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Course
| Subject: | Mathematics |
| Views: | 40,505 |
Instructor
Name
Francis Su
Copyright Information: All rights reserved to Prof. Francis Edward Su and Harvey Mudd College
Lecture Description
This video lecture, part of the series Real Analysis I with Prof. Su by Prof. Francis Su, does not currently have a detailed description and video lecture title. If you have watched this lecture and know what it is about, particularly what Mathematics topics are discussed, please help us by commenting on this video with your suggested description and title. Many thanks from,
- The CosmoLearning Team
- The CosmoLearning Team
Course Index
- Constructing the Rational Numbers
- Properties of ℚ
- Construction of the Reals
- The Least Upper Bound Property
- Complex Numbers
- Principle of Induction
- Countable and Uncountable Sets
- Cantor Diagonalization and Metric Spaces
- Limit Points
- 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
- Convergence of Sequences
- Subsequences, Cauchy Sequences
- Complete Spaces
- Series
- Series, Convergence Tests, Absolute Convergence
- Functions - Limits and Continuity
- Continuous Functions
- Uniform Continuity
- Discontinuous Functions
- The Derivative and the Mean Value Theorem
- Taylor's Theorem, Sequence of Functions
- Ordinal Numbers and Transfinite Induction
Course Description
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.
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