Math 311. Introduction to Real Analysis
MTWF 11:00 - 11:50 pm in Young Hall 207
Office Hours: MWF between 10 to 11:00 am, and MW from 2:30 to 3:30pm. You can also arrange a meeting by appointment.
Young Hall 105
Phone Ext.: #6187
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:
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.
- Infinite Summations
- Differentiability and Continuity
- The Convergence of Infinite Series
- Understanding Infinite Series
- Fourier Series
The course grade will be based on:
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
- The first midterm will be given on Friday September 15 and due on September 22. Feedback on September 25. Resubmit by September 29.
- The second midterm will be given on Friday October 27, due on November 3. Feedback on Nov. 14. Resubmit by November 20.
- The final exam will be given on Monday November 27, due on December 4. Feedback on December 6. Turn in the final product by Monday December 11 by 11:30am.
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:
I expect you to come to every class, pay attention, and to ask questions when you have questions. Some classes will have
when these occur, you should be working on the task at hand. I will also take points off for falling asleep or using a
(or a laptop) in class.
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 http://www.lakeforest.edu/academics/resources/disability/.
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.