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:

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). Solutions.
  • 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). Solutions.
  • 09/25/17: Lecture 7 - Permutation Groups. [Notes. Reading: Gallian, Chapter 5.]
  • 09/27/17: Lecture 8 - Isomorphisms and Cosets.[Notes. Reading: Gallian, Chapters 6 and 7.]
  • 09/27/17: PS 4 Out. Due 10/11/17. (submission link). Solutions.
  • 10/02/17: Lecture 9 - Membership in Permutation Groups in Polynomial Time. [Notes. 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. [Notes. Reading: Gallian, Chapters 7, 8, 11.]
  • 10/11/17: PS 5 Out. Due 10/17/17. (submission link). Solutions.
  • 10/16/17: Lecture 11 - Normal Groups and Homomorphisms.[Notes. Reading: Gallian, Chapters 9, 10.]
  • 10/18/17: Lecture 12 - Symmetry Groups and Crystallography [Notes. Additional Handout. Reading: Gallian, Chapter 27, 28.]
  • 10/18/17: PS 6 Out. Due 10/25/17. (submission link). Solutions.
  • 10/23/17: Lecture 13 - Rings [Notes. Reading: Gallian, Chapters 12, 13.]
  • 10/25/17: Lecture 14 - More Rings [Notes. Reading: Gallian, Chapters 12, 13.]
  • 10/25/17: PS 7 Out. Due 10/31/17. (submission link). Solutions.
  • 10/30/17: Lecture 15 - Ideals and Ideal Homomorphisms. [Notes. Reading: Gallian, Chapter 14.]
  • 11/01/17: Lecture 16 - Polynomial Rings.[Notes. Reading: Gallian, Chapter 16.]
  • 11/01/17: PS 8 Out. Due 11/07/17. (submission link). Solutions.
  • 11/06/17: Lecture 17 -  Divisibility and Factorization of Polynomials. [Notes. Gallian, Chapter 16.]
  • 11/08/17: Lecture 18 - Error-Correcting Codes. Decoding Reed-Solomon Codes. [Notes. Advanced topic.]
  • 11/13/17: Quiz 2
  • 11/15/17: Lecture 19 - Fields and Extensions. [Notes. Reading: Gallian, Chapters 20 and 21.]
  • 11/15/17: PS 9 Out. Due 11/29/17. (submission link). Solutions
  • 11/20/17: Lecture 20 - Vector spaces and Finite Fields. [Notes. Reading: Gallian, Chapters 19 and 22.]
  • 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]
  • 12/14/17 (2pm): Final exam in Northwest B-101 (source here).