Math 131B: Introduction to Real Variables
Spring 2007

(class no. 32840, sec. 3)

Contents of this page

Late breaking news
Lecture time and location
Prerequisite
Office hours
Textbook
Syllabus
Exams
How to...
Grading policy
Handouts
Homework
Policy on calculators
Academic integrity
Anonymous feedback

Late breaking news

(5/23) Final exam solutions are here!

(5/22) If you would like to see your final exam before I finalize the grades, you can stop by my office on Thursday between 2 and 3:30. I will post the solutions tomorrow afternoon.

It was a great pleasure for me to teach this class! Have a great summer, everyone, and hope to see you in the Fall. Check out the classes I am teaching: Math 134: Dynamical Systems and Math 213: Advanced Differential Geometry. Email me if you would like to know more about these classes.

(5/16) I just posted homework 10 solutions. Old homework assignments, including graded rewrites of HW 9, are all in an envelope outside my office door.

(5/15) Here is the final exam. It is due on Wednesday, May 23 at noon. If you think the exam is challenging, well, that's because I think you are a very capable group of students, and besides, there are a lot of extra credit problems (plus some hints as well).

Btw, if you are interested, I will most likely be able to show you your (graded) exam on Thursday, May 24 in the afternoon, before I finalize the grades. I'll post the exact time later. Good luck and let me know if you have any questions!

(5/14) Solutions to homework 9 have been posted. Remember that rewrites of HW 10 are due on May 16 (give them to the staff in MH 308). My office hours for the remainder of the semester will be:

May 16: 2:30-4, May 21: 11:30-1 & 2:30-4, May 23: 10:30-12.

Here's a sample final (from 2006) with solutions. Last year's final with solutions is here.

(5/8) Three reminders: (1) Homework 10 is due tomorrow (5/9); (2) rewrites of HW 9 (which I will bring tomorrow) are due on Monday, May 14; (3) take-home final will be posted here on May 16 in the morning and will be due on May 23 at noon. Also, I will bring the SOTE forms to class tomorrow.

(5/7) I changed (read: made it easier) the last problem in Homework 10. Instead of showing that every continuous function is measurable, you need to show that every piecewise constant function is measurable. If you already proved the former, you just turn that in.

(5/6) I will not be able to hold my 4-5 office hour tomorrow, so I will be available only from 10:30 to 12 noon and 3 to 4. Sorry about that!

(5/3) Homework 8 solutions have been posted. Homework 10 (the last one!) is also there and is due May 9.

(4/30) Here's an opportunity for you to hear a great mathematician and speaker (and entertaining on top of that!): Vladimir Arnold is giving a talk entitled "Real algebraic geometry" at Santa Clara University (Daly Science room 206) on Wednesday, May 9, at 7:30 PM. For details, check the BAMA website. If you can, do attend!

(4/26) Just posted: HW 7 solutions and Homework 9, due Wednesday, May 2.

(4/22) I have noticed that some of you do not perform too well on in-class exams (I believe many of you could have done a lot better on the second midterm), so I have decided to make the final exam take-home. The dates I have in mind are May 17-23. Let me know if you have a very strong reason to object to this.

(4/20) The Math Department colloquium next Wednesday is going to be very interesting and instructive, so I not only encourage you to attend, but I will give one point of extra credit to those who attend and write a short summary of the talk (at least one paragraph and at most one page). The speaker, Alexander Givental from UC Berkeley is an amazing mathematician who became famous for, among other things, solving the so called "Mirror conjecture" (on the interface of math and physics). So, do attend!

(4/19) Homework 8 has been posted and is due on Wednesday, April 25.

(4/18) Midterm 2 solutions have been posted. Btw, I will post HW 8 tomorrow. I'll bring back HW 7 on Monday (sorry for the delay).

(4/16) Solutions to homework 5 and 6 have been posted. Solutions to the sample midterm are here.

(4/14) Two things: (a) starting from April 16, my new office hours will be

MW 10:30-12:00, M 3-5, and by appointment.

(b) The best way to prepare for the midterm is (as usual) to go over the homework and the problems in its epsilon-neighborhood in the book. Btw, you can bring a 3 X 5 inch index card with your notes to the exam.

(4/13) Correction: since you will get Homework 7 back on Monday, only revisions of HW's 5 and 6 are due that day (4/11), whereas you can turn your revision of HW 7 on Wednesday (4/18).

Remember to prepare your questions and problems you would like to discuss. On Monday, I plan to go over some homework problems and this sample midterm 2 from Spring 2006.

(4/9) Revisions of homework assignments 5-7 are all due on Monday, April 16 (the day I come back) at the end of class. I will then post solutions to these assignments on the web. Recall that Midterm 2 is on April 18. It will cover sections 7.3, 8.1, 8.2, and 9.1-9.4 from Bartle-Sherbert. We'll review for the midterm this Wednesday and next Monday.

(3/31) Hi everyone, hope you've enjoyed your spring break! I finally posted the solutions to Homework 4. More to come soon. Btw, I will most likely be back on April 16.

(3/21) Homework 7 has been posted and is due on April 4. Enjoy your spring break!

(3/14) Homework 6 has been posted and is due on March 21. Also, as Professor Grantcharov mentioned in class, you can turn in Homework 5 to him on Friday.

(3/8) Homework 5 has been posted and is due on Wednesday, March 14.

As I mentioned before, I'll be on paternity leave until about April 9 or 11, during which time Professor Dimitar Grantcharov will bu substituting for me. You should turn in your assignments to him at the end of class (on the day the assignment is due, of course). I will try to be available by email as much as possible, so feel free to email me your questions. You can also see Prof. Grantcharov during his office hours which can be found here.

(2/28) Since I didn't have time to talk about zero sets and other things today, you can turn in Homework 4 on Wednesday, March 7 instead of March 5. Solutions to Homework 3 have been posted.

(2/27) Homework 4 has been posted and is due on Monday, March 5. Recall that revisions of Homework 3 are due tomorrow, Feb. 28.

(2/26) Midterm 1 solutions have been posted.

(2/23) Homework 2 solutions have been posted. (The broken link is now fixed.)

(2/20, part 2) I forgot to mention you can check out last year's Midterm 1 here.

(2/20) Midterm 1 (on 2/26) will cover sections 6.1-6.4, 7.1 and 7.2 from the Bartle-Sherbert book. Tomorrow I plan to finish section 7.2 and discuss several exercises. On Friday, 2/23, the review session will be at 1:30. Let's meet at my office (MH 318A) and look for a room. And of course, prepare your questions!

On a related note, please try to ask more questions, give more comments and in general be more active in class! It will make the lectures more interesting and useful for you, and it will help me get a sense of how fast or slow I should go and what I should focus on. Some feedback (also via the anonymous feedback form below) would be helpfull as well.

(2/14, part 2) You can pick up graded Homework 2 from my office (there's an envelope hanging outside). The revisions are due next Wednesday. And btw, we do have class on Monday, 2/19.

(2/14) Solutions to Homework 1 have been posted.

(2/11) Tomorrow, February 12, I will have only one office hour, from 10 to 11. However, on Wednesday, February 14, I'll have an extra office hour from 4:20 to 5:20. Also, on Friday, February 23, I'll hold a midterm review session, either 10-10:50 or 1:30-2:20, yet to be determined.

Also, Homework 3 has been posted and is due on Wednesday, February 21.

And one last thing: I have decided to move Midterm 2 from April 9 to April 18. The main reason is that I will be on paternity leave, probably from March 8 to April 8 or so. My most likely substitute will be Professor Dimitar Grantcharov.

(2/4) Homework 2 has been posted and is due on Monday, February 12. I also posted a handout entitled "How discontinuous can f' be?". The answer, in short, is: not too much.

(1/31) As I said in class, the due date for Homework 1 has been moved to Monday, February 5.

(1/28) I had to move my M 2-3 office hour to M 3-4. So my new office hours are MW 10-12 and M 3-4.

(1/23) Homework 1 has been posted and is due on Wednesday, January 31.

(1/15) Our first class meeting will be on Wednesday, January 24.


Lecture time and location

MW 12:00-1:15, MH 233

Prerequisite

Math 131A (with a grade of "C-" or better) or instructor consent.


Office hours

MW 10:30-12:00, M 3-5 (note another change), and by appointment


Textbook

Required text:
R. G. Bartle and D. R. Sherbert: Introduction to Real Analysis, John Wiliey & Sons, 3rd edition, 2000
Recommended reading: C. C. Pugh: Real Mathematical Analysis, Springer-Verlag, UTM, 2002

This is a more advanced book but it's beautifully written and covers a lot of interesting topics.


Syllabus

Green sheet
Differentiation (Ch. 6). The Riemann integral (Ch. 7). Sequences and series of functions (Ch. 8 & 9). Basic topology (Ch. 11). The Lebesgue integral (Pugh's book).


Exams

There two midterms and a final exam. The exam schedule:
Midterm 1: February 26.
Midterm 1 solutions

Midterm 2: April 18 (note the change).
Midterm 2 solutions

Final exam: take-home, May 16-23.
There will be no make-up exams.


How to...

How to study for this and other math classes

How to take the exam


Grading policy

Homework 20%, Midterms 40%, Final 40%


Handouts

How discontinuous can f' be?


Homework

There will be weekly homework assignments.

Late homework policy:

1 class late: 50% penalty; 2 classes late: 75% penalty; 3 classes late: no credit.

Policy on revisions. I will accept one revision per homework. After you get your graded assignment back from me, you can turn in your revision during or after the next class (i.e., you will have two or three days to revise) to be regraded.

# Due date Assignment Solutions
1 2/5 Sec. 5.2, #7. Sec. 5.3, #6, 17. Sec. 6.1, #4, 13, 16.
Sec. 6.2, #4, 16, 20.
HW 1
2 2/12 Sec. 6.3, #5, 10, 11. Sec. 6.4, #3, 10, 18. HW 2
3 2/21 Sec. 7.1, #9, 11, 12. Sec. 7.2, #8, 10, 17. HW 3
4 3/7 Sec. 7.3, #10, 12, 16, 20, 21. HW 4
5 3/14 Sec. 8.1, #4, 14, 19, 23. HW 5
6 3/21 Sec. 8.2, #3, 4, 5, 11, 13, 20. HW 6
7 4/4 Sec. 9.4, #1abc, 6abc, 7, 9, 11, 17. HW 7
8 4/25 Sec. 11.1, #5, 7, 9, 13. HW 8
9 5/2 Sec. 11.2, #1, 3, 8, 10. Sec. 11/3, #5, 10. HW 9
10 5/9 Homework 10 HW 10


Policy on calculators

Calculators will not be permitted on exams.


Academic integrity

By default, I regard my students as honest individuals and expect them to abide by the University policy on academic integrity.


Anonymous feedback

If you have any comments or suggestions, please fill out this anonymous feedback form.
Slobodan N. Simić

Last modified: Wed May 23 14:24:29 PDT 2007