Department of Mathematical Sciences
University of Colorado Denver
This web page http://www-math.cudenver.edu/~jmandel/classes/5070s08 serves
as the class syllabus and source of further information. Homeworks, material
covered, and handouts are in the homework file.
Photographs and scans will be in the photos directory.
Draft prelim syllabus based on the book for this course is
now available. Please send me any comments or questions.
The final is Tuesday 4-6PM.
Prerequisites: MATH
4320. A prerequisite to MATH 4320 is MATH
4310. For students who got at least B in 4310 I will treat 4320 as a
co-requisite. Otherwise, the prerequisites will be strictly enforced and students who do not have the prerequisites
and do not obtain my consent before the class starts will be administratively
dropped. MATH 4310 covers: “Calculus of one variable, the real number
system, continuity, differentiation, integration theory, sequence and
series”. MATH 4320 covers: “Convergence, uniform convergence; Taylor’s theorem;
calculus of several variables including continuity, differentiation and
integration; Picard’s theorem in ordinary differential equations and
Fourier series.”
Textbook: Berndt
S. W. Schroder, Mathematical Analysis. A
Concise Introduction. Wiley-Interscience 2007. ISBN 9780470107966
Time and location: Tuesday and Thursday 4-5:15 CU 656
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 jan.mandel@cudenver.edu. I am usually
pretty good at answering email even at late hours.
Objectives
- Build mathematics problem solving and writing skills to the level
required for the PhD Preliminary Examination in Applied Analysis
- Revisit selected areas of
analysis and their applications in more depth
- Transition from real line to
analysis on abstract spaces
It is
not the purpose of this class to cover all material needed for the Analysis
Prelim. That would be MATH 4310/4320.
Instead, this class will
- recall (but not teach) the prerequisites and solve problems with
attention to detail
- cover few select topics in more depth
- present new material.
Material
to be covered: selected sections from
- Functions of a single real variable: Ch. 1-5, 7, 10, 11
- Metric spaces: Ch.
15,16
- Differentiation and the implicit function theorem: Ch. 17
- Further topics as time allows
Learning philosophy
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. Before you apply a
theorem, check if the assumptions are satisfied.
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 knowledge 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. 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
20. 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 – you also need to write it so that
it can be verified and understood. 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.
Other 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; these will be handled
according to University
policies.
UCD
Academic Calendar
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Spring
2008 CLAS Academic Policies
The following policies
pertain to all students and are strictly adhered to by the College of Liberal Arts
and Sciences (CLAS).
- Every student MUST check and verify their schedule
prior to the published drop/add deadlines. Failure to verify a schedule is not
sufficient reason to justify a late add or drop later in the
semester. It is the student’s
responsibility to make sure that their schedule is correct prior to the
appropriate deadlines.
- CLAS students must use their email.cudenver.edu
email address. Email is the
official method of communication for all University
of Colorado at Denver
and Health
Sciences Center
business. All email
correspondence will take place using your UCDHSC email address. Go to http://www.cudenver.edu/registrar
to update and/or change your email address.
- Students are
NOT automatically added to a course off a wait list after wait lists
are dropped. If a student is told
by a faculty member that they will be added off the wait list, it
is the responsibility of the student to complete the proper paperwork to
add a course. Students are NOT automatically added to a course
off the wait list after the 5th day of the semester when wait
lists are dropped.
- Students are not automatically notified
if they are added to a class from a wait-list. Again, it is the responsibility of the
student to verify their schedule prior to any official dates to drop or
add courses.
- Students must complete and submit a drop/add
form to make any schedule changes.
Students are not automatically dropped from a class if they
never attended, stopped attending or do not make tuition payments.
- Late adds will be approved only when
circumstances surrounding the late add are beyond the student’s
control and can be documented independently. This will require a petition and
documentation from the student.
Late adds will only be approved if the student has not taken any
exams, quizzes, or has not completed any other graded assignments. Independent verification of this from
the professor of record will be required. Please note that the signature of a
faculty member on an add form does not guarantee that a late add
petition will be approved.
Petitions are available in NC 2024.
- Late drops will be approved only
when circumstances surrounding the late drop have arisen after the
published drop deadlines, are beyond the student’s control, and
can be documented independently.
This will require a petition and documentation from the
student. Pre-existing
circumstances (circumstances that existed prior to the published drop
deadlines) regarding illness, work, family, or other confounding issues
will not be considered adequate reason to drop or withdraw from courses
after the published University and/or College drop deadlines. Please note that the signature of a
faculty member does not guarantee that a late drop petition will be
approved. Petitions are available
in NC 2024.
- Students wishing to graduate in spring of 2008 must meet with their academic advisor by the end of the drop/add
period to obtain a graduation application. This application must be completed and
submitted by 5 PM on February 6,
2008. You can obtain an
application ONLY after meeting with your academic advisor. There are no exceptions to
this policy or date.
- Students are responsible for completing
financial arrangements with financial aid, family, scholarships, etc. to
pay their tuition. Students will
be responsible for all tuition and fees for courses they do not
officially drop using proper drop/add procedures and forms.
- Students who drop after the published drop/add
period will not be eligible for a refund of the COF hours or tuition.
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Important
Dates
- January
22, 2008; First day of Class
- January
27, 2008 ; Last day to be
added to a wait list using the SMART system.
- January
27, 2008: Last day to add a
course using the SMART system.
- January
22-January 28, 2008; Students
are responsible for verifying an accurate spring 2008 course schedule
via the SMART registration system.
Students are NOT notified of their wait-list status by the
university. All students must
check their scheduled prior to January 28, 2008 for accuracy.
- January
28, 2008: LAST DAY TO DROP WITHOUT DROP CHARGE.
- January
28, 2008: Wait Lists are dropped.
Any student who was not
added to a course automatically from the wait list by this date and time
MUST complete a drop/add form to be added to the class. Students are NOT automatically added
to the class from the wait list after this date and time. If your name is not on the official
student roster, you are not registered for the course.
- January
29, 2008: First day instructor
may approve request to add a student to a full course with a Schedule
Adjustment Form.
- January
29 – February 6, 2008:
Drops allowed using SMART system.
Drop charge applies. Full term courses may be added using
Schedule Adjustment Form.
- February
6, 2008 at 5 PM; Last day to add structured courses without a
written petition for a late add. This
is an absolute deadline and is treated as such. This
deadline does not apply to independent study, internships, and
late-starting modular courses.
- February
6, 2008 at 5 PM; Last day to
drop a spring 2008 course with
a tuition refund minus the drop
charge and no transcript notation.
Drops after this date will appear on your transcript. This is an absolute deadline and
is treated as such.
- February
6, 2008 at 5 PM; Last day to
completely withdraw from all spring 2008 courses with a tuition refund and no transcript notation. Drop charge applies. Drops after
this date will appear on your transcript. This is an absolute deadline and
is treated as such.
- February
6, 2008 at 5 PM; Last day to
request pass/fail option for a course.
- February
6, 2008 at 5 PM: Last day to
request a no credit option for a course.
- February
6, 2008 at 5 PM: Last day to
register for a Candidate for Degree.
- February 6, 2008 at 5 PM: Last day to petition for a reduction in thesis
or dissertation hours.
- February 6, 2008 at 5 PM: Last day to apply for spring 2008 graduation. You must make an appointment and see
your academic advisor to apply for graduation.
- After February 6, 2008 all schedule
changes require a petition.
Petitions are available in NC 2024.
- February 27, 2007: Early Alert System OPEN for
faculty.
- March 10, 2007: Early Alert System CLOSES for faculty.
- April
7, 2008 at 5 PM; Last day for non CLAS
students to drop or withdraw from all classes without a petition and
special approval from the student’s academic Dean. This is treated as an absolute
deadline.
- April
7, 2008 at 5 PM; Last day for CLAS students to drop or withdraw
from all classes without a petition and special approval from the
student’s academic Dean. This
is treated as an absolute deadline.
- No
schedule changes will be granted once finals week has started. There are NO exceptions to this
policy.
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