Intro to Analysis
Please feel free to come by my office any time during scheduled
You are welcome to
come at other times, but in that case you might want to make
an appointment, just to make sure that I will be there then. You can
make an appointment simply by talking to me before or after class, by
calling me at my
or at home, or by sending e-mail.
You may also ask any questions directly via phone or e-mail. If I'm
not in when you call, please leave a message on the voice-mail or
answering machine with your name, number, and a good time for me to
call you back. I will try to respond to your phone or
as soon as possible.
You may also contact Dr. Knaust,
teaching the other section of this class, for help. He may be found
Hall 120, 747-5761, MWF 10:30-11:30.
I will assume that you have a thorough knowledge of the material
covered in the first two Calculus courses. If you consider taking
Math 3325, I strongly recommend that you take Math 3325 "Principles
of Mathematics" before you take Math 3341.
Real Analysis is "Calculus with Proofs". I expect you to
- thoroughly understand the definitions of the basic
concepts of Analysis such as convergence, continuity,
differentiability and integration;
- become familiar with the fundamental results
of "Analysis on the Real Line" (highlights of the course include
the Intermediate Value Theorem, the Mean Value Theorem, and the
Fundamental Theorem of Calculus); and
- continue to develop your
ability to use the method of proof to establish these
You will receive these notes in class. These notes differ from other
texts for proof-based courses, in that the proofs of the theorems are
not included. The point of this is for you, the student, to fill in
these details, in order to be more actively involved with the
material. Read the preface carefully for more details.
In order to further your active engagement, most class time will be
devoted to student discussions of the material, while I serve
primarily as a moderator.
- Participation (40%):
The course participants will take center stage during class
meetings. You will regularly give presentations of proofs of results
in the notes and present solutions to problems in class. Your
presentations are the most important part of the course. Your
chances of passing the course without spending a significant amount of
time on preparing in-class demonstrations are zero. Your
in-class work will be evaluated for both quality of the content and
When you are in the audience, you are still expected to be actively
engaged in the presentation. This means checking to see if every step
of the presentation is clear and convincing to you, and speaking up
when it is not. When there are gaps in the reasoning, the class will
work together to fill the gaps.
At all times, the conversation will be guided by the principles of
"mathematically accountable" talk.
- Homework (20%):
I will regularly assign written homework.
Assignments will be due at the beginning of class.
No late homeworks! (Incomplete homeworks will be accepted, though.)
If an emergency prevents you from delivering your homework on time (or
having someone else deliver it for you), please let me know as soon as
You are encouraged to work together on your homework, but you must
write up your solutions by yourself.
- Tests (10% each):
There will be two in-class, closed-book tests on the following days:
- Fri., 1 Oct.
- Fri., 12 Nov.
Makeup tests can be given only in extraordinary and unavoidable
circumstances, and with advance notice.
- Final (20%)
- The final exam will be comprehensive over all
material we discuss in class. The
final will be on
Wed., 8 Dec., 10:00-12:45 p.m.
Due to the course structure, attendance is mandatory. An unexcused
absence will result in a presentation grade of 0 for the day of the
absence. I will usually excuse an absence if you tell me about it in
advance, or, in cases of emergencies, as soon as possible afterwards.
The deadline for student-initiated drops with a
W is Mon., 18 Oct. After this date, you can only drop with the
Dean's approval, which is granted only under extenuating
I hope everyone will complete the course successfully, but if you are
having doubts about your progress, I will be happy to discuss your
standing in the course to help you decide whether or not to drop.
You are only allowed three enrollments in this
course, so please exercise the drop option judiciously.