Day 
Week/
Chapter 
Topic 
Assigned/
Due 
M 8/26 
1
Chapter 1 
what do we know about the real numbers? 
Assignment #1 
W 8/28 

what do we know about calculus? 

F 8/30 
Chapter 3 
metric spaces and normed vector spaces 

M 9/2 
2 
no class: Labor Day 

W 9/4 

Early Quiz (30 min)
vector spaces 
A #1 due
Assignment #2 
F 9/6 

l_{p} space 

M 9/9 
3 
inequalities in normed vector spaces: CauchySchwarz, Young's 

W 9/11 

inequalities cont.: Holder's, Minkowski's 
A #2 due
Assignment #3 
F 9/13 
Chapter 4 
convergence in metric spaces
open and closed sets 

M 9/16 
4 
cont. 

W 9/18 
Chapter 5 
continuity 
A #3 due
Assignment #4 
F 9/20 

cont. 

M 9/23 
5
Chapter 7 
complete metric spaces 

W 9/25 

proofs of completeness 
A #4 due
Assignment #5 
F 9/27 

Banach fixedpoint theorem 

M 9/30 
6 
applications: ODEs, IFSs, Newton iteration 

W 10/2 

cont. 
A #5 due 
F 10/4 
Chapter 8 
totallybounded sets 
Assignment #6 
M 10/7 
7 
compactness 

W 10/9 

cont.
review guide for Midterm I 
A #6 due 
F 10/11 

Midterm Exam I 
Midterm I 
M 10/14 

chaos
equivalent metrics 
Assignment #7 
W 10/16 
8
Chapter 10 
sequences of functions 

F 10/18 

uniform continuity/convergence 

M 10/21 
9 
a nowhere differentiable function
weierstrauss.m 

W 10/23 
Chapter 11 
Weierstrauss theorem
(polynomial approximation in C[a,b])
bernstein.m 
A #7 due
Assignment #8 
F 10/25 

overview of integration 

M 10/28 
10
Chapter 16 
Lebesgue outer measure m* 

W 10/30 

measure zero sets
Cantor set 
A #8 due
Assignment #9 
F 11/1 

m*(I)=length(I) 

M 11/4 
11 
m* is countably subadditive
measurable sets
Lebesgue measure 

W 11/6 

m is countably additive
measurable sets form a sigmaalgebra 
A #9 due
Assignment #10 
F 11/8 

nonmeasurable sets
characterization of Riemann integrability 

M 11/11 
12
Chapter 17 
measurable functions 

W 11/13 

simple functions
extended real values 
A #10 due
Assignment #11 
F 11/15 

basic construction
Borel's theorem 

M 11/18 
13
Chapter 18 
Lebesgue integral (simple; nonnegative measurable; integrable)
review guide for Midterm II 

W 11/20 

monotone convergence theorem 
A #11 due 
F 11/22 

Midterm Exam II 
Midterm II 
M 11/25 
14 
Fatou's lemma
dominated convergence theorem 
Assignment #12 
W 11/27 

no class: Thanksgiving 

F 11/29 

no class: Thanksgiving 

M 12/2 
15 
L_{1} is complete
review guide for Final Exam 

W 12/4 
Chapter 19 
approximation in L_{1}
L_{p} spaces 

F 12/6 

Fourier series
a bit of review 
A #12 due 
F 12/13 

Final Exam
1:00 pm  3:00 pm 
Final Exam 