Course Topics:
We will cover the first four chapters of Stoll. As time permits, we will cover parts of Chapters 5, 6. At times I'll refer to Trench book (see above link)
The topics are:
- Chapter 1: Real Numbers, Methods of proof, Axioms of real number system
- Chapter 2: Limits, Bolzano-Weierstrauss Theorem, Cauchy sequences
- Chapter 3: Topology of Real line, Compact sets, Cantor Set
- Chapter 4: Limits, uniform continuity
- Chapter 5: Differentiation
- Chapter 6: Integration theory
The point of this course is to understand in depth the real number system.
Many basic properties of calculus that you are already familiar with will be
proved. However, along the way a number of additional theorems of calculus that should be new to most people will be covered, if not proved.
A very important part of the course is to develop an ability to
write clear and correct proofs. This is a necessary skill for people
planning on teaching high-school or community college calculus, as well
as those that are planning on persuing advanced degrees in engineering,
statistics, economics and a variety of other fields.
Calculators
are basically useless for this course.
Course Policy
The course grade is based upon about 200 total points from from quizzes and homework (50 percent of course grade), two mid-term
exams (15 percent each), and final exam (20 percent). Expect the first test the first week of October, the second in ht esecond week of November. (Exact dates will be announced obout two weeks in advance.
Due to the
high amount of theory, I have a
grade scale that is more spread-out than usual. I may curve a bit, but
I expect approximately an 85-70-55-40 percent scale.
Homework:
I'll assign many problems to work on. Most of these will be
"practice problems" that
will not be collected, but may be discussed in class or be problems we do as a group
on the board. Other problem sets are to be turned in and graded. You will have about 5 or 6 homework sets over the semester.
Late homework will be downgraded.
After I go over it in class it will no longer be accepted for any credit.
Practice Problems:
Most fridays will include some time to solve
practice problems on the board, and may include a short quiz on the
previous week's practice problems. Students that work practice problems (PP's) on the board will get some extra credit for turning in a write-up of the problem the next class period (2-3 pts each depending on the problem- up to a limit of 5 problems). Quizzes will be 5 pts each, no make-up will be given for missed quizzes.
Attendance:
Regular attendance is considered an important part of
the course. Therefore excessive absences may result in a grade reduction
depending on the number of missed classes that I am able to record.
(I only keep track of absences of students that routinely miss classes.)
There will not be any penalty for missing a few classes. If you
need to miss over two weeks of classes for legitimate reasons, please
discuss your situation with me. Note that quizzes can not be made up if a
class is missed.
My Webpage Policy
The classroom is always the
primary source of information. For convenience, I will try to regularly post
the assignments, important comments on the course webpage, but
from time to time, I make some typo or get something wrong. So please
correct me if you think I have something posted incorrectly. (When in doubt, go with what was stated in class, until you hear otherwise.)
Disabilities
If you have a documented disability and anticipate
needing accommodations in this course, please make arrangements with me soon.
You will need to provide documentation of your disability to the Disability
Resources office located on the main floor of the student services building,
Room 1076, 294-6624.
Last updated 1-5, 2009