REAL VARIABLES 1
Math 551, Fall 2019
Instructor: Adrian Tudorascu
Office: Armstrong Hall 410F
e-mail: adriant@math.wvu.edu
Office phone: 304-293-5339
· Lecture Schedule
The class will
meet three times a week, on Monday, Wednesday and Friday in ARM 403 from 10:30
a.m. to 11:20 a.m. We will not meet on official holidays and on dates
I need to travel for scientific purposes. On those dates, someone else may
substitute; you will be notified in advance.
· Course Description and Goals
Most of the
material will be presented in a manner consistent with the presentations in the
text. Students are expected to read and study the examples and related material
in the text and to work on the assigned problems sets. Similar problems will be
used as examples during lectures as preparation for the exams.
The topics covered include: Sets, Mappings, Relations; Real Line Axioms, Countable
and Uncountable Sets; Open, Closed, Borel Sets;
Sequences of Real Numbers; Continuity of Real Functions of Real Variable;
Measures and Measurable Sets; Lebesgue Outer Measure; Sigma-Algebra of Lebesgue
Measurable Sets; Outer and Inner Approximations of Lebesgue Measurable Sets; Nonmeasurable Sets; Riemann Integral; Lebesgue Integral
etc.
Upon completion of this
course, the student should be able to apply the covered notions and techniques to
problem solving. For this, the student is expected to have thoroughly
understood the theory linking the concepts.
· Textbook
Halsey Royden, Patrick Fitzpatrick, Real Analysis (Classic
Version), 4th edition, Updated Printing
· Grading Policy and Evaluation
There will
be homework, two tests and one
final examination. The highest scored test will be be worth 30%, and 25% the second best. The final exam
counts 30% towards the final grade. The homework will contribute 15% (best
eight assignments). The quiz scores may be used to bolster the final grade in
the course. The cutoffs will be 90% for an A, 80% for a B, 70% for a C, and 60%
for a D. The tests will be taken in class during the assigned lecture
time and are scheduled for October 02 (Wednesday) and November
20 (Wednesday).
The Final
Exam is cumulative and is scheduled for December 19 (Thursday) at 2:00 p.m. in
room ARM 403.
· Homework
Will be
assigned here; please check this link periodically (assigned
problems are in red, along with the due date). Students are strongly encouraged to work on all
the problems at the end of each section and collaborate (see Course Policy
below). Be aware that the problems and exercises tested on quizzes may
be similar or even identical to some homework assignments. No late homework will be accepted (the due
date will be posted along with the assignment).
· Office Hours
When: Monday
2:30 p.m.--3:20 p.m.
Wednesday 9:00 a.m.—9:50 a.m
Friday by
appointment.
Where: My Office.
· Course Policy
Class
attendance is encouraged. The Office Hours are to be used only after
you will have thoroughly read the material and tried to understand it.
Normally, no make-up tests or quizzes will be given for
any reason. Failure to take a test or a quiz will result in a score of
zero. Exceptions may be granted if permission to miss a test or a quiz is
obtained in advance.
Most likely, no calculators will be allowed on any test.
It is important that you not discard returned quizzes and tests! Not only do
they constitute good material for review but they are also the only acceptable
proof in case of misrecorded grades.
You may discuss your assignments with each other; however, solutions
should be written down individually. You should not read anyone else's
completed work or show yours to anyone else.
Exams and quizzes are to be worked on and written down strictly
individually.
How to succeed in this class:
·
Attendance will not be
taken in this class, however, it is expected that you will attend class regularly.
If you do miss a class it is your responsibility to find out what was covered
and whether any important announcements were made.
·
The single most
important thing that you should do is work out at least the
assigned homework. You should do the assigned problems, along with an
assortment of unassigned problems, as a study aid.
·
Collaboration on
homework is a good thing. You are encouraged to discuss the homework and to
work together on the problems.
·
Like all mathematics,
the material in the course cannot be learned passively. However reasonable,
simple, or rational you may find what you read or hear, you do not understand
it if you cannot apply it yourself. Thus it is imperative that you test
yourself by doing problems. If you have difficulty with a problem, ask your
instructor or your fellow students about it; do not assume that the difficulty
will cure itself without treatment.
Have you questions or concern about the course, please see me during
the office hours!
Good luck!