
Section/Topic Covered 

HW due 
September  
3 
rational numbers 
HW#1 

5 
ordered sets, sup and inf 


8 
ordered fields, real numbers, Archimedean property 

HW#1 
10  the rationals are dense in the reals, examples of sup and inf, 
HW#2 

12  Nested Interval Theorem, finite/infinite sets  

15 
countable/uncountable 


17 
conclusion, start of metric spaces, examples 
HW#3 
HW#2 
19 
limit points, closed sets 


22  open sets, closure of a set begun 

24 
closure completed, compact sets begun 
HW#3 

26 
more on compactness 
HW#4 

29 
kcells are compact 


October 

1 
HeineBorel theorem, connected sets 

3 
sequences, convergence  HW#4 

6 
norm of a linear space, properties of sequences  
8 
more properties 

10  midterm
1 solutions 

15 
subsequences, Cauchy sequences 

17 
complete metric spaces 
HW#5 

20 
monotone sequences, series  

22 
geometric series, Cauchy Condensation Test 


24 
ratio test 
HW#5 

27 
root test 
HW#6 

29 
integral test, alternating series 


31 
alternating harmonic series, rearrangements 

November 


3 
rearrangements finished, functions started 
HW#7 
HW#6 
5 
limits of functions, sequential equivalence 

7 
continuity and compactness 

10 
continuity and connectedness, uniform continuity 
HW#7 

12 
discontinuities 
HW#8 

14 
continuity/discontinuity examples 

17 
the derivative 

19 
properties of the derivative 
HW#8 

21 
midterm 2 solutions


24 
examples 


December  

1 
extrema, mean value theorem 
HW#9 

3 
more on the MVT 


5 
intermediate value property 

8 
Cantor set 
HW#9 

10 
Cantor set concluded, questions 

18 
Final 12:30 p.m. 