General information homework, syllabus, etc. 
  
Students in the course    
Gloss 
Some words from Selberg 

I graded the final exam and this morning (Sunday, December 21)
posted course grades on the Registrar's computer system. I assigned grades
based on a "figure of merit" which gave 50% of the weight to homework
and 50% of the weight to exams. As the course evolved I decided this
would be a fair way to assess student accomplishment, both in
restricted time (exams) and on tasks with more reflection allowed
(homework).
I hope you have a nice winter break. 
Title (with PDF links) 
What is it?  Handed out or posted 

The final exam  Here is the final exam, in a more compact format. Although I
haven't prepared answers, here is a version of the exam
with some comments which students might find useful.
Grades ranged from 39 to 156.  12/20/2008 
Homework #6  The assignment is chapter 5: 2, 3, 5, 8, 11, 15, 21. Graded homework can be picked up on or after Monday, December 15.  12/15/2008 
The second exam  The second exam was given on November 24. A takehome version was
handed out on November 27, due December 1 due to what some students
perceived as a tragedy (i.e., they couldn't do enough of the exam
perfectly). I tried to address this feeling with comments in class.
The grades on the version given in class ranged from 10 to 72. The grades on the takehome version ranged from 34 to 100. I remark that with few exceptions (mostly students whose homework was markedly better than their exam performance) the rank ordering of the exams was very close.  12/8/2008 
Homework #5 
I think that the assignment is Chapter 3: 6, 10 and Chapter 4: 4, 6,
7, 11. YOU can do problem 5 of the fourth chapter also if you wish. I
decided not to ask my colleague's question. Perhaps I will save it for
another occasion.
Some controversy has arisen about whether we or the textbook has proved the following result: if X and Y are compact metric spaces, then XxY is a compact metric space. I think that some volunteer student should step up and send me a proof via email. I will post this proof, and then everyone can use this result. A 411 proof now exists, thanks to Mr. Leven, and I will give him credit as if this were a presentation. Thank you very much! Now everyone can use this fact!  11/7/2008 
The first exam Some possible answers to the first exam 
Here is a compact version of the first exam and some possible
answers. 11/23/2008 The answer to the second question (about connectedness) has been substantially rewritten, thanks to comments from Mr. Ratner. He expressed some correct concerns about its logic and expression. I believe the current version is an improvement. Here are further comments on the grading and the exam questions.  10/21/2008 
Homework #4  The fourth homework assignment, due on Thursday, October 23. The problems on this assignment discuss material which may be tested on our first exam on Monday, October 20. The homework assignment also discusses the material to be tested.  10/16/2008 
Homework #3  The third homework assignment, due on Thurday, October 9. For those who care, the assignment number is now correct, the due date is on the assignment, and the ches (a silly problem caused by a T_{E}X error) no longer appears. The N/B disagreement has been fixed (I think of Neighborhoods as Balls, and my notation sometimes shows a leak from thought to action!). I thank Ms. Pritsker for an advisory message about some of these issues. Sigh.  9/29/2008 
Homework #2  The second homework assignment, due in a week (Thursday, 9/25)
if we cover enough material in today's class and Monday's
class. Added in the evening: several slight misprints in problem 1 detected by Mr. Ratner have been corrected. I thank him and wonder if there are any more. Hot news (sigh): another correction has been made. Now, in problem 2, the max has been changed to a min. I am happy to thank Ms. Slusky for this. Happy happy happy ... Will there be more corrections? Could your name be here next? Added 9/22/2008: Mr. Skalit wonders what I want for the last part of problem 2. My response included this: If (X,d) is a metric space, then there is a metric D on X so that the open sets obtained from (X,D) are exactly the same as the open sets obtained from (X,d), and also the diameter of D (which is sup{D(x,y) : x and y in X}) is a finite number. That is, the two topologies (the Dopen and the dopen), which are subsets of the set of subsets of X, are the same. Math 411: timedependent homework is a good thing.  9/18/2008 9/19/2008 
Some answers to the entrance exam  Here are, indeed, some answers to the entrance exam.  9/11/2008 
Homework #1  The first homework assignment, due in a week (Monday, 9/15). All of the problems are due on that day, please. Also, I've gotten some inquiries about problem #1. I mean the following: take the real field, R, and define Dedekind cuts just as we did for Q (the same statements, but now with all of the elements involved real numbers). The result is a field, probably. Or maybe. What is the result? Is it a field we could call the Superreals, and maybe it is even more complete ("exceptionally complete"). Heh heh heh ...  9/8/2008 
Not a reading list  A discussion of some literature relevant to this course.
I forgot to include on the list the book Foundations of Analysis by Landau ($26). This has the complete story starting with the "natural numbers" and finishing with the complex numbers: 130 pages of details. I had a copy of this book with both the original German text and with an English translation and with a short English/German dictionary, all in one volume. It helped me learn how to read math in German.  9/1/2008 
Information sheet  A form to be passed out on the first day of class.  9/1/2008 
Entrance exam  The purpose of this assignment is to allow me to assess students'
abilities to write proofs. Answers are due on Monday, September
8. Added 9/6 I am not so clever and just proved problem 1 with a direct induction argument. If you decide to verify it using some sort of "magic" (for example, you may assert these numbers count something) then you should explain carefully (I mean: Prove!) that your assertion is correct.  9/1/2008 

Maintained by greenfie@math.rutgers.edu and last modified 9/2/2008.