Applied Math 106: Applied Algebra

Prof. Salil Vadhan

Lecture Notes, Handouts, and Assignments

To compile LaTeX versions of lecture notes, use macros.tex and header.tex.

Date Title Notes Reading
Tue 9/4 Course Overview, Induction pdf, tex Gallian Ch. 0
Thu 9/6 The Integers pdf, tex Gallian Ch. 0
  Problem Set 0 (due 9/14) pdf, tex  
Tue 9/11 Modular Arithmetic, Relations, Algorithms pdf, tex  
Thu 9/13 Measuring Complexity, The Euclidean Algorithm pdf, tex  
  Problem Set 1 (due 9/21) pdf, tex  
Tue 9/18 Extended Euclid, Primality & Factoring, Intro to Groups pdf, tex Gallian Ch. 2
Thu 9/20 More Groups and Basic Properties pdf, tex Gallian Ch. 1,2
  Problem Set 2 (due 9/28) pdf, tex  
Tue 9/25 Subgroups, Cyclic Groups pdf, tex Gallian Ch. 3,4
Thu 9/27 Cyclic Groups & Cryptography pdf, tex Gallian Ch. 4
  Practice Quiz I    
Tue 10/2 Permutation Groups pdf, tex Gallian Ch. 5
Thu 10/4 Quiz I    
  Problem Set 3 (due 10/12) pdf, tex  
Tue 10/9 Isomorphisms and Cosets pdf, tex Gallian Ch. 6-7
Thu 10/11 Cosets pdf, tex Gallian Ch. 7
  Problem Set 4 (due 10/19) pdf, tex  
Tue 10/16 Direct Products pdf, tex Gallian Ch. 8, 11
Thu 10/18 Normal Subgroups & Factor Groups pdf, tex Gallian Ch. 9
  Problem Set 5 (due 10/26) pdf, tex  
Tue 10/23 Homomorphisms, Isometries pdf, tex Gallian Chs. 10, 27

Thu 10/25

Group Theory & Crystallography

pdf, tex,
handout

Gallian Ch. 28
  Problem Set 6 (due 11/2) pdf, tex  
Tue 10/30 Rings pdf, tex Gallian Chs. 12, 13
Thu 11/1 Properties of Rings pdf, tex  
  Problem Set 7 (due 11/10) pdf, tex  
Tue 11/6

EthiCS Module led by Kate Vredenburgh:
Basic vs. Applied Research

pdf Effective Altruism, Strangers Drowning,
Mathematician's Apology
Thu 11/8 Ideals and Factor Rings pdf, tex Gallian Ch. 14
  Practice Quiz II pdf, tex  
Tue 11/13 Ring Homomorphisms pdf, tex Gallian Ch. 15
Thu 11/15 Quiz II    
  Problem Set 8 (due 11/30) pdf, tex  
Tue 11/20 Polynomial Rings pdf, tex Gallian Ch. 16
Thu 11/22 No Class - Thanksgiving    
Tue 11/27 Factorization & Ideals in Polynomial Rings, Field Extensions pdf, tex Gallian Chs. 16-17
Thu 11/29 Vector Spaces pdf, tex Gallian Ch. 19
  Problem Set 9 (due Monday 12/10) pdf, tex  
Tue 12/4 Error-Correcting Codes pdf, tex  
Thu 12/6 Conclusions pdf, tex  
  Final Exam Practice pdf, tex  
Thu 12/13 Review Session I (7-9pm, MD 223)    
Sun 12/16 Review Session II (7-9pm, MD 223)    
Wed 12/19 Final Exam (9am-12pm, Harvard Hall 102)