18.100A | Fall 2020 | Undergraduate, Graduate

Real Analysis


Course Meeting Times 

Lectures: 2 sessions / week, 1 hour / session

Recitations: 1 session / week, 1 hour / session


18.02 Multivariable Calculus

Course Description

This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts through a study of real numbers, and teaches an understanding and construction of proofs.


Lebl, Jiří. Basic Analysis I: Introduction to Real Analysis, Volume 1. CreateSpace Independent Publishing Platform, 2018. ISBN: 9781718862401.

This book is available as a free PDF download. You can purchase a paper copy by following a link at the same site.

Homework and Exams

The written homework is extremely important (mathematics is not a spectator sport). The best way to test your knowledge of a concept is to try and use it; this is why you work problems. Collaboration with other students in the class is encouraged, but separate solutions must be written up and collaborators documented at the top right-hand corner of all submitted work. In general, late homework will not be accepted. However, circumstances may arise that warrant an extension; such an extension request should be emailed to the instructor. The lowest individual homework grade will be dropped when computing the final homework grade for the course.

The midterm exam is a 24-hour take-home exam.


Assignments 1-12 account for 50% of the course grade, the midterm accounts for 25% of the course grade, and the Final Assignment accounts for the remaining 25% of the course grade.

Schedule Note

This class took place during the COVID-19 pandemic while students were not on campus. Prerecorded lectures for each week were posted on the class website each Monday. Recitations and Office Hours were conducted online.

Course Info

As Taught In
Fall 2020
Learning Resource Types
Lecture Notes
Lecture Videos
Problem Sets