Introduction to Real Analysis

Course outline

This course aims to provide a thorough introduction to the subject of real analysis. The work done corresponds to the period of Fall, 2008.

Course requirements

The following knowledge is required or desirable on commencement of study of this course:

• Knowledge of basic methods of proof
• Calculus of One Variable
• Differential Equations
• Basics of Set Theory

Syllabus

The course will follow Rudin's Principles of Mathematical Analysis scheme. Course material can be obtained from Wikibooks, MIT's OCW and other free online resources, including the work done by participants during this and other semesters (cycles).

Lecture series

1. The Real and Complex Number System
2. Basic Topology
3. Numerical Sequences and Series
4. Continuity
5. Differentiation
6. The Riemann-Stieltjes Integral
7. Sequences and Series of Functions
8. Some Special Functions
9. Functions of Several Variables
10. Integration of Differential Forms
11. The Lebesgue Theory

Assignments

Will be posted, with suggestions of solutions, after each lecture is finished

Examinations

• Examination #1 should be taken after all the material from lectures 1-3 is studied.
• Examination #2 should be taken after all the material from lectures 4-6 is studied.
• Examination #3 should be taken after all the material from lectures 7-9 is studied.
• Examination #4 should be taken after all the material from lectures 10-11 is studied.
• The Final Examination should be taken after all the material from all the lectures is studied.

Recommended student evaluation scheme

Group work is encouraged: discussions, corrections and observations are greatly welcome. Questions can be posted in the discussion pages for each topic and answers can be attempted by all members of the class.

Evaluation is self-assesed. Each assignment should be done after the material from the lectures is understood, and should be used as preparation for the examinations. Solutions will be posted with each assignment and examination.

A success percentage above 75% indicates dominion over the topics.

Sign Up List

If you are interested in taking (or helping with) this course, please indicate so here. I'm as serious as you are:

• --Cœlispex 06:17, 2 September 2008 (UTC)
• Love to take it. W3asal 23:50, 20 September 2008 (UTC)
• I would be happy to help give it. Thenub314 15:11, 20 February 2009 (UTC)
• I would also love to take this course. Sorry, I don't have a login name. 96.28.49.232 09:33, 2 April 2009 (UTC)
• Would also love to take this. Sorry I don't have a login name either
• I plan to take this course in my university next semester. I am willing to help whenever needed.--Fj217 23:32, 7 November 2009 (UTC)