Home page for Math 411, fall 2008

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General information
homework, syllabus, etc.
Students in the course |

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.

Links to other class material

(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.

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 take-home 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 take-home 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.

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 e-mail. 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!

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.
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 TEX 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.
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 D-open and the d-open), which are subsets of the set of subsets of X, are the same.

Math 411: time-dependent homework is a good thing.
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 ...
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.
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.
Old Math 411 material
I last taught this material many years ago and I don't have anything to post about how I taught it. But last year Professor Teixeira taught the course, and there is much material available, including exams and review problems, linked here. I suspect that our progress will not be as rapid as that of last year's course.

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