MAT 127A Fall 2019)

MAT 127A: Real Analysis (Fall 2019)
Homework Assignments

Each assignment is due by the end of lecture on the given date. Late homework will not be accepted. Solve the assigned problems in order, staple the properly assembled pages, and print your name clearly on the front page and write the number of your section (either A1 or A2) in red on the top right corner of the front page. Do not fold. Your assignment will be graded and then then returned to you in the discussion session. Assignments will be graded not only on correctness but also on the quality of writing; in particular, the reader is instructed to stop reading if a solution is incoherent.

The problems listed below (from Abbott's book) are those that you need to turn in, unless explicitly stated otherwise. Some solutions will be provided, but will not be carefully proofread, so check for mistakes!

Due Date Problems
HW1 Fri., Oct. 4 1.2: 1, 3(a,c,d,e), 6(d), 7(c), 9(b), 11 , 12, 13.

Review of logic and set theory. Do not turn in this assignment.

Solutions.

HW2 Fri., Oct. 11 1.3: 3(a), 7, 8, 9, 11.

1.4: 1, 2, 3, 5.

Solutions

HW3 Fri., Oct. 18 2.2: 2(a), 5(b), 7.

2.3: 1(b), 3, 4 (assume an are in (0,1)), 9, 10(a,b,c). Optional: 11.

Solutions

HW4 Fri., Oct. 25 2.4: 1, 3(b), 5, 7.

2.5: 1(a)(b)(c), 2(b)(c)(d), 5, 7.

Solutions

HW5 Fri., Nov. 1 2.6: 2, 5.

2.7: 4, 7 (before 7(b), prove 7(*): if Σnxn converges absolutely and (yn) is bounded, then Σnxnyn converges absolutely) 8, 11.

Solutions

HW6 Fri., Nov. 8 3.2: 1(b), 2, 3, 4, 7(a), 11.

Solutions

HW7 Fri., Nov. 15 3.3: 1, 2(a)(b)(d)(e), 4, 5, 11(only give an example for 2(b)), 13

Solutions

HW8 Fri., Nov. 22 All problems on Discussion Problems 9.

The solutions are provided, but you are not allowed to look at them while you write your solutions. The problems will also be discussed in the Discussion session.

HW9 Mon., Dec. 2

Note the due date, due to Thanksgiving break.

4.2: 2(a), 5(c), 6, 7, 11.

4.3: 1, 6(a)(b)(e), 8.

Solutions