ELEMENTARY NUMBER THEORY
EXAM I SOLUTIONS
(1) Prove that the system of congruences has a simultaneous solution exactly when
a b (mod (u, v), in which case the solution is unique mod [u, v].
xa
(mod u)
xb
(mod v)
(2) Given that f (x) 0 (mod 15) has solutio

ELEMENTARY NUMBER THEORY
TAKEHOME QUIZ 2
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(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
Thursday, September 8th, 2016
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HOMEWORK 3 SOLUTIONS/HINTS MATH 4341 (FALL 2016)
Problem 1. a) Suppose T1 and T2 are two different topologies on a set X. When is the
identity map id : X X given by id(x) = x a continuous map from (X, T1 ) to (X, T2 )?
b) Show that the subspace topology T

ELEMENTARY NUMBER THEORY
TAKEHOME QUIZ 1
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(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
Thursday, September 1st, 2016
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STAT 4351: Notes on Conditioning
Yuly Koshevnik
What We Need to Know
These notes summarize technical details about conditioning, that is conditional probabilities and
conditional expectations. The textbook (Chapters 3 5) has several gaps and the notes pre

Electric Potential Energy and Potential
We so far looked at
i) electric charge (Q, measured in C)
ii) Force (F, measured in N)
iii) Field (E, measured in N/C)
iv) Flux (! , measured in Nm2/C)
Now, let us introduce electric potential
energy; well denote it

HOMEWORK 2 SOLUTIONS MATH 4341 (FALL 2016)
Problem 1. Define a relation on R by
C = cfw_(x, y) | x y Z.
Show that C is an equivalence relation and describe the set of equivalence classes of C.
Proof. (Description of equivalence classes) Every real number

Course Syllabus:
Course Information
Course Number/Section
Course Title
Term
Days & Times
PHYS2326.501
FALL 2016
PHYSICS2326.501.16F
Electromagnetism & Waves
Fall 2016
Tuesdays and Thursdays 5:30pm-6:45pm SLC 1.102
First class meeting August 23rd
Professor

Course Syllabus
Elementary Number Theory
Course Information
MATH 3323.001 Elementary Number Theory, Fall 2015, course number 87509
Class meets Tuesdays and Thursdays, 10:00 am to 11:15 am in CB1 room 1.106.
Professor Contact Information
Dr. Paul Stanford,

ELEMENTARY NUMBER THEORY
TAKEHOME QUIZ 2 SOLUTIONS
1. Definitions
All variables represent integers.
Denition 1 (Divides). a | b when ax = b for some integer x.
Denition 2 (Coprime). a b when, for all d, d | a and d | b = d | 1.
Denition 3 (Greatest Common

ELEMENTARY NUMBER THEORY
TAKEHOME QUIZ 1 SOLUTION
Date: October 19, 2015.
1
2
TAKEHOME QUIZ 1 SOLUTION
1. Questions
(1) Question:
Use the Extended Euclidean Algorithm to nd the greatest common divisor of
the given numbers, and other requested values. Your

ELEMENTARY NUMBER THEORY
TAKEHOME QUIZ 1
Full Name:
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Due Date:
Tuesday September 22nd, 2015
Date: September 14, 2015.
1
2
TAKEHOME QUIZ 1
(1) Please print this takehome quiz and ll in your name
and net id clearly.
(2) You may insert additional blan

HOMEWORK 1 SOLUTIONS MATH 4341 (FALL 2016)
Problem 1. Let A be a set and let B be a collection of sets. Show that:
[
[
A
B =
(A B),
BB
A
\
BB
B =
BB
A\
[
\
(A B),
BB
B =
BB
A\
\
\
(A \ B),
BB
B =
BB
[
(A \ B).
BB
Proof. I will prove theTlast equality. The