The
class is over. Thanks all students for great semester!
Important announcements will be put
here during
the
semester. It is a good idea to check this space regularly before the
class or
before you want to come to my office.
Textbook:
1. Herbert S. Gaskill, P. P. Narayanaswami,
Elements
of Real Analysis, Prentice Hall 1997 2. Maxwell
Rosenlicht,
Introduction
to Analysis, Dover, 1986
Time and location:
Tuesday and Thursday 4-5:15 SI 109
Office hours: UCD building 640
Tuesday and Thursday 2:00-3:30PM. 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 off hours.
The objectives of the
class are
- become used to critical and accurate thinking needed for Analysis
- learn how to solve problems in Analysis
- gain a thorough understanding of basic methods of Analysis
- refresh and build on material from Advanced Calculus
- prepare (in part) for PhD preliminary
examination in Applied Analysis
Material to be covered
- Basic Logic
- Completeness and real numbers
- Limits of sequences and functions
- Basic Topology
- Differentiation
- Riemann integral
- Infinite series
- Sequences and series of functions
- Exponential, logarithmic, and
trigonometric functions
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 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 must 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 Thursdays and
due
always the following Thursday, 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% the 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 15, 2005 . The final will be
during the finals week as determined by the Auraria
finals schedule. 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.
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.
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.
However: Please do your homeworks
ahead of
time, and
try not to 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) or
partial
credit. I usually need few minutes before the
class
to get organized, so please respect the end of the office hours
and do not show up right before the class.
Grading
The 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.
Spring
2005 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.
* 12 January (5:00 pm)
Payment plan deadline for students registering by 17 December
2004. Students not on financial aid are administratively
disenrolled for non-payment.
* 20 January Last day
to be added to the wait-list for a closed course.
* 24 January - 1
February Students are responsible for verifying an accurate
Spring 2005 registration via SMART.
* 27 January (midnight) Last
day to add courses via the web SMART system.
* 2 February (5:00 pm) Last
day to add 16-week structured courses. Treated as an absolute
deadline. The 2 Feb deadline does not apply to independent
study, internships, and late-starting modular courses.
* 2 February (5:00 pm) Last
day to drop a Spring 2005 course for tuition refund and no transcript
notation.
* 2 February Last day
for undergraduates and graduates to apply for May, 2005 graduation.
* 4 April Last day to
drop a Spring 2005 course without college approval.
* 15 April Last
day to drop a Spring 2005 course for CLAS students. Treated as an
absolute deadline.
Consult the Academic Calendar for details on registration/payment
deadlines:
http://www.cudenver.edu/registrar
Last updated 5/10/05