Info

Announcements

Other links for this course

Calendar and Handouts (Lecture Notes, Problem Sets)