Math 651, Real Variables 2, Spring 2005 

Instructor          K. Chris Ciesielski 
Office              308G Armstrong Hall
Office hours        Wednesday 2:00-3:30 pm, Thursday 10:00-11:30am, and by appointment 
Phone               293 2011 Ext. 2337
E-mail              KCies@math.wvu.edu

Classes meet        Wednesday 3:30-4:45pm & Thursday 8:30:00-9:45am in 309 Armstrong Hall

TEXTBOOK:           Real Analysis, third edition,  H. L. Royden,
                    MacMillan Publishing Company, New York.
      
TENTATIVE           Homework                       30%
GRADING SCHEME:     Mid Term Test                  30%
                    Comprehensive Final Test       40%


Prerequisites:      Math 551 Real Variables 1

HOMEWORK            will be a very important part of this course. 
                    I will be assigning many exercises, 
                    especially at the beginning of the course,
                    to keep the constant flow of information of students
                    level of understanding the material. 
                    The exercises causing problems will be solved
                    either in class or in the handouts. 


COVERED MATERIAL    I will start following the text at Chapter 3 (Lebesgue Measure).
                    During the semester we will certainly cover also
                    and plan to cover at least Chaprters 4-6 (The Lebesgue Integral,
                    Differentiation and Integration, and The Classical Banach Spaces).
                    We may also Chapters 11 and 12, time depending. 

                    I assume that the material covered in Chapters 1 (Set Theory)
                    and 2 (The Real Number System) of our text was covered in sufficient 
                    details in prerequisite course. 


TESTS FORMAT        I plan to give you "semi-take-home" exams.
(TENTATIVE)         I mean by it that few days before I will give you
                    you a set of 5-10 exercises from which I will choose
                    3-5 exercises for IN CLASS test.
                    You will be NOT ALLOWED to use your notes during the test.
                    Moreover, each test may also contain few theoretical
                    question in form of: 
                    - define a notion;
                    - state a given theorem; or
                    - sketch the proof of a given theorem.