Class Information:
- << the syllabus will go here >>
Study Guides:
- << study guides will go here >>
Test solutions
- << test solutions will go here >>
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 | 1/22 - lecture notes | |
| 2 | 1/27 - lecture notes | 1/29 - lecture notes |
| 3 | 2/3 - lecture notes | 2/5 - lecture notes |
| 4 | 2/10 - lecture notes | 2/12 - lecture notes |
| 5 | 2/17 - lecture notes | 2/19 - lecture notes |
| 6 | 2/24 - lecture notes | 2/26 - lecture notes |
| 7 | 3/3 - lecture notes | 3/5- lecture notes |
| 8 | 3/10 - lecture notes | 3/12 - lecture notes |
| 9 | 3/17 - lecture notes | 3/19 - TEST 1 |
| 10 | 3/24 - lecture notes | 3/26 - lecture notes |
| SPRING BREAK | 3/31 - HOLIDAY | 4/2 - HOLIDAY |
| 11 | 4/7 - lecture notes | 4/9 - lecture notes |
| 12 | 4/14 - lecture notes | 4/16 - lecture notes |
| 13 | 4/21 - lecture notes | 4/23- lecture notes |
| 14 | 4/28 - lecture notes | 4/30 - TEST 2 |
| 15 | 5/5 - lecture notes | 5/7 - lecture notes |
| Finals week | 5/12 - 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.