REAL VARIABLES 1
Math 551, Fall 2019

 

 

Instructor: Adrian Tudorascu 
Office: Armstrong Hall 410F
e-mailadriant@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!