#### Assignments

(in Adobe .pdf)

Assignment 1

Assignment 2

Assignment 3

Assignment 4

Assignment 5

Assignment 6

Assignment 7

#### Solutions

(in Adobe .pdf)

1.1 - 1.3

1.4 - 1.7

1.10 - 1.11

2.1 - 2.2

A3 extra problems

2.3 - 2.5

A4 extra problems

Midterm Solutions

2.6 - 2.7

A5 extra problems

2.8 - 2.10

A6 extra problems

## MATH 340-3: Algebra II: Rings and Fields, Fall 2017

- We meet Mondays at 11:30am-12:20pm in AQ 3003, Wednesdays and Fridays at 11:30-12:20pm in K9500
- The final exam is on Sunday December 10th at 12:00-15:00pm. Room TBA.
- The textbook
*Introduction to Applied Algebraic Systems*by Norman Reilly is available online. - For more info see the course information sheet here.

### Content

- Proving theorems about the integers, the Euclidean algorithm and modular arithmetic.
- Rings and fields: polynomial rings, the field of complex numbers.
- Finite fields: their construction and application to error correcting codes.
- An introduction to ideals and groups.

## Handouts posted here.

Euclidean Algorithm (.pdf) theorem Handout for Monday Sept 11th.

Vector Spaces (.pdf) fact sheet Handout for Friday October 6th.

Extended Euclidean Algorithm in F[x] handout for Friday October 13th.

GF(9) addition and multiplication table handout for Monday October 30th.

GF(9) table of powers from Monday November 6th.

GF(9) isomorphism example from Friday November 17th.

Notes on complex numbers, the fundamental theorem of algebra, and roots of unity: ComplexNumbers.pdf