Math 5201 Real Variables
Syllabus
Fall 2008
Prof. Peckham
- Instructor: Bruce Peckham, Assoc. Professor, Dept. of Mathematics and Statistics
- Office: 104 Solon Campus Center, 726-6188,
bpeckham@d.umn.edu
- Office Hours: M 2-2:50, T 1-1:50, W 2-2:50, Th 9:30-10:30, F 10-10:50
or by appointment
- Meeting times: MWF 3:00-4:05 in LSBE 129
- Text: Real Mathematical Analysis,
by Charles C. Pugh, Springer, 2002.
Syllabus
The course will cover standard topics in real analysis: sets
and functions, countability, limits, convergence of
sequences and series of real numbers,
metric spaces, convergence in metric spaces,
continuous functions on metric spaces, connectedness,
completeness, compactness, contraction mapping theorem.
A variety of applications such as the existence and
uniqueness theorem for ordinary differential equations will also be covered.
The course material is mostly covered in Chapters 1-4 of the Pugh text.
Some supplemental material, not included in the text, will occasionally
be presented in lecture.
Related material in other courses:
Many of the topics in this course are introduced in Calculus I, II and III
(Math 1296, 1297, and 3298).
Some of these topics are studied in more detail in
Intermediate Analysis (Math 3299).
Integration theory, especially
the Lebesgue integral, is largely left to Real Analysis (Math 8201).
Other References
- Your Calculus textbook
- Analysis with an Introduction to Proof, Steven R. Lay
(text for Intermediate Analysis, Math 3299). Lower level than Pugh.
- Introduction to Real Analysis, 3rd edition, Bartle and Sherbert, 2000.
Comparable to Pugh, but with more details filled in, but less material on topology.
- Real Analysis with Real Applications, by Kenneth R. Davidson and Allan P. Donsig, 2002. Similar level to Pugh, used in the past for Math 5201, lots of interesting applications.
- Methods of Real Analysis by R. Goldberg, 1976.
Used in the past for this course.
(Many other texts at this level exist. Any of
them might offer alternative explanations to many topics.)
- Fractals Everywhere, 2nd edition, Michael Barnsley, 1993. An introduction
to Fractal Geometry. Nice example of an interesting metric space and
use of the contraction mapping theorem.
Course Prerequisites
Intermediate Analysis (Math 3299) or equivalent or
permission of the instructor.
Grading (Topics and dates are tentative)
Exam 1: Fri. Oct. 17 Ch's 1-2 15%
Exam 2: Wed. Nov. 26 Ch's 3-4? 15%
Final Exam: Wed. Dec. 15 12-2pm Cumulative 20%
HW sets, Quizzes?, Take-home exams, ...: 55%
Subtract part of lowest grade: -5%
-------------------------- ---
Total: 100%
HW Corrections: Correcting incomplete or incorrect homework is strongly
encouraged. Half credit will be assigned for corrections.
General policy statement
Lectures, material in the text, homework sets, and tests are
all intended to complement each other. No one is a replacement for any of the
others. You are, in general, expected to learn material which is covered via
any of these sources.
Homework Sets and Ground Rules
Homework will be turned in roughly every week.
All work should be neatly written,
well-organized, and complete.
For proofs, it is generally OK to use only rusults that we have
already covered in the course.
For regular homework sets, you are encouraged to exchange
ideas with each other, but each person should write up his/her
solutions completely
in his/her own words. It is never appropriate to give a written version of a
problem/proof to another classmate, except to have the classmate read and
evaluate your work with you present.
It is OK to verbally explain your ideas to another classmate, as long as the
classmate then writes up his/her work on his/her own.
One person copying a classmate’s solutions is expressly forbidden
and will result in both students receiving zeroes for that complete
homework set and facing academic disciplinary action.
It is often instructive to read extra problems at the end of
each section and think about how you would solve them, even if you don't actually
attempt to solve them.
Assignments will be confirmed by email, and all past and
current assignments will be posted on the web
at `www.d.umn.edu/~bpeckham/5201/F2008/'.
Missed Exams or Quizzes
Missed quizzes
or exams will
be assigned a zero score unless you provide a valid written, signed
(by a Doctor, for example) excuse for
your absence; unless it is not possible to do so, you must provide verbal
notice ahead of time to your
instructor for an absence. Arrangements
for a makeup should be made as soon as you know you will miss.
Do not wait for the next
class. You can leave the instructor
a message 24 hours a day by phone or email.
Oversleeping,
poor preparation, slight colds, and cold weather are not valid excuses.
Disabilities
Please inform me of any disabilities of
which I should be aware
in order to provide for equitable participation.
This page is maintained by
Bruce Peckham (bpeckham@d.umn.edu)
and was last modified on
Thursday, 04-Sep-2008 13:18:34 CDT.