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There is a Harvey Mudd College first semester real analysis course posted at http://www.youtube.com/user/Learnstream, based on the classic text

The topics are roughly:

- Construction of the Rational Numbers

- Construction of the Real Numbers via Dedekind Cuts

- The Real and Complex Fields

- Induction and Well-Ordering

- Cardinality

- Metric Spaces and Their Topology

- Compact Sets and Spaces

- The Cantor Set and Connected Sets and Spaces

- Sequences

- Completeness

- Series

- Continuity and Uniform Continuity

- Differentiation and the Mean-Value Theorem

There's still a few lectures left before the semester finishes, so the syllabus above isn't complete. Since the Learnstream project has gone to the trouble to post these outstanding lectures for the public, I think they'd appreciate appreciate seeing lots of people using their work.

**Principles of Mathematical Analysis**(Baby Rudin), by Walter Rudin. Professor Francis Su, who delivers these lectures, does a great job helping to tie this difficult book together with intuitive geometric and topological arguments in the first 15 or so lectures I have watched so far (there are 23, with a few more coming).The topics are roughly:

- Construction of the Rational Numbers

- Construction of the Real Numbers via Dedekind Cuts

- The Real and Complex Fields

- Induction and Well-Ordering

- Cardinality

- Metric Spaces and Their Topology

- Compact Sets and Spaces

- The Cantor Set and Connected Sets and Spaces

- Sequences

- Completeness

- Series

- Continuity and Uniform Continuity

- Differentiation and the Mean-Value Theorem

There's still a few lectures left before the semester finishes, so the syllabus above isn't complete. Since the Learnstream project has gone to the trouble to post these outstanding lectures for the public, I think they'd appreciate appreciate seeing lots of people using their work.

*PF Mentors, Advisors, and Homework Helpers, I think this would be a useful resource for the Calculus & Beyond Learning Materials forum, so please place the thread there if you agree.*
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