- The syllabus is here
- Test 1 solutions are here.
- Test 2 solutions are here. Here's another way to do problem 5 that a student proved on their test.
- 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
Here is another 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
- 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!
My Lecture notes:
- 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.
Student lecture notes from Spring 2018:
(Thank you Cynthia for all the notes, except for week 13 part 2 which was provided by Amy.)