# InfoCoBuild

## Math 131: Real Analysis I

Math 131: Real Analysis I (Spring 2010, Harvey Mudd College). Taught by Professor Francis Su, this course is a rigorous analysis of the real numbers, as well as an introduction to writing and communicating mathematics well. Topics will include: construction of the real numbers, fields, complex numbers, topology of the reals, metric spaces, careful treatment of sequences and series, functions of real numbers, continuity, compactness, connectedness, differentiation, and the mean value theorem, with an introduction to sequences of functions. (from math.hmc.edu)

 Lecture 10 - The Relationship between Open and Closed Sets

Go to the Course Home or watch other lectures:

 Lecture 01 - Constructing the Rational Numbers Lecture 02 - Properties of Q Lecture 03 - Construction of the Reals Lecture 04 - The Least Upper Bound Property Lecture 05 - Complex Numbers Lecture 06 - The Principle of Induction Lecture 07 - Countable and Uncountable Sets Lecture 08 - Cantor Diagonalization and Metric Spaces Lecture 09 - Limit Points Lecture 10 - The Relationship between Open and Closed Sets Lecture 11 - Compact Sets Lecture 12 - Relationship of Compact Sets to Closed Sets Lecture 13 - Compactness and the Heine-Borel Theorem Lecture 14 - Connected Sets, Cantor Sets Lecture 15 - Convergence of Sequences Lecture 16 - Subsequences, Cauchy Sequences Lecture 17 - Complete Spaces Lecture 18 - Series Lecture 19 - Series Convergence Tests, Absolute Convergence Lecture 20 - Functions - Limits and Continuity Lecture 21 - Continuous Functions Lecture 22 - Uniform Continuity Lecture 23 - Discontinuous Functions Lecture 24 - The Derivative and the Mean Value Theorem Lecture 25 - Taylor's Theorem, Sequence of Functions Lecture 26 - Ordinal Numbers and Transfinite Induction