MATH 4460 - Theory of Numbers

Class Information:

Past Lecture Notes:

Homework:

HW 1
HW 2
HW 3
HW 4
  • Here are the problems and solutions
  • Here is an additional problem:
    Problem: If n is not a perfect square, then the square root of n is irrational.  
    Solution: The proof is here.

HW 5
HW 6


Schedule and lecture notes:

week

Monday Wednesday

1

1/24- lecture notes

1/26 - lecture notes

2

1/31 - lecture notes

2/2 - lecture notes

3

2/7 - lecture notes

2/9 - lecture notes
                 +
         proof of general
      theorem from class

4

2/14 - lecture notes

2/16 - lecture notes

5

2/21 - lecture notes

2/23 - lecture notes

6

 2/28 - lecture notes

3/2- lecture notes

7

3/7 - lecture notes

3/9 - TEST 1 

8

3/14 - lecture notes

3/16 - lecture notes

9

3/21 - lecture notes

3/23 - lecture notes

Spring break

3/29 - HOLIDAY

3/31 - HOLIDAY

10

4/4- lecture notes

4/6 - lecture notes

11

4/11 - lecture notes

4/13 - lecture notes

12

4/18 - lecture notes

4/20 - lecture notes

13

4/25 - TEST 2

4/27 - lecture notes

14

5/2 - lecture notes

5/4 - lecture notes

15

5/9 - lecture notes

5/11- lecture notes

Finals week

5/16 -

final
2:30 - 4:30

5/18 -

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: