Math 5201 Real Variables
Syllabus
Fall 2016
Prof. Peckham
- Instructor: Bruce Peckham, Professor, Dept. of Mathematics and Statistics
- Office: 140B Solon Campus Center, 726-6188,
bpeckham@d.umn.edu
Office Hours: M 12-2, 4:30-5, T 3:30-5, W 10:30-11:30, 4:30-5, Th 4-5, F 12-2, 4:30-5, or by appointment
- Meeting times: MWF 3:00-4:05 in Chem 251
EXCEPTIONS: Up to 2 hours for tests may be allowed: Wed. Oct 5, Wed Nov. 16. No class Friday Nov 4 (I am attending the Midwest Dynamical Systems conference.) Individual classes may run as long as 3-4:30. Comparable time will be decreased on other days, or the extra time will make up for the missed class on Nov. 4.
- Text: Real Mathematical Analysis,
by Charles C. Pugh, Springer, 2002. Paperback version published in 2010, or second edition published in 2015 are all acceptable.
- Prerequisites:
UMD's Math 4201, Elementary Real Analysis, or
permission of the instructor.
Syllabus
The course will cover standard topics in real analysis: sets
and functions, construction of the reals,
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 and its use
in proving the existence and
uniqueness theorem for ordinary differential equations.
The course material is mostly covered in Chapters 1-5 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
Elementary Real Analysis (Math 4201).
Integration theory, especially
the Lebesgue integral, is largely left to Real Analysis (Math 8201, next taught Spring 2017).
Other References
- Your Calculus I, II, III textbook
- Analysis with an Introduction to Proof, Steven R. Lay
(text for Elementary Real Analysis, Math 4201). 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.
Cuts not used to construct the real numbers.
- Methods of Real Analysis by R. Goldberg, 1976.
Used in the distant 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.
General policy statement
Lectures, material in the text, assignments, 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.
Assignment Sets and Ground Rules
Written assignments will be turned in roughly every week or two.
All work should be neatly written or typed (say in latex),
well-organized, and complete.
For proofs, it is generally OK to use results only if we have
already covered them in the course.
For regular written assignment 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
assignment and facing academic disciplinary action.
ANY SOLUTIONS WHICH COME FROM THE WEB, OR FROM BOOKS OTHER THAN THE TEXTBOOK,
OR OTHER PEOPLE SHOULD BE FULLY CREDITED.
The goal of the course is to have you learn how to understand and create proofs,
not how to copy them from the web.
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.
All past and
current assignments will be posted on the web at
www.d.umn.edu/~bpeckham/5201/F2016/index.html..
Email notices will be sent by the instructor to alert students of changes in the
course web page. It is the student's responsibility to check email and the course web
page at least once every 48 hours.
Assignment Corrections: Correcting incomplete or incorrect assignments is strongly
encouraged. Half credit will be assigned for extra points earned for corrections.
Late Assignment Policy
Students will be allowed 5 grace days per semester for late assignments.
Once the grace days are used up, 10% per day will be deducted from any
subsequent late assignment until it is one week late.
Weekends count as one day.
After one week late students must make arrangements with the instructor to hand in work for credit of 50%.
Grading
| ITEM | DATE | TENTATIVE MATERIAL | WEIGHT |
| Test 1 | Wed. Oct. 5, 3-4:30 | Ch's 1-2, seqs, series | 15% |
| Test 2 | Wed. Nov. 16, 3-4:30 | Ch's 3-4 | 15% |
| Final | Wed. Dec. 14 10-11:55 | Cumulative: Chs 1-5 | 15% |
| Assignments/Quizzes | Various times | See course web page | 55% |
| Total | | | 100% |
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 written or 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.
Students with Disabilities
It is the policy and practice of the University of Minnesota Duluth to create inclusive learning environments for all students, including students with disabilities. If there are aspects of this course that result in barriers to your inclusion or your ability to meet course requirements - such as time limited exams, inaccessible web content, or the use of non-captioned videos - please notify the instructor as soon as possible. You are also encouraged to contact the Office of Disability Resources to discuss and arrange reasonable accommodations. Please call 218-726-6130 or visit the DR website at
www.d.umn.edu/access
for more information.
This page is maintained by
Bruce Peckham (bpeckham@d.umn.edu)
and was last modified on
Tuesday, 30-Aug-2016 18:32:21 CDT.