Class Information:
Homework:
- Homework #1: problems and solutions
Here's another way to solve problem 10: part 1, part 2 - Homework #2: problems and solutions
- Homework #3: problems and solutions
- Homework #4: problems and solutions
HW 4 additional problem: If n is not a perfect square, then the square root of n is irrational. The proof is here. - Homework #5: problems and solutions
- Homework #6: problems and solutions
Schedule and lecture notes:
week |
Monday | Wednesday |
1 |
1/25- lecture notes |
1/27 - lecture notes |
2 |
2/01 - lecture notes |
2/03 - lecture notes |
3 |
2/08 - lecture notes |
2/10 - lecture notes (General case proof of theorem in class if interested) |
4 |
2/15 - lecture notes |
2/17 - lecture notes |
5 |
2/22 - lecture notes |
2/24 - lecture notes |
6 |
3/01 - lecture notes |
3/03- lecture notes |
7 |
3/08 - lecture notes |
3/10 - lecture notes |
8 |
3/15 - lecture notes |
3/17 - TEST 1 |
9 |
3/22 - lecture notes |
3/24 - lecture notes |
Spring break |
3/29 - HOLIDAY |
3/31 - HOLIDAY |
10 |
4/5- lecture notes |
4/7 - lecture notes |
11 |
4/12 - lecture notes |
4/14 - lecture notes |
12 |
4/19 - lecture notes |
4/21 - lecture notes |
13 |
4/26 - lecture notes |
4/28 - TEST 2 |
14 |
5/3 - lecture notes |
5/5 - lecture notes |
15 |
5/10 - lecture notes |
5/12- lecture notes |
Finals week |
5/17 - FINAL EXAM |
5/19 - |
My notes from my notebook (if you want to look ahead):
- Topic 0 - Assumptions about the integers
- Topic 1 - Division and Primes
Note: Pages 12--15 are a handout that I will give you. - Topic 2 - GCD
(Note: There is no page 5 in the GCD notes above, that's a numbering mistake in the page numbering) - Topic 3 - Linear Diophantine Equations
- Topic 4 - The Fundamental Theorem of Arithmetic
- Topic 5 - Construction of Z_n and the properties of Z_n
- Topic 6 - Pythagorean Triples
- Topic 7 - The Multiplicative Structure of Z_n
- Topic 8 - Gaussian Integers
- Topic 9 - Fermat's Last Equation for n = 4 - This will be a handout that I will give you.
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.