## Math 4320, Intro to Real Analysis II, Spring 2018

Course Syllabus

## Assignments, Announcements, Hand-Outs, etc.

Welcome to Math 4320 Reall Analysis II. Take a look at the course syllabus, and if you're ready you can start on Homework #1..
Homework will (usually) be posted here on Monday or Tuesday, and due in class the following
Monday (unless stated otherwise). We will usually go over the homework problems on the day they are due,
but I will not collect or grade your homework solutions. Sometimes there will be a short quiz after we
discuss the homework which will be graded.

Homework #1, due Monday, January 29
Section 10.1 #2,7

Section 10.2 #1,2

Section 10.3 #1,2,7,11

Homework #2, due Monday, February 5
Section 11.1 #4,5,6,9

Section 11.2 #1,6,7,9,10

Homework #3, due Monday, February 19
Section 12.1 #3,4,5

Section 12.2 # 1,2,8,9,10

Note that I just changed the due date for HW#3 to next week.
Also, according to the syllabus, Exam #1 is Wednesday, February 21.
The exam will cover the material we covered in chapters 10,11,12, including the "bonus material"
on the topological definition of compactness. Monday, 2/19 will be a review day.

Here are a few practice problems on point-set topology.
1) What is the boundary of the set Q = rational numbers (subset of R^1)?

2) Prove that x is on the boundary of A if and only if for every epsilon, the open ball
B_epsilon(x) intersects A and A^c (A compliment).

3) Use the topological definition of compactness (via open covers) to prove that any closed subset
of a compact set is compact. (Don't use the closed and bounded charactarization of compact subsets
in Euclidian space.)

Here are solutions for Exam #1.