MIT OpenCourseWare

Browse materialsMIT 18.100A · Fall 2020

Real Analysis

Subjects: Calculus · Mathematics

Art: Max Brückner (1860 – 1934), Brückner Vielflache Tafel 07 · Public domain

Instructor: Dr. Casey Rodriguez
Term: Fall 2020
Level: Undergraduate, Graduate
What's inside: 25 videos · 3 exams · 4 lecture notes · 114 other files · 4 web pages
Materials open: Videos here · files on MIT OCW

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About this course

Source: MIT OpenCourseWare 18.100A Real Analysis, Fall 2020, Dr. Casey Rodriguez — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 22, 2026. How RedLectern is built.

Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.

Before you start

Prerequisites are not listed here. Check MIT's own syllabus for this course.

This course’s cited books, in our reading lists: Basic Analysis I: Introduction to Real Analysis, Volume 1

How this course was organized

What's here, and what isn't

MIT's own materials here did not support a verified, course-wide order, so they are grouped by section instead.

Not included here

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Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Lecture Notes and Readings

53 files

Recitations

8 files

Assignments and Exams

14 files

Other materials from this course

20 files

25 video transcripts

MIT OpenCourseWare, Dr. Casey Rodriguez, 18.100A Real Analysis, Fall 2020.

License: CC BY-NC-SA 4.0 · Edition: Fall 2020 · Open the original course on OCW ↗

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Real Analysis

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Notes and Readings

Recitations

Assignments and Exams

Other materials from this course

Lecture 1: Sets, Set Operations and Mathematical Induction

Lecture 2: Cantor's Theory of Cardinality (Size)

Lecture 3: Cantor's Remarkable Theorem and the Rationals' Lack of the Least Upper Bound Property

Lecture 4: The Characterization of the Real Numbers

Lecture 5: The Archimedian Property, Density of the Rationals, and Absolute Value

Lecture 6: The Uncountabality of the Real Numbers

Lecture 7: Convergent Sequences of Real Numbers

Lecture 8: The Squeeze Theorem and Operations Involving Convergent Sequences

Lecture 9: Limsup, Liminf, and the Bolzano-Weierstrass Theorem

Lecture 10: The Completeness of the Real Numbers and Basic Properties of Infinite Series

Lecture 11: Absolute Convergence and the Comparison Test for Series

Lecture 12: The Ratio, Root, and Alternating Series Tests

Lecture 13: Limits of Functions

Lecture 14: Limits of Functions in Terms of Sequences and Continuity

Lecture 15: The Continuity of Sine and Cosine and the Many Discontinuities of Dirichlet's Function

Lecture 16: The Min/Max Theorem and Bolzano's Intermediate Value Theorem

Lecture 17: Uniform Continuity and the Definition of the Derivative

Lecture 18: Weierstrass's Example of a Continuous and Nowhere Differentiable Function

Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem

Lecture 20: Taylor's Theorem and the Definition of Riemann Sums

Lecture 21: The Riemann Integral of a Continuous Function

Lecture 22: Fundamental Theorem of Calculus, Integration by Parts, and Change of Variable Formula

Lecture 23: Pointwise and Uniform Convergence of Sequences of Functions

Lecture 24: Uniform Convergence, the Weierstrass M-Test, and Interchanging Limits

Lecture 25: Power Series and the Weierstrass Approximation Theorem