Math 316 Midterm 3
Wednesday, November 13, 2013
Professor Michael VanValkenburgh
Name:
Instructions: Show all of your work, and clearly indicate your answers. Use the backs of pages as scratch
paper. You will need pencils/pens and erasers, nothing more. K
Math 316 Midterm 2
Monday, October 14, 2013
Professor Michael VanValkenburgh
Name:
Instructions: Show all of your work, and clearly indicate your answers. Use the backs of pages as scratch
paper. You will need pencils/pens and erasers, nothing more. Keep
Math 316 Midterm 1
Friday, September 20, 2013
Professor Michael VanValkenburgh
Name:
Instructions: Show all of your work, and clearly indicate your answers. Use the backs of pages as scratch
paper. You will need pencils/pens and erasers, nothing more. Kee
Math 316 Midterm 1
Friday, September 20, 2013
Professor Michael VanValkenburgh
Name:
Instructions: Show all of your work, and clearly indicate your answers. Use the backs of pages as scratch
paper. You will need pencils/pens and erasers, nothing more. Kee
Math 316 Midterm 2
Wednesday, March 5, 2014
Professor Michael VanValkenburgh
Name:
Instructions: Show all of your work, and clearly indicate your answers. Use the backs of pages as scratch
paper. You will need pencils/pens and erasers, nothing more. Keep
Math 316 Midterm 2
Wednesday, March 5, 2014
Professor Michael VanValkenburgh
Name:
Instructions: Show all of your work, and clearly indicate your answers. Use the backs of pages as scratch
paper. You will need pencils/pens and erasers, nothing more. Keep
Math 316 Midterm 1
Friday, February 7, 2014
Professor Michael VanValkenburgh
Name:
Instructions: Show all of your work, and clearly indicate your answers. Use the backs of pages as scratch
paper. You will need pencils/pens and erasers, nothing more. Keep
Math 316 Midterm 1
Friday, February 7, 2014
Professor Michael VanValkenburgh
Name:
Instructions: Show all of your work, and clearly indicate your answers. Use the backs of pages as scratch
paper. You will need pencils/pens and erasers, nothing more. Keep
CLOSED SETS
MICHAEL VANVALKENBURGH
This is the lecture I wouldve given today (October 4, 2013) had I not been sick.
Last time: Open Sets.
Today: Closed Sets.
(1)
(2)
(3)
(4)
The denition of limit point.
Examples.
Theorem 3.2.5 in the book. Try to prove it
CONNECTED SETS
MICHAEL VANVALKENBURGH
Contents
1.
2.
3.
4.
5.
6.
Clopen Sets
The Relative Topology
Connected Sets
Magical Proofs
Consistency with the Book
Advanced Topic: the Lebesgue Covering Lemma
2
2
3
4
6
7
We have already joked about clopen sets. Suc
MATH 316, HOMEWORK 3
DUE WEDNESDAY, FEBRUARY 12, 2014
Exercise 1. We say that a sequence (an ) converges to a R if > 0 N N such that
n=1
|an a| < n N .
We say that a sequence (an ) klonverges to a R if > 0 N N such that |an a|
n=1
n N .
We say that a seq
MATH 316, HOMEWORK 2
DUE WEDNESDAY, FEBRUARY 5, 2014
Exercise 1. (This exercise will not be graded.) Prove the following theorem:
Theorem 1. For every real x > 0 and every n N, there is a unique positive real
number y such that y n = x.
Here is an outline
MATH 316, HOMEWORK 1
DUE WEDNESDAY, JANUARY 29, 2014
Exercise 1. In class, I gave the truth tables for and, or, implies, and not. Now
prove, using truth tables, that:
(a) (P or Q) ( P )&( Q).
(b) (P Q) P &( Q).
Exercise 2. Prove, using truth tables, that
Math 316 Final Exam
Tuesday, December 17, 2013
Professor Michael VanValkenburgh
Name:
Instructions: Show all of your work, and clearly indicate your answers. Use the backs of pages as scratch
paper. You will need pencils/pens and erasers, nothing more. Ke
Math 316 Final Exam
Tuesday, December 17, 2013
Professor Michael VanValkenburgh
Name:
Instructions: Show all of your work, and clearly indicate your answers. Use the backs of pages as scratch
paper. You will need pencils/pens and erasers, nothing more. Ke