MATH 3320 HOMEWORK ASSIGNMENT #6
DUE IN CLASS FRIDAY OCTOBER 11
Check several times, homework may be added as material is covered
You should do the problems as we cover the material. Look for similar problems with solutions in
the book, and check your ans
MATH 3320 HOMEWORK ASSIGNMENT #1
DUE IN CLASS FRIDAY SEPTEMBER 6
You should do the problems with solutions from the book rst and check your answers to
be sure you understand the methods.
Book problems:
page 32, 1, 3, 6, 12, 13
Other problems:
A: Find gcd(
MATH 3320 HOMEWORK ASSIGNMENT #8
DUE IN CLASS FRIDAY NOVEMBER 1
Read the section on sums of squares page 227. Read sections on Gaussian integers in
chapter 11
Book problems:
Work through problems 8-24 and 8-25.
Work through problems 11-1 through 11-5.
Han
MATH 3320 HOMEWORK ASSIGNMENT #9
DUE IN CLASS FRIDAY NOVEMBER 9
Read the section on x2 + y2 = z2 , Pythagorean Triples. Class notes are posted on the
web.
Book problems:
Work through problems 8-1, 8-4, 8-5, 8-8.
Hand in:
Page 263, 1, 5, 6.
It would be mos
MATH 3320 HOMEWORK ASSIGNMENT #10
DUE IN CLASS FRIDAY NOVEMBER 22
Read the section on continued fractions of irrational numbers in chapter 9.
Hand in:
Page 308, 18a, 21, 30.
1
MATH 3320 HOMEWORK ASSIGNMENT #7
DUE IN CLASS FRIDAY OCTOBER 18
These are review problems from chapter 5
You should do the problems as we cover the material. Look for similar problems with solutions in
the book, and check your answers to be sure you under
MATH 3320 HOMEWORK ASSIGNMENT #4
DUE IN CLASS FRIDAY SEPTEMBER 27
Check several times, homework may be added as material is covered
You should do the problems as we cover the material. Look for similar problems with
solutions in the book, and check your a
MATH 3320 HOMEWORK ASSIGNMENT #2
DUE IN CLASS FRIDAY SEPTEMBER 13
You should do the problems with solutions from the book rst and check your answers to
be sure you understand the methods.
Book problems:
page 64: 4, 7, 25, 27, 28
Read section on Day of the
Math 3320 Problem Set 11
1
1. As a sort of converse to Wilsons theorem, show that if n is not a prime then (n 1)!
is not congruent to 1 mod n . More precisely, when n > 4 and n is not prime, show
that n divides (n 1)! , so (n 1)! 0 mod n . What happens wh
MATH 3320 HOMEWORK ASSIGNMENT #3
DUE IN CLASS FRIDAY SEPTEMBER 20
There will be a Quiz on Friday with problems similar to the Homework
You should do the problems as we cover the material. Look for similar problems with
solutions in the book, and check you
Mathematics 3320: EXAM 1, October 20, 2013
Name and Student Number:
For credit you MUST show ALL work.
Academic Integrity is expected of all students of Cornell University at all times,
whether in presence or absence of members of the faculty.
Understandi
Mathematics 3320: SOLUTION TO EXAM 1
Problem 1 (10 pts): Use Wilsons theorem to show that (p1)! p1 ( p(p1).
Solution: We know (p 1)! 1 (p) by Wilsons theorem. We claim (p 2)!
=
1 (p). Write (p 2)! a (p). Then
1 (p 1)! = (p 1)(p 2)! = p(p 2)! (p 2)! a (p)
MATH 3320 HOMEWORK ASSIGNMENT #10
DUE IN CLASS FRIDAY NOVEMBER 16
Read sections in chapter 9:
Finite continued fractions, Solutions to ax + by = c, Innite continuous fractions, Innite continued
fraction of an irrational number.
Results from the sections o
Mathematics 3320: REVIEW, Fall 2013
I will use the suggested problems below when I make up the quiz(es) and nal.
You need not do all of them, and many were covered already in the homework.
But having worked through the solutions, looked up the results use
MATH 3320 HOMEWORK ASSIGNMENT #12
DUE IN CLASS FRIDAY DECEMBER 6
This problem provides a framework to review the Euclidean Algorithm and its relation to Continued
Fractions, the Chinese remainder theorem, and Eulers theorem. You can use a symbolic algebra
MATH 3320 HOMEWORK ASSIGNMENT #5
DUE IN CLASS FRIDAY OCTOBER 4
Check several times, homework may be added as material is covered
You should do the problems as we cover the material. Look for similar problems with
solutions in the book, and check your answ
1
Math 3320 Prelim Solutions
1. In this problem let us call a rectangle whose length equals twice its width a domino.
(a) Show that a 2970 rectangle can be covered with a nite number of nonoverlapping
dominoes of various sizes, with no two dominoes having
1
Math 3320 Take-Home Prelim
Rules: The only person you can communicate with about any of the problems is the
instructor, who you are free to consult for clarication of the meaning of any of the
problems.
1. In this problem let us call a rectangle whose l
Math 3320 Problem Set 9 Solutions
1
1. Preliminary comments: A quadratic form Q(x, y) = ax 2 + bxy + cy 2 is called primitive if the greatest common divisor of the coecients a, b, c is 1 . If Q is not primitive, it can obviously be written as dQ where Q i
Math 3320 Problem Set 8 Solutions
1
1. Determine the number of equivalence classes of quadratic forms of discriminant = 120 and list one form from each equivalence class. Solution : We use the relationship = h2 + 4pq which holds for each edge of the
separ
Math 3320 Problem Set 1 Solutions
1
1. (a) Make a list of the 16 primitive Pythagorean triples (a, b, c) with c 100 , regarding (a, b, c) and (b, a, c) as the same triple. Solution: Plugging in values for p and q of opposite parity in the formulas x = 2pq
Math 3320 Problem Set 11
1
1. Make a list of all the Gaussian primes x + yi with 7 x 7 and 7 y 7 . (The only actual work here is to gure out the primes x + yi with 0 y x 7 , then the rest are obtainable from these by symmetry properties.) 2. Factor the fo