MATH 4460 - Theory of Numbers

Class Information:

Homework:

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
covers 
HW 1 and HW 2

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
covers
HW 3, 4, 5

14

5/3 - lecture notes

5/5 - lecture notes

15

5/10 - lecture notes

5/12- lecture notes

Finals week

5/17 - 

FINAL EXAM
2:30pm - 4:30pm

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: