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Last updated:

September 23, 2023

Duration:

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FREE

This course includes:

Unlimited Duration

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Description

Math 131: Real Analysis I (Spring 2010, Harvey Mudd College). Taught by Professor Francis Su, this course is a rigorous analysis of 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)

Course Curriculum

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

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