Math 131A: Introduction to Analysis
Fall 2006

(12/13) Here are the solutions to the final exam. You can email me to find out your grade. I'll most likely be done grading tomorrow night, so if you'd like to take a look at your exam, stop by my office on Friday between 1 and 2:30.

(12/11) Solutions to Homework 11 have been posted.

(12/10) I suggest that you carefully review the following homework problems:

Sec. 2.3, ex. 5, 10
Sec. 3.1, ex. 10, 16
Sec. 3.2, ex. 7, 9, 13
Sec. 3.3, ex. 4, 13
Sec. 3.4, ex. 5, 11
Sec. 3.5, ex. 7, 12
Sec. 3.7, ex. 6, 8
Sec. 4.1, ex. 11d, 14
Sec. 4.2, ex. 3, 4, 5
Sec. 5.1, ex. 4c, 11, 12
Sec. 5.2, ex. 4, 8
Sec. 5.3, ex 3, 6, 17
Sec. 5.4, ex. 2
Sec. 5.6, ex. 9, 10, 12.

I plan to go over some of them tomorrow, 1-2. Let's gather in my office (MH 318A) at 1 and look for a classroom.

(12/9) You may have noticed that problem 4 from the sample final has a pretty trivial solution. (Thanks to Alex W. for pointing that out.) Here's a corrected version.

(12/8) After you're done reviewing, try this sample final.

(12/7) Recall that the final exam is MH 234 on Wednesday, Dec. 13, 9:45-12.

If you are interested in doing a CAMCOS project with me or someone else, it's a good idea (plus you get free food) to come to the CAMCOS reports day, tomorrow (12/8) 10:30-noon. You can also check out my CAMCOS web page from Spring 2006.

(12/5) Solutions to Homework 10 have been posted.

(12/3) I just posted a handout called Math 131A essentials. We'll go over it tomorrow.

(12/1) Here's a flyer for Math 131B. If you are a math major, I strongly encourage to take this class, since it covers some of the most fundamental topics in mathematics. Hope to see many of you there in the Spring!

By the way, I will hold a review session on Monday, December 11, from 1 to 2 (room TBA), followed by office hours from 2 to 4. I'll announce my other office hours after December 6 soon.

Actually, here they are:

Friday, 12/8: 1:30-4
Monday, 12/11: 2-4
Wednesday, 12/13: 2-4
Friday, 12/15: 12:30-2:30

(11/28) I plan to bring the SOTE (Student Opinions of Teaching Effectiveness) forms on Monday, December 4.

(11/27) Homework 9 solutions have been posted.

(11/25) Homework 11 (the last one!) has been posted and is due on Monday, December 4.

(11/16) Homework 10 has been posted and is due November 27. Here are two more extra credit problems: sec. 5.2, ex. 9 and 13.

(11/15) Solutions to Homework 8 have been posted.

(11/7) Homework 9 has been posted and is due on November 15. Here's another extra credit problem: sec. 4.2, ex. 12.

(11/1) Midterm 1 solutions have been posted.

(10/30) Homework 7 solutions have been posted.

(10/28) Here is a sample midterm 2.

(10/27) Solutions to Homework 6 have been posted.

(10/27) Midterm 2 next Wednesday will cover Chapter 3. I would start reviewing for it by going over the theory and homework assignments 5-8, and then trying the practice test I will post this weekend. Solutions to homework 6 will be posted later today.

(10/24) Homework 8 has been posted and is due on November 1.

(10/18) Homework 7 has been posted and is due on October 23. (Note that there are only 5 problems. Since it's due on Monday, you'll be able to get it back on Friday before the second midterm.)

Also, I posted a handout on limsup and liminf, which includes an extra credit problem.

(10/17) Solutions to Homework 5 have been posted.

(10/13) Good news, everyone: the due date for homework 6 has been moved to Wednesday, October 18.

(10/11) Today in class I said that inductively defined sequences can be viewed as dynamical systems. More on that in the handout "Sequences as dynamical systems".

(10/10) Solutions to Homework 4 have been posted.

(10/8) Homework 6 has been posted and is due on October 16

(10/3) Tomorrow (10/4) I will have no office hours in the morning - sorry about that.

(10/1) Homework 5 has been posted and is due on October 9.

(9/28) Midterm 1 solutions have been posted. Tomorrow (9/29) I will not be available from 10:30-11:20 (I'm substituting for a colleague).

(9/25) Solutions to Homework 3 have been posted.

(9/23) Recall that the first midterm (on 9/27) will cover Chapters 1 and 2 from Bartle and Sherbert. There will be four problems. It is a closed-book and no-calculators exam. However, you can bring your notes written on one 3 X 5 inch index card.

To review for the midterm, I suggest that you first go over the main results, then go over the homework, and then try a practice midterm. You can design one (just pick 4 problems from the book, from different sections), or you can try this one: 1.2, ex. 5, 1.3, ex. 4, 2.2, ex. 15, and 2.4, ex. 4(b).

(9/21) Solutions to Homework 2 have been posted.

(9/18) I will collect the rewrites of Homework 2 on Wednesday, September 20. Homework 2 solutions will be posted the same day.

(9/17) Homework 4 has been posted and is due on September 27. Recall that Midterm 1 will be on September 27, covering Chapters 1 and 2.

(9/13) If you haven't done so already, please send me a blank email with the subject "Math 131A".

(9/8) Homework 3 has been posted and is fue September 18.

If you are planning to apply to a Ph.D. program, here's a workshop for you.

(9/7) Homework 1 solutions have been posted.

(9/1) Since there is no class on Monday (I keep forgetting that), Homework 2 is actually due on Friday, September 8. Revisions of Homework 1 are due on September 6.

(8/30) Howework 2 has been posted and is due September 6.

(8/28) There's another version of the Principle of Mathematical Induction that you should feel free to use in the homework. It goes as follows. Suppose that P(n) is a statement about a natural number n and suppose that: (1) P(1) and P(2) are true; (2) For every natural number k, P(k) and P(k+1) imply P(k+2). Then P(n) is true for all n.

(8/28) At the beginning of each homework, you should write down all the relevant definitions and result (theorems, propositions, lemmas) used in the assignment. As you may have already seen, Homework 1 is mostly about playing with definitions. This means that you need to make sure that you really understand all the newly defined symbols and objects.

(8/23) Here's a link to the story about Grigory Perelman and the Poincare conjecture in the NY Times I mentioned today in class.

(8/22) Welcome, everyone! The first class meeting is tomorrow, August 23. Homework 1 has been posted below and is due on August 30.

Lecture time and location

MWF 11:30-12:20, MH 234

Prerequisite

Math 32 and Math 108 (with a grade of "C-" or better in each) or instructor consent.

Office hours

MWF 10:10-11:30, M 2:45-3:45, 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

Preliminaries (Ch. 1). Real numbers (Ch. 2). Sequences and series (Ch. 3). Limits (Ch. 4). Continuity (Ch. 5) and differentiation (Ch. 6).

Exams

There two midterms and a final exam. The exam schedule:

Midterm 1: September 27 (Midterm 1 solutions)

Midterm 2: November 1 (Midterm 2 solutions)

Final exam: December 13, 9:45-12

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

Math 131A essentials

Limsup and liminf

Sequences as dynamical systems

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. After you receive your graded homework assignment, you are allowed to revise it and turn in the revision to be regraded. I will accept only one revision per homework which you have to turn in the class after you receive my feedback.

# Due date Assignment Solutions

1 8/30 Sec. 1.1: #12, 13, 14, 17, 20. Sec. 1.2: #1, 2, 7, 18, 20. HW 1

2 9/8 Sec. 1.3: #3, 7, 9, 11, 12. Sec. 2.1: #7, 8, 9, 18, 19. HW 2

3 9/18 Sec. 2.2: #2, 10, 16. Sec. 2.3: #2, 4, 5, 6, 8, 10, 11. HW 3

4 9/27 Sec. 2.4: #1, 3, 7, 9, 18. Sec. 2.5: #2, 8, 9, 14. HW 4

5 10/9 Sec. 3.1: #5a, 8, 10, 16, 17. Sec. 3.2: #7, 9, 13, 22. HW 5

6 10/18 Sec. 3.3: #2, 4, 9, 12, 13. Sec. 3.4: #5, 7bd, 11, 12. HW 6

7 10/23 Sec. 3.5, #5, 7, 9, 12. Sec. 3.6: #9. HW 7

8 11/1 Sec. 3.7, #3bc, 4, 6, 8, 11. HW 8
9 11/15 Sec. 4.1, #6, 7, 11cd, 14. Sec. 4.2, #3, 4, 5, 9, 10. HW 9

10 11/27 Sec. 4.3: #9. Sec. 5.1: #4c, 7, 10, 11, 12.
Sec. 5.2: #3, 4, 7, 8, 11. HW 10

11 12/4 Sec. 5.3: #3, 6, 13, 17. Sec. 5.4: #2, 8.
Sec. 5.6: #8, 9, 10, 12. HW 11

#	Due date	Assignment	Solutions
1	8/30	Sec. 1.1: #12, 13, 14, 17, 20. Sec. 1.2: #1, 2, 7, 18, 20.	HW 1
2	9/8	Sec. 1.3: #3, 7, 9, 11, 12. Sec. 2.1: #7, 8, 9, 18, 19.	HW 2
3	9/18	Sec. 2.2: #2, 10, 16. Sec. 2.3: #2, 4, 5, 6, 8, 10, 11.	HW 3
4	9/27	Sec. 2.4: #1, 3, 7, 9, 18. Sec. 2.5: #2, 8, 9, 14.	HW 4
5	10/9	Sec. 3.1: #5a, 8, 10, 16, 17. Sec. 3.2: #7, 9, 13, 22.	HW 5
6	10/18	Sec. 3.3: #2, 4, 9, 12, 13. Sec. 3.4: #5, 7bd, 11, 12.	HW 6
7	10/23	Sec. 3.5, #5, 7, 9, 12. Sec. 3.6: #9.	HW 7
8	11/1	Sec. 3.7, #3bc, 4, 6, 8, 11.	HW 8
9	11/15	Sec. 4.1, #6, 7, 11cd, 14. Sec. 4.2, #3, 4, 5, 9, 10.	HW 9
10	11/27	Sec. 4.3: #9. Sec. 5.1: #4c, 7, 10, 11, 12. Sec. 5.2: #3, 4, 7, 8, 11.	HW 10
11	12/4	Sec. 5.3: #3, 6, 13, 17. Sec. 5.4: #2, 8. Sec. 5.6: #8, 9, 10, 12.	HW 11

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 Dec 20 17:37:06 PST 2006

Math 131A: Introduction to Analysis Fall 2006

(class no. 41672, sec. 1)

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