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Course

Code:	MATH 131
Subject:	Mathematics
Topic:	Real Analysis
Views:	40,848

Educator

Name:	Harvey Mudd College (HMC)
Type:	University

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Instructor

Name

Francis Su

Real Analysis I with Prof. Su

Video Lectures

Displaying all 26 video lectures.

I. Introduction to Set Theory
Lecture 1 Play Video	Constructing the Rational Numbers
Lecture 2 Play Video	Properties of ℚ
Lecture 3 Play Video	Construction of the Reals
Lecture 4 Play Video	The Least Upper Bound Property
Lecture 5 Play Video	Complex Numbers
Lecture 6 Play Video	Principle of Induction
II. Countability & Cardinality
Lecture 7 Play Video	Countable and Uncountable Sets
Lecture 8 Play Video	Cantor Diagonalization and Metric Spaces
Lecture 9 Play Video	Limit Points
III. Sets and Compactness
Lecture 10 Play Video	The Relationship Between Open and Closed Sets
Lecture 11 Play Video	Compact Sets
Lecture 12 Play Video	Relationship of Compact Sets to Closed Sets
Lecture 13 Play Video	Compactness and the Heine-Borel Theorem
IV. Connectedness and Spaces
Lecture 14 Play Video	Connected Sets, Cantor Sets
Lecture 15 Play Video	Convergence of Sequences
Lecture 16 Play Video	Subsequences, Cauchy Sequences
Lecture 17 Play Video	Complete Spaces
Lecture 18 Play Video	Series
Lecture 19 Play Video	Series, Convergence Tests, Absolute Convergence
V. Continuity & Functions
Lecture 20 Play Video	Functions - Limits and Continuity
Lecture 21 Play Video	Continuous Functions
Lecture 22 Play Video	Uniform Continuity
Lecture 23 Play Video	Discontinuous Functions
VI. Differentiation
Lecture 24 Play Video	The Derivative and the Mean Value Theorem
Lecture 25 Play Video	Taylor's Theorem, Sequence of Functions
Lecture 26 Play Video	Ordinal Numbers and Transfinite Induction