## Math 141 Homework Assignments

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(a-e), 14, 18; Section 1.3 #3a,  #6(h,i), 7b;  Section 1.4 #19a, 22 Welcome aboard! Homework 1 (scanned) Tues. Sept. 5 Section 2.1  # 5b,7,11,13, 21, 25 Homework 2 (scanned) Thurs. Sept 7 Section 2.2 #11(b,f,h), 12(a-f), 16,17, 29, 32 Homework 3 (scanned) 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 Review sheet for midterm Tues. Oct 10 Section 3.4 # 2 (a,b,g,h,i), 3,4,5, 7 (f,g,h) Powerpoint slides: 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 Homework 17 Tues. Nov. 7 MIDTERM 2 Review sheet for midterm Tues. Nov. 14 Section 5.1 #4, 6a, 13, 16 There is a typo in #4 – it should be x2 + 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 – we will discuss these in class Mon. Dec 11 FINAL 1:30 – 4:15 in 200 Perkins