AM106 (AM206): (Advanced) Applied Algebra

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.
Other links for this course:
  • Course announcement; Detailed information about the course. Make sure you read this for Collaboration Policy, Grading Policy, Important Dates, and other details.
  • Canvas Sites (AM 106, AM 206): You will need this link to submit your problem sets.
  • Piazza site. Q&A site for the course. Sign up here.
  • Essays (for AM 206): Instructions and a list of topics is here. Select your topics right away!

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). Solution (pdf).
  • 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. Solution (pdf).
  • 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. Solution (pdf).
  • 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. Solution (pdf).
  • 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. Solution (pdf).
  • 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. Solution (pdf).
  • 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. Solutions (pdf).
  • 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. Solution (pdf).
  • 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. Solution (pdf).
  • 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. Solution (pdf).
  • 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. Solution (pdf).
  • 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.