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Basic and Real Analysis
Various instructors and tutors
Course topics and videos

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1. Sets and Metric Spaces
The Least Upper Bound Property
Constructing the Rational Numbers
Properties of Q
Construction of the Reals
Limit Points
Cantor Diagonalization and Metric Spaces
Countable and Uncountable Sets
Principle of Induction
Complex Numbers
The Relationship Between Open and Closed Sets
Compact Sets
Relationship of Compact Sets to Closed Sets
Compactness and the Heine-Borel Theorem
Connected Sets, Cantor Sets
2. Sequences and Series
Convergence of Sequences
Subsequences, Cauchy Sequences
Complete Spaces
Series Convergence Tests, Absolute Convergence
3. Functions and Continuity
Functions - Limits and Continuity
Continuous Functions
Uniform Continuity
Discontinuous Functions
4. Derivatives
The Derivative and the Mean Value Theorem
5. Taylor's Theorem
Taylor's Theorem, Sequence of Functions

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