MATH S4061X (2):
Intro to Modern Analysis
Summer 2008

Tue and Thu, 10:450am - 12:20pm, Room 417 Math
May 27 - August 15

1.  Course Details

2. Schedule of Lectures and Homeworks

Course Details

Instructor:  Donovan McFeron (408 Mathematics, dmcferon@math.columbia.edu)

Office Hours: By appointment.

Teaching Assistant: James McIvor

Text: Rudin, Walter. Principles of Mathematical Analysis.

Course description: We'll cover the following (mostly, but not exclusively, from Chapters 1-8 Rudin):

Policies: Here are some suggested policies:

1.  Active participation is strongly encouraged.

2.  Reading the book is helpful. Please try to read the material we are going to cover before class.

3.  Please go to class.

4.  Do the homework. Collaboration is encouraged, as long as the work you hand in is your own. Also, staple your homework.

5.  For all written work, solve the problems in organized fashion, with clear explanations.

6.  Ask questions if something is not clear, both in class and outside of class. Help is always available from the Help Room (Mathematics 406, 10am-5pm Mon-Thur), me, or the TA.

 

Homework: Homework will be assigned daily and will be due on Tuesdays by 5pm. Turn homework into the drop box outside of room 406 labeled "12 week Analysis". Late homework will not be accepted.

Exams: There will be two midterms, and a final.
There will be no make-up exams without a note from a doctor or a dean.

Grading: The tentative grading scheme is as follows:

1. Final: 35%

2. Midterms: 20% and 25%

3. Homeworks: 20%

Class Schedule and Homework Assignments

This schedule is tentative and WILL change. Please check regularly for current homework information.

Date

Topics/Sections covered

Remarks

Homework

Date Due

Suggested Probelms

May 27

Sets and Fields

Ch 1

1-5, 8, 9, 11, 15, 18

June 3

 

May 29

The Real Field, Complex Field, and Euclidean Space

Ch 1

 

 

 

June 3

Finite, Countable, and Uncountable Sets

Metric Spaces

Ch 2

2, 5, 6, 8, 11, 13, 17, 18, 22, 23

June 10

 

June 5

Compact, Perfect, and Connected Sets

Ch 2

 

 

 

June

10

 Sequences and Series

Ch 3

 4, 7-13, 20, 23

 July 01

 19

June 12

 

Ch 3

 

 

 

June 17

 

Ch 3

 

 

 

June 19

Review

Ch's 1-3

 

 

 

June 24

Midterm 1

Ch's 1-3

 

 

 

June 26

Power Series

Absolute Convergence

Rearrangements

 Ch 3

 

 

 

July 1

 Limits, Continuity, and Compactness

 Ch 4

 1-13, 18, 23, 24

 July 08

 

July 3

 Connectedness, Discontinuities, and Monotonic Functions

 Ch 4

 

 

 

July 8

 Derivatives

 Ch 5

 4,6,9,10,15

 July 22

 

July 10

 Taylor’s Theorem

 Ch 5

 

 

 

July 15

 Riemann-Stieltjes Integral

 Ch 6

 

 

 

July 17

Properties of Stieltjes Integral

Review

Ch 6

Ch's 3-5

 

 

 

July 22

 Midterm 2

Ch's 3-5

 

 

 

July 24

 Integrals and Differentiation

 Ch 6

 1-6, 11, 15, 16, 18

 Aug 5

 

July 29

 Sequences and Series of Functions

Ch 7 

 3, 4, 8, 11, 12, 23

 Aug 12

 

July 31

 Uniform Convergence and Continuity, Differentiation, and Integration

 Ch 7

 

 

 

Aug 5

Stone-Weierstrass Theorem

Ch 7

 

 

 

Aug 7

 

 

 

 

 

Aug 12

Review

 

 

 

 

Aug 14

Final Exam

 

 

 

 

 

 

 

 

 

 

 

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