Math 311. Introduction to Real Analysis

Fall 2017


Archimedes' quadrature. This is the original work of Archimedes (translated to English). Hard to understand the notation, but it's fun to see.

Fourier Mathematica notebook. Right-click and save-as, then open with Mathematica.
Alternating Harmonic Series Mathematica notebook.Right-click and save-as, then open with Mathematica.

Self-Explaining Booklet, is a short file with tips that can help you read proofs better.

The homework assignments can be found below:
Homework Assignments


A radical approach to Real Analysis (Second Edition) by David Bressoud.

Topics we will cover

In this class we will go deeply into why the theorems and techniques from Calculus are valid. We will explore the realm of the infinite and the infinitesimal. Our approach is to follow how these topics were developed chronologically. We will follow the motivations that lead to mathematicians to search for these proofs.


The course grade will be based on:
Homework 48%,
Questionnaire 5%,
Class Participation 8%,
Midterms 24% (12% each),
Final Exam 15%.


The course will have the following structure. There will be homework assignments on a roughly weekly basis. I will assign them usually on a Friday. On the Monday or Tuesday following the assignment, you can meet with me to ask for hints on problems you are stuck. I will only provide hints if I see evidence that you have worked at least 4 hours on the assignment. To figure this out, I will ask questions such as "What have you tried?" and perhaps ask you to show me your work so far. After this hint-day, you have three more days to complete the assignment and turn it in on Friday. You are allowed to work with others on the homework, but your homework should be your own. Furthermore, you will not be allowed to use the internet (other than things I post on this website) or other books as aids.
There will be 8 homework assignments. Each homework assignment will be worth 6% of your grade. Homework will not be accepted late.

There will be two midterms and one final exam. The three exams will be take-home exams and will have the same structure as the homework. You will get the assignment, have 3 days (or four) to work on it. Ask for hints on Tuesday and then turn it in on Friday. One big difference with homework assignments is that in exams you will be able to resubmit after feedback. Another difference with homework assignments is that on exams you will have to work entirely on your own (except for asking me questions) with the same restriction of NO INTERNET and no use of other books.

The (tentative) dates for the exams are

Videos and Questionnaire

The week of November 5 to 10, I will be attending the Mexican Mathematical Olympiad. There will be no class sessions. As a substitution, I will assign you to watch several videos related to Analysis. The list will be displayed here later. As part of the week, you will have to answer a questionnaire that will have questions related to the videos you will watch.

Videos to watch: Questionnaire.
Class Participation

I expect you to come to every class, pay attention, and to ask questions when you have questions. Some classes will have in-class activities, when these occur, you should be working on the task at hand. I will also take points off for falling asleep or using a smartphone (or a laptop) in class.

Accommodations Statement

If you believe that you need accommodations for a disability, please consult with The Learning and Teaching Center. Since accommodations may require early planning and are not retroactive, please contact the center as soon as possible. For details about the services for students with disabilities and the accomodations process, visit

You are also welcome to contact me privately to discuss your academic needs. However, all disability-related accommodations must be arranged through Teryn Robinson at the Learning and Teaching Center.

Last modified on November 28, 2017.