Department of Mathematics
University of Colorado at Denver
This web page http://www-math.cudenver.edu/~jmandel/classes/5070s06 serves as the class syllabus and source of further information. Homeworks, material covered, and handouts are in the homeworks file. Photographs and scans are in the photos directory.
Final: Tuesday, May 9
Prerequisites: MATH 4320
Textbook: Walter Rudin, Principles
of Mathematical Analysis, McGraw-Hill, 3rd edition, 1976
Time and location: Tuesday and Thursday 4-5:15 WC 144
Office hours: UCD building 640, Tuesday and Thursday 2-3:30. I am also
available at other times, ask.
Contact: Phone 303-556-4475; email jmandel@math.cudenver.edu. I am
usually pretty good at answering email even at late hours.
The objectives of the class are to learn how to
This is the minimum of Analysis needed for applications and to prepare (in part) for the PhD Preliminary Examination in Applied Analysis.
Material
to be covered
Selected sections from the following, depending on the progress of the class:
Further required material is in the following recommended exercises. You may need to consult other books to solve some of the exercises.
The class will cover about 50-70% of the above material. Students who plan to take the prelim will need to study the rest on their own.
Class approach
This class is unusual. It does not teach
"material" as much as the way of careful and brutally honest
thinking - no fog can be tolerated. Do not trust
anything until you have verified it - this includes what I say and what is in
the book. This will take great time and effort. Please budget your time and
energies accordingly.
Sometimes students say "What was the class for? I had to learn
everything by myself." But this is exactly how it should be. No
amount of lecturing and explanations in the
class can replace the process of understanding and internalizing the knowlege
that you must go through by yourself.
So, the class time will focus on an overview of the material and some discussion
and problem solving, but you are expected to study in detail the complete
sections in the book that are covered and solve or at least attempt seriously
all recommended exercises. The good thing about exercises is that only the
first few from any topic are hard; then, once the first exercises make you go
back to the text many times and you get the general idea, the rest are easy. I
strongly recommend that you study in groups, work on the exercises in groups,
and bring to class or office hours the exercises where you need help - but work
on them seriously first. The homeworks can cover only a very small part of the
exercises; again, you should solve all the exercises yourself even if you do
not turn them in.
The progress of the class will be recorded and all assigments available in the class notes file.
Assignments and tests
There will be homeworks given most Tuesdays and due
always the following Tuesday, mostly consisting of exercises from the textbook.
Homeworks will be considered on time if they are turned in on the due date at
the beginning of the class or left at my office before the class. Late
homeworks will not be accepted except when arranged in advance, and then at 50%
if the rest of the homeworks was already graded. Please do not send
homeworks by email. There will be a midterm and final exams in
class. You cannot use any books, computers, or notes at the exams, except for
one 3" by 5" card where you can write anything you want. The midterm
will be on March 16. The final will be during the finals week as
determined by the Auraria finals schedule. The final will be from material
since the midterm. Because the grading system allows for skipping one of the
exams or all homeworks and still getting the full score, there will be no
make-up exams or work for extra credit.
Office hours
I enjoy discussing technical topics related to the class with my students during my office hours or any other time you walk in. Please do your homeworks ahead of time, and do not come to my office on the day the homework is due and expect me to do it for you. Please do not try to negotiate grades (except in the case of clear error on my part), and especially not partial credit. I usually need few minutes before the class to get organized, so please respect that and do not show up right before the class.
Grading
In all homeworks and exams, please show clearly all your work, but do not write irrelevant things just to fill more paper - this will not help, just the opposite because more writing means more opportunity for errors. Do not write incorrect statements. Points will be taken off for incorrect statements even if they are not relevant to the problem being solved. It is not enough that you understand the mathematics correctly – so that we can understand your solution, you must also follow the rules for mathematical writing. The point of most problems is the justification rather than a formal solution, so formal solutions count for little even if correct.
All work will be graded on the scale 0-4: 0=nothing relevant, 1=understands definitions and the problem, or a correct formal solution 2=good progress or a correct partial solution, 3=some minor glitch, 4=OK
The final score will be determined by the sum of the best 2 out out of the following, each scaled separately from 0 to 50: 1. homeworks 2. midterm 3. final. The letter grades will be A >= 90, A- >= 85, B+ >= 80, B >= 75, B- >=70, C+ >= 65, C >= 60, C- >= 55, D+ >= 50, D >= 45, D- >= 40.
Class Policies
Students are encouraged to study in groups, so certain similarity in the solutions (and errors) in homeworks is OK. Solutions clearly taken as a whole from other sources, such as another book or internet, in an obviously different setting than as done in the course, with mature elegant formulation, etc., will receive zero credit unless student can explain the solution well during office hours. Students found plagiarizing solution during in-class exams will receive zero credit for the exam and will be reported to the department and the college for disciplinary action.
Please do not eat during the class. Drinks are OK. All cell phones must be turned off before the class. Cell phone calls are very disruptive. If your cell phone rings, you will be asked to take the call outside and you cannot return to the class.
If you need any accommodation because of religion or disability, please let me know.
Incomplete grades
Incomplete grades (IW or IF) are NOT granted for low academic performance. To be eligible for an incomplete grade, students MUST (1) successfully complete a minimum of 75% of the course, (2) have special circumstances beyond their control that preclude them from attending class and completing graded assignments, and (3) make arrangements to complete missing assignments with the original instructor via completion of a CLAS Course Completion Agreement. Verification of special circumstances is required. The CLAS Course Completion Agreement is available from the CLAS Advising Office, NC 2024 or from the Department of Mathematics.
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Spring 2006 Registration and Academic Deadlines ·
CLAS students must always have an accurate mailing and
e-mail address: http:/www.cudenver.edu/registrar ·
Students are responsible for completing financial
arrangements with financial aid, family, scholarships, etc. ·
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January 17
– January 27, 2006 Students are
responsible for verifying an accurate Spring 2006
registration via SMART. ·
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