## SEE: Guide to Download YouTube Video Lecture

## Lecture Details :

Real Analysis, Spring 2010, Harvey Mudd College, Professor Francis Su. Get notes and study tools at http://gosuapm.com/

## Course Description :

Contents:

Constructing the rational numbers,Properties of Q,Construction of R,The Least Upper Bound Property,Complex Numbers,The Principle of Induction,Countable and Uncountable Sets,Cantor Diagonalization, Metric Spaces, Limit Points,Relationship b/t open and closed sets,Compact Sets,Relationship b/t compact, closed sets,Compactness, Heine-Borel Theorem,Connected Sets, Cantor Sets,Convergence of Sequences,Subsequences, Cauchy Sequences. ,Complete Spaces,Series,Series Convergence Tests,Functions - Limits and Continuity,Continuous Functions,Uniform Continuity,Discontinuous Functions. ,The Derivative, Mean Value Theorem,Taylor's Theorem,Ordinal Numbers, Transfinite Induction.

## Other Resources :

### Citation |

## Other Mathematics Courses

- An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves by IIT Madras
- Several Variable Calculus / Vector Calculus by Other
- Pre-algebra by Khan Academy
- Math 95 - Intermediate Algebra by Portland Community College
- Introduction to Geometry by Other
- A Basic Course in Real Analysis by IIT Kharagpur
- Computational Science and Engineering I by MIT
- Mathematical Methods for Engineers II by MIT
- Calculus by The University of New South Wales
- Statistical Inference by IIT Kharagpur

### » check out the complete list of Mathematics courses