I will be putting the assignments
on this page (probably after the class).
Date Due 
Set # 
Problems 
Comments 
Thurs. Aug 31 
Section 1.1 #4(a,b,d),8,10; Section 1.2 #4(a,d), 6(ae), 14, 18; Section 1.3 #3a, #6(h,i), 7b; Section 1.4 #19a, 22 
Welcome aboard! 

Tues. Sept. 5 
Section 2.1 # 5b,7,11,13, 21, 25 

Thurs. Sept 7 
Section 2.2 #11(b,f,h), 12(af), 16,17, 29, 32 

Tues. Sept 12 
Section 2.3 # 5b, 8, 10, 15(b,e), 18 


Thurs. Sept 14 
Section 2.3 #19, 22, 26, 27. Section 2.4 # 3(a,c,e) 


Tues. Sept 19 
Section 2.4 # 3d, 4, 9, 10, 11, 12 (hint –use #11) 
Cool article about new result on cardinalities of two infinite sets 

Thurs. Sept 21 
Section 2.4 #17, 23; Section 3.1 #3, 23(b,c), 24 


Tues. Sept 26 
Section 3.2 #3(d,g,i), 4, 6(b,c), 12b, (13 – optional, just for fun) 
You can use 6a to prove 6b. Note I changed problem 12 to just part b. 

Thurs. Sept 28 
Section 3.3 # 3, 4, 6, 8 
We will also review for the midterm on Thursday – bring your questions. 

Tues. Oct. 3 

MIDTERM 1 

Tues. Oct 10 
Section 3.4 # 2 (a,b,g,h,i), 3,4,5, 7 (f,g,h) 
Powerpoint slides: Section 3.1, Section 3.2, Section 3.3, Section 3.4, Section 3.5, Section 3.6 

Thurs. Oct 12 
Section 3.4 #6, 7(a,b,c,e), 10, 12, 14, 15, 18c; Section 3.5 #3 


Tues. Oct 17 
Section 3.5 #5, 7, 8, 9, 10a, 
Hint on 7a. Show that each of these open sets has a rational number in it and that these rational number are all different. Hence the number of such sets can’t be uncountable. Hint on 8a. Start with an open covering of T, extend this to an open cover of S (using the fact that T is closed) and then use the fact that S is compact to get a finite subcover (of S and then of T). 

Thurs. Oct 19 
Section 3.5 #2,6; Section 3.6 # 3,7,8 


Tues. Oct 24 
Section 4.1 #4, 5, 6(a, b, c, d), 10 


Thurs. Oct 26 
Section 4.1 #7(a,e), 12, 13, 14 Section 4.2 #4a (just the first part) 


Tues. Oct. 31 
Section 4.1 #6f; Section 4.2 # 3a, 5(b,c,d,i,j,k,l); 8,12, 15c; Section 4.3 #3(a,d) 
(On problem 5 – no proof necessary, unless you want to, but maybe give an indication of why you gave your answer. 

Thurs Nov. 2 


Tues. Nov. 7 

MIDTERM 2 

Tues. Nov. 14 
Section 5.1 #4, 6a, 13, 16 
There is a typo in #4 – it should be x^{2} +
2x – 8. 

Thurs. Nov 16 
Section 5.1 #1,6c,14; Section 5.2 #3,4,18 


Tues. Nov. 28 
Section 5.2 #6(a,d,e,f), 10,14, 16, Also, find a continuous function f: R > R and an open set U such that f(U) is not open. Can you also find a closed set C with f(C) not closed? 
Happy Thanksgiving!!! 

Thurs. Nov. 30 
Section 5.3 # 3(a,b,c,e,f), 4,7 
Hint: All assigned parts of #3 are false – you should find a counterexample for each. 

Tues. Dec. 5 
Section 5.3 #6,9; Section 9.1 #3, (#4 optional) 


Thurs. Dec 7 

Review day 
Some review problems – we will discuss these in class 
Mon. Dec 11 

FINAL 
1:30 – 4:15 in 200 Perkins 
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