AM106: Applied Algebra

General Info:
  • Lecturer: Madhu Sudan;  MD 339; email: first name at cs dot harvard dot edu; Office Hours: M 4-5pm
  • TFs: 
    • Max Hopkins. email: nhopkins at college ; Office Hours: Tuesday 10pm-midnight (location: Adams dining hall).
    • Richard Wang. email: richardmwang at college ; Office Hours: Monday: 8pm-9pm (location: Winthrop dining hall).
  • Canvas link: Will be needed to turn in assignments.
  • Piazza link: Will be used for announcements and also the best way to contact the staff.
  • Lecture Time and Location: MW 2:30-4:00 in Pierce 209.
  • Sections:  W 5-6pm in MD 221; Th 5-6pm in MD 223.
Announcements:
  • Read the course announcement!
  • Other announcements will be posted here and on Piazza. Sign up now to the piazza site for the course if you're even slightly interested in the course. You can always unsubscribe later.
  • If you are enrolling late in this class, you must still complete all psets including PS0 (without consulting the posted solutions) and turn them in.
  • PS3 is out. Due 09/26/17. (Remember to list all sources and collaborators! Note policy on lateness from here.)
  • Quiz 1 will be held *in class* on Wednesday 10/04/2017, with a single page of two-sided, handwritten cheatsheet on letter-sized paper allowed. Closed book, closed notes. Here's a practice quiz with solutions.

Calendar and Handouts (Lecture Notes, Problem Sets):

  • 08/30/17: Lecture 1 -  Introduction, Induction. [Notes. Madhu's notes. Reading: Gallian, Chapter 0.]
  • 08/30/17: PS 0 Out. Due 09/01/17 (submission link). Solutions.
  • 09/04/17: Labor Day - No classes.
  • 09/06/17: Lecture 2 - Integers: Basic Properties: Division, Remainder, Prime numbers, Factorization, Modular Arithmetic. [Notes. Madhu's notes. Reading: Gallian, Chapter 0.]
  • 09/06/17: PS 1 Out. Due 09/12/17 (submission link). Solutions.
  • 09/11/17: 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 or Lehman-Leighton-Meyer, Chapter 9.]
  • 09/13/17: Lecture 4 - Groups. [Notes. Reading: Gallian, Chapter 2.]
  • 09/13/17: PS 2 Out. Due 09/19/17 (submission link).
  • 09/18/17 Lecture 5 - Subgroups. [Notes. Reading: Gallian, Chapter 3.]
  • 09/20/17: Lecture 6 - Cyclic groups. Application: Diffie-Hellman Cryptosystem. [Notes. Reading: Gallian, Chapter 4.]
  • 09/20/17: PS 3 Out. Due 09/26/17. (submission link).
  • 09/25/17: Lecture 7 - Permutation Groups. [Reading: Gallian, Chapter 5.]
  • 09/27/17: Lecture 8 - Isomorphisms and Cosets.[Reading: Gallian, Chapters 6 and 7.]
  • 09/27/17: PS 4 Out. Due 10/06/17.
  • 10/02/17: Lecture 9 - Membership in Permutation Groups in Polynomial Time. [Advanced topic. Not available in Gallian]
  • 10/04/17: Quiz 1
  • 10/09/17: Columbus Day - no classes
  • 10/11/17: Lecture 10 - Cosets (contd.). Direct Products of Groups. Classifying Abelian groups. [Reading: Gallian, Chapters 7, 8, 11.]
  • 10/11/17: PS 5 Out. Due 10/17/17.
  • 10/16/17: Lecture 11 - Normal Groups and Homomorphisms.[Reading: Gallian, Chapters 9, 10.]
  • 10/18/17: Lecture 12 - Symmetry Groups and Crystallography [Reading: Gallian, Chapter 27, 28.]
  • 10/18/17: PS 6 Out. Due 10/24/17.
  • 10/23/17: Lecture 13 - Rings [Reading: Gallian, Chapters 12, 13.]
  • 10/25/17: Lecture 14 - More Rings [Reading: Gallian, Chapters 12, 13.]
  • 10/25/17: PS 7 Out. Due 10/31/17.
  • 10/30/17: Lecture 15 - Ideals and Ideal Homomorphisms. [ Reading: Gallian, Chapter 14.]
  • 11/01/17: Lecture 16 - Polynomial Rings.[eading: Gallian, Chapter 16.]
  • 11/01/17: PS 8 Out. Due 11/07/17.
  • 11/06/17: Lecture 17 - Error-Correcting Codes. [Advanced topic.]
  • 11/08/17: Lecture 18 - Decoding Reed-Solomon Codes. [Advanced topic.]
  • 11/13/17: Quiz 2
  • 11/15/17: Lecture 19 - Fields and Extensions. [Reading: Gallian, Chapters 20 and 21.]
  • 11/15/17: PS 9 Out. Due 11/21/17.
  • 11/20/17: Lecture 20 - Vector spaces and Finite Fields. [Reading: Gallian, Chapters 19 and 22.]
  • 11/20/17: PS 10 Out. Due 11/28/17.
  • 11/22/17: Thanksgiving holidays - no classes
  • 11/27/17: Lecture 21 - Fast Algorithms: Polynomial multiplication, FFT, and Root-finding. [Advanced topic]
  • 11/29/17: Lecture 22 - Wrap-up root-finding algorithm. Wrap-up course. [Advanced topic]
  • Date TBD: Final exam during finals week.