Math 311. Introduction to Real Analysis
Spring 2025
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Instructor:
Enrique Treviño
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Lectures:
MWF 9:00 - 9:50 am in Brown Hall 121
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Office Hours: MTWF from 11am to 11:30am and R from 9am to 11:00am. You can also arrange a meeting by appointment.
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Office:
Brown Hall 123
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Email:
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Phone Ext.: #6187
Announcements
Archimedes'
quadrature. This is the original work of Archimedes (translated to English).
Hard to understand the notation, but it's fun to see.
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
Course Description
A rigorous course covering the following introductory real analysis topics: axioms for the real numbers, sequences, boundedness, limits, monotone functions, continuity, uniform continuity, Cauchy criterion for convergence, cluster points, compactness, differentiability, integration, and infinite series. Prerequisites: Mathematics 210 and 230.
Textbook
A radical approach to Real Analysis (Second Edition) by David Bressoud.
Topics we will cover
- Infinite Summations
- Differentiability and Continuity
- The Convergence of Infinite Series
- Understanding Infinite Series
- Fourier Series
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.
Student Learning Outcomes
- Understand the formal definition of a limit.
- Be able to prove limits exist and evaluate those limits.
- Understand the formal definition of continuity and be able to prove functions are continuous.
- Understand convergence.
- Understand the proof of the Fundamental Theorem of Calculus.
Grading
The course grade will be based on:
Homework 20%,
Class Participation 5%,
Midterms 45% (15% each),
Final Exam 30%.
Homework
The course will have the following structure. There will be homework assignments on a roughly bi-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 7 homework assignments. Each homework assignment will be worth 3% of your grade. Homework will not be accepted late. Turning in a homework assignment automatically gets 1% of the grade. I will then choose two random problems in the homework and grade each one, each one will be 1% of the grade.
Exams
There will be three midterms and one final exam.
The (tentative) dates for the exams are:
The first midterm will be on Friday February 14.
The second midterm will be on Wednesday March 26.
The third midterm will be on Wednesday April 23.
The final exam will be a cumulutive three hour exam.
The date for the final exam is Monday May 5 from 8:30am to 11:30am.
Class Participation
I expect you to come to every class, pay attention, and to ask questions when you have questions. Some classes might have
in-class activities,
when these occur, you should be working on the task at hand.
Description of instructional time and expectations:
This course meets 3 times per week for 3.0 hours per week. The course carries 1.0 course credit (equivalent to four semester credit hours).
Students are expected to devote a minimum of 12 hours of total work per week (in-class time plus out-of-class work) to this course.
Academic Honesty
Please read the College's information on Academic Honesty. If a student cheats in an exam,
quiz or homework assignment, I will proceed with charging the student with the Academic Honesty Judicial Board. The usual (first) penalty is a 0 in the assignment on which the
cheating occured plus some ethics lectures the student would take. The second penalty is usually suspension.
Academic Resources, Protocols, and Policies
Click here: Academic Resources, Protocols, and Policies
Last modified on March 5, 2025.