#  Applied Math 106/206: Applied Algebra 

 



## Lecture Notes, Handouts and Assignments

Sort**Date****Title****Notes****Reading**1 Sep 10

Course Overview, Induction

[Notes #1](https://people.seas.harvard.edu/~salil/am106/fall10/IntroInduction.pdf)

Gallian Ch. 0

 

Problem Set 0 (due 9/10)

[PS #0](https://people.seas.harvard.edu/~salil/am106/fall10/ps0.pdf)

 

8 Sep 10

The Integers

[Notes #2](https://people.seas.harvard.edu/~salil/am106/fall10/Integers.pdf)

Gallian Ch. 0

 

Problem Set 1 (due 9/17)

[PS #1](https://people.seas.harvard.edu/~salil/am106/fall10/ps1.pdf)

 

13 Sep 10

Relations, Algorithms

[Notes #3](https://people.seas.harvard.edu/~salil/am106/fall10/Algorithms.pdf)

 

15 Sep 10

More on Algorithms

[Notes #4](https://people.seas.harvard.edu/~salil/am106/fall10/MoreAlgorithms.pdf)

 

20 Sep 10

Intro to Groups

[Notes #5](https://people.seas.harvard.edu/~salil/am106/fall10/Groups.pdf)

Gallian Ch. 2

 

Problem Set 2 (due 9/24)

[PS #2](https://people.seas.harvard.edu/~salil/am106/fall10/ps2.pdf)

 

22 Sep 10

S_n, D_n, Subgroups

[Notes #6](https://people.seas.harvard.edu/~salil/am106/fall10/Subgroups.pdf)

Gallian Ch. 1,3

27 Sep 10

Cyclic Groups & Cryptography

[Notes #7](https://people.seas.harvard.edu/~salil/am106/fall10/Cyclic.pdf)

Gallian Ch. 4

 

Problem Set 3 (due 10/1)

[PS #3](https://people.seas.harvard.edu/~salil/am106/fall10/ps3.pdf)

 

29 Sep 10

Permutation Groups

[Notes #8](https://people.seas.harvard.edu/~salil/am106/fall10/PermutationGroups.pdf)

Gallian Ch. 5

4 Oct 10

Isomorphisms

[Notes #9](https://people.seas.harvard.edu/~salil/am106/fall10/Isomorphisms.pdf)

Gallian Ch. 6

6 Oct 10

Quiz I

 

up to 9/27, PS3, Ch. 4

 

Midterm Feedback

[Feedback](https://people.seas.harvard.edu/~salil/am106/fall10/survey-responses.pdf)

 

 

Problem Set 4 (due 10/15)

[PS #4](https://people.seas.harvard.edu/~salil/am106/fall10/ps4.pdf)

 

11 Oct 10

Columbus Day - no class

 

 

13 Oct 10

Cosets

[Notes #10](https://people.seas.harvard.edu/~salil/am106/fall10/Cosets.pdf)

Gallian Ch. 7

18 Oct 10

Direct Products

[Notes #11](https://people.seas.harvard.edu/~salil/am106/fall10/DirectProducts.pdf)

Gallian Chs. 8, 11

 

Problem Set 5 (due 10/22)

[PS #5](https://people.seas.harvard.edu/~salil/am106/fall10/ps5.pdf)

 

20-25 Oct 10

Normal Subgroups, Factor Groups, and Homomorphisms

[Notes #12](https://people.seas.harvard.edu/~salil/am106/fall10/NormalandHomomorphisms.pdf)

Gallian Ch. 9, 10

25 Oct 10

Intro to Rings

[Notes #13](https://people.seas.harvard.edu/~salil/am106/fall10/Rings.pdf)

Gallian Ch. 12, 13

 

Problem Set 6 (due 10/29)

[PS #6](https://people.seas.harvard.edu/~salil/am106/fall10/ps6.pdf)

 

27 Oct 10  
- 1 Nov 10

Symmetry Groups & Crystallography

[Notes #14](https://people.seas.harvard.edu/~salil/am106/fall10/Symmetry.pdf)  
+[Handouts](https://people.seas.harvard.edu/~salil/am106/fall10/SymmetryHandouts.pdf)

Gallian Chs.27-28

1 Nov 10

More on Rings

[Notes #15](https://people.seas.harvard.edu/~salil/am106/fall10/MoreRings.pdf)

Gallian Chs. 12, 13

 

Problem Set 7 (due 11/5)

[PS #7](https://people.seas.harvard.edu/~salil/am106/fall10/ps7.pdf)+  
[Si(111)](https://people.seas.harvard.edu/~salil/am106/fall10/Si(111)-reconstructed.pdf)

 

2 Nov 10

AM206 Essay I due

 

 

3-8 Nov 10

Ideals, Factor Rings, and Ring Homomorphisms

[Notes #16](https://people.seas.harvard.edu/~salil/am106/fall10/IdealsHomomorphisms.pdf)

Gallian Ch. 14-15

8 Nov 10

Polynomial Rings

[Notes #17](https://people.seas.harvard.edu/~salil/am106/fall10/PolynomialRings.pdf)

Gallian Chs. 16

10-15 Nov 10

Factorization and Ideals in Polynomial Rings

[Notes #18](https://people.seas.harvard.edu/~salil/am106/fall10/PolyDivisibility.pdf)

Gallian Chs. 16-17

15 Nov 10

Quiz II

 

up to 11/1, PS7, Ch. 13

 

Problem Set 8 (due 11/19)

[PS #8](https://people.seas.harvard.edu/~salil/am106/fall10/ps8.pdf)

 

17 Nov 10

Extension Fields

[Notes #19](https://people.seas.harvard.edu/~salil/am106/fall10/ExtFields.pdf)

Gallian Ch. 20-21

22 Nov 10

Vector Spaces & Algebraic Extensions

[Notes #20](https://people.seas.harvard.edu/~salil/am106/fall10/VectorSpaces.pdf)

Gallian Ch. 19, 21

24 Nov 10

Class cancelled

 

 

 

Problem Set 9 (due 12/3)

[PS #9](https://people.seas.harvard.edu/~salil/am106/fall10/ps9.pdf)

 

30 Nov 10

Finite Fields

[Notes #21](https://people.seas.harvard.edu/~salil/am106/fall10/FiniteFields.pdf)

Gallian Ch. 22

1 Nov 10

Error-Correcting Codes

[Notes #22](https://people.seas.harvard.edu/~salil/am106/fall10/Codes.pdf)

 

 

Problem Set 10 (due 12/10)

[PS #10](https://people.seas.harvard.edu/~salil/am106/fall10/ps10.pdf)

 

7 Dec 10

AM 206 Essay II due

 

 

9 Dec 10

AM 206 Presentations

 

 

17 Dec 10

Final Exam