# Math 521

## Office hours

M-Th 12:45-1PM in the class room
T and Th 2:15-5Pm in 718 Van Vleck Hall with Chandan Biswas

## Exams

There will be an in-class final on Thursday, 8/10.

## Homework

Please note: It is okay, even encouraged, if you work on the homeworks in groups. The written solutions, though, must be your own. Note that it is painfully obvious when a solution is simply copied and not understood.

There will be regular homeworks posted here:
1. Due 6/26: In Edition 1 of Pugh: Chapter 1: 1,2,3,9,10,12,13,14,15,16,*30,36
In Edition 2 of Pugh: Chapter 1: 1,2,3,9,11,13,14,15,16,18,*31,39
2. Due 7/3: In Edition 1 of Pugh: Chapter 2: 1, 2, 3, 5, 11, 12, 17, 18, 19, 20, 22, 23, 29, 30, 31
In Edition 2 of Pugh: Chapter 2: 23, 24, 25, 26, 29, 40 (a,b,c,e), 13, 14, 15, 16, 18, 19, 39, 9, 10, 11(a,b)
3. Due 7/10: In Edition 1 of Pugh: Chapter 2: 34,(a-e) , 14, 25
In Edition 2 of Pugh: Chapter 2: 28(a-e), 30, 31, 34,55
4. Due 7/17: If every closed and bounded subset of a metric space M is compact, does it follow that M is complete? (Proof or counterexample.) , Show that the 3 metrics we discussed on the product space $X\times Y$ are in fact metrics, 38, 39, 40, 27
In Edition 2 of Pugh: Chapter 2: 22, 38, 41, 43, 44, 52
5. Due 7/26: In Edition 1 of Pugh: 6, 10, Prove that if $A$ and $B$ are compact, disjoint, non-empty subsets of $M$, then there are points $a\in A$ and $b\in B$ so that for any $x\in A$ and $y\in B$, $d(a,b)\leq d(x,y)$. In other words, $a$ and $b$ are the closest you get a point in $A$ and a point in $B$ to each other., 28, 43,14,41,54,55,56,59,64a, 68,69,74,77
In Edition 2 of Pugh: 27,33,46,48,53,55,56,57,58,59,62,66a,70,71,76,77
6. Due 8/2: In Edition 1 of Pugh: 44-53, 109(a-d), 118,89,91, 92, 130
In Edition 2 of Pugh: 85-94, 99(a-d),103,122, 124, 125, 152
7. Due 8/14 (Either to Chandan Biswas's mailbox on the 2nd floor of Van Vleck or scanned and e-mailed to cbiswas@math.wisc.edu):
In Edition 1 of Pugh: 1, 2, 3, 5, 7, 8, 28, 30, 32, 34, 50, 51, 52, 53
In Edition 2 of Pugh: 1, 2, 3, 5, 6, 7, 27, 29, 31, 33, 51, 52, 53, 54,
*Problems with a star are either harder or require some more serious detail-work.