Class Information:
Study Guides:
Test solutions
Lecture Notes: These are the notes I'm using to teach the class. Notes for
specific days for our class will be in the calendar below.
- Topic 1 - Division and primes
- Topic 2 - GCD
- Topic 3 - Fundamental theorem of arithmetic
- Topic 4 - Z_n, the integers modulo n
- Topic 4.5 - Application to Pythagorean triples
- Topic 5 - Multiplicative structure of Z_n
- Topic 6 - Gaussian integers
Homework:
| HW 1 | |
| HW 2 | |
| HW 3 | |
| HW 4 | |
| HW 5 | |
| HW 6 |
Schedule and lecture notes:
|
week |
Monday | Wednesday |
|
1 |
1/23- lecture notes |
1/25 - lecture notes |
|
2 |
1/30 - lecture notes |
2/1 - lecture notes |
|
3 |
2/6 - lecture notes |
2/8 - lecture notes |
|
4 |
2/13 - lecture notes |
2/15 - lecture notes |
|
5 |
2/20 - lecture notes |
2/22 - lecture notes |
|
6 |
2/27 - lecture notes |
3/1- lecture notes |
|
7 |
3/6 - |
3/8 - lecture notes |
|
8 |
3/13 - lecture notes |
3/15- TEST 1 |
|
9 |
3/20 - lecture notes |
3/22 - lecture notes |
|
Spring break |
3/27 - HOLIDAY |
3/29 - HOLIDAY |
|
10 |
4/3- lecture notes |
4/5 - lecture notes |
|
11 |
4/10 - lecture notes |
4/12 - lecture notes |
|
12 |
4/17 - lecture notes |
4/19 - lecture notes |
| 13 |
4/24 - lecture notes |
4/26 - TEST 2 |
|
14 |
5/1 - lecture notes |
5/3- lecture notes |
|
15 |
5/8 - lecture notes |
5/10- lecture notes |
| Finals week |
5/15 - FINAL EXAM 2:30 pm - 4:30 pm |
Computer Programs:
- Here is a program to find z and w in the Gaussian integers where N(z) divides N(w) but z does not divide w.
It finds non-trivial cases, ie ones where N(z) is not 1 and not equal to N(w).
I only ran it with 1 < N(w) <= 10. - Here is a program that finds all the divisors of a Gaussian integer and also tests if a Gaussian integer is prime.
It does what we do in the HW but way faster.
Note that z = 100 has 180 divisors!
For Fun:
- Sums of three cubes is an unsolved problem. Computation results on this problem.