PMAT 435 Analysis I (Fall 2011)


Welcome! This page contains information about the course PMAT 435 L01 for Fall 2011. All information is tentative and subject to change. For the latest updates and announcements, go to the bottom of this page.

Content of the Course

Our textbook is: Steven R. Lay, Analysis with an introduction to proof. Fourth edition. Pearson / Prentice-Hall, 2006.

Other references: There are many textbooks on analysis that are at roughly the same level as our textbook. The following are, in my opinion, particularly good.

For those who want to pursue the subject further, the standard text is:

Credit Components

Provided you pass the Final Exam, your grade will be determined by the following credit components:

Eight Assignments (20%)
Two Midterm tests (30%)
A Final Examination (50%)

Assignments

There are eight assignments each having 5 questions and being worth 2.5 % of the course. Assignments are due at 4 PM on Fridays. While you may discuss the questions with your classmates, you must write up and submit your own work.

Assignment

Due date (due at 4 PM)

Questions to be handed in

1

September 30

p.88 #8.5, p.104 #10.11, p.105 #10.22, p.115 #11.6(a), p.116 #11.7

2

October 7

p.127 #12.7(a), p.128 #12.12 (a) and (b), p.136 #13.9, p.136 #13.11, p.136 #13.17

3

October 14

p.144 #14.3(d), p.144 #14.5, p.144 #14.8, p.164 #16.6 (b) and (c), p.164-165 #16.9 

4

October 28

p.173 #17.17, p.174 #17.19(a) and (d), p.179-180 #18.3 (e), p.181 #18.15, p.189 #19.9

5

November 4

p.197 #20.5, p.198 #20.6 (c), p.208 #21.9, p.208 #21.13, p.208 #21.16

6

November 18

p.215 #22.13(a), p.215 #22.14, p.222 #23.4(c), p.240 #25.8, p.250 #26.15

7

December 2

p.266 #28.6, p.276 #29.11, p.284 #30.5, p.285 #30.19, p.293 #31.19

8

December 9

p.301-302 #32.10, p.302 #32.11, p.310 #33.5 (b) and (h), p.317 #34.3(h), p.327 #35.4

 

Midterm Tests

There are two midterm tests, each 50 minutes long, and together they are worth 30% of the course. The dates are October 21 (Friday) and November 25 (Friday).

 

Midterm Test 1 (October 21) sections 6 to 16 inclusive, omitting sections 9 and 15.

Details:

 

The first question (25%) is on Definitions. You will be asked to give the definition for five terms from the following list:

 

Countable sets

Supremum

Infimum

Interior points

Boundary points

Open sets

Closed sets

Accumulation points

Closure

Compact sets

Convergence of a sequence

 

Then you answer 3 of the next 5 questions. Each is worth 25% of the paper. All 5 questions are proofs.

 

Midterm Test 2 (November 25) from section 17 to 28 inclusive, omitting section 24.
Details:

 

The first question (25%) is on Definitions. You will be asked to give the definition for five terms from the following list:

 

Monotone sequences

Cauchy sequences

Subsequential limits

Limit superior

Limit of a function at a point

Continuity of a function at a point

Uniformly continuous functions

Derivative of a function at a point

 

Then you answer 3 of the next 5 questions. Each is worth 25% of the paper.



Final Examination

There is a final examination, worth 50% of the course and to be scheduled by the Registrar's Office. As stated in the Course Outline: A passing grade in the Final Examination is essential for an overall grade of C- or better.

Date: December 21, 2011
Time: 8:00 am – 11:00 am
Place: MS 431

There are 13 questions. You answer ANY TEN of your choice. It covers sections 7 to 31, omitting sections 9, 15 and 24.

You will NOT be asked to reproduce definitions. You will NOT be asked to give the statement for any theorem. However, you may be asked to give the proof for a theorem or two from this list:

·         Theorem 13.10, p.132

·         Theorem 18.12 (Cauchy Convergence Criterion), p.177-178

·         Theorem 23.6, p.218-219

·         Theorem 30.1, p.277

·         Theorem 30.2, p.277-278

As stated in the Course Outline: A passing grade in the Final Examination is essential for an overall grade of C- or better.

 

Lectures and Tutorials

Chapter 1 concerns logic and proofs. I will not specifically talk about them in the lectures, but will spend the first two tutorials discussing exercises from these sections. You should read them on your own, and prepare the exercise questions for the tutorial. The way I see it is that most of the proofs, argumentations and deductions we do in this course follow simple-minded everyday logic, although there is a formal language of logic. So, we shall start with chapter 2. Here is a tentative schedule, showing the sections of the textbook we are covering in each class.

 

Monday

Tuesday (Tutorial)

Wednesday

Friday

September 12-16

sec 5

sec 1, 2

sec 6, 7

sec 7

September 19-23

sec 8

sec 3, 4

sec 8

sec 10, 11

September 26-30

sec 12

sec 12

sec 13 (Assignment 1 due)

October 3-7

sec 13

sec 14

sec 14  (Assignment 2 due)

October 10-14

------

sec 16

sec 17 (Assignment 3 due)

October 17-21

sec 18

sec 18, 19

Midterm Test 1

October 24-28

sec 19

sec 20

sec 21 (Assignment 4 due)

October 31-November 4

sec 21, 22

sec 22

sec 23 (Assignment 5 due)

November 7-11

sec 23

sec 25

------

November 14-18

sec 26

sec 27, 28

sec 29 (Assignment 6 due)

November 21-25

sec 30

sec 30, 31

Midterm Test 2

November 28-December 2

sec 31

sec 32, sec 33

sec 33 (Assignment 7 due)

December 5-9

sec 34

sec 35

sec 36 (Assignment 8 due)


During the tutorial hours, we will discuss the solutions to some pre-assigned exercises from the textbook. You are strongly urged to do these questions before attending the tutorial.

 

Updates and Announcements

September 6, 2011

September 12, 2011

·         Major update with lots of changes.

October 12, 2011

·         Information about Midterm Test 1 added.

November 15, 2011

·         Information about Midterm Test 2 added.

·         Date, Time, Place for Final Exam added.

·         Questions for assignments 7 and 8 added/updated.

November 23, 2011

·         Information about the Final Exam added.

Created: September 6, 2011
Last updated: November 23, 2011