Math 8100

Real Analysis


Location: Boyd, Room 326
Time:  MWF  12:20 -1:10
Call #  22-839

Instructor: Akos Magyar
Office: 603B Boyd
Email:  magyar@math.uga.edu
Phone: 542-2543

Office hours: M 8:30-9:20 WF 2:00-2:50

Problem  Sessions: Fri 3:30 pm,   Room 326    

Textbook: E.M. Stein:   Real Analysis  (Princeton Lecture Series in Analysis III)

Tests:  There will be a take home Midterm and an in-class Final Exam.

Final Exam:  Wed, Dec 12  , 12-3:00 pm                       Fall 2007 Final Exam Schedule                         

Homework:  Will be assigned and grade on a weekly basis. We will also have Problem solving sessions each week.
Doing the homework assignments and the problems are very important for preparations toward the exams!

Grading:  Grades will be based on Homeworks the Midterm and the Final. Roughly distributed as follows:

                Homeworks (30%)           Midterm:  (30%)            Final:  (40%)  



Description:   The aim of the course is to give an introduction to the basic concepts of real analysis and measure theory as well as to prepare for the Real Analysis Qualifying Exam.
                       We discuss Chapters 1-4, Chapter 5: Sections 1-2, Chapter 6: Sections 1-4.
                       We will select from the following topics if time permits also depending on interests: 
                        Partial Diff. Eq. (Ch. 5.3), Ergodic theorems (Ch. 6.5), The Spectral theorem (Ch.6.6), Hausdorff measure (Ch.7.1, 7.4)

Note:    I will post homework problems, notes and links to related material on this page, so please check it regularly!

Homeworks/Problems: Here I'll list the homework assignments with their due dates, as well as the problems for the problem sessions. The abbreviations Ex. and Pr. means Exercises and Problems from the textbook and the number after them refers to the appropriate chapter. The solutions of the problems don't have to be turned in.
WEEK
 PROBLEM SESSION
 HOMEWORKS
 DUE
8/20 - 24
 Pr.1:  1, 3, 4      Ex.1:  9, 10, 11
 Ex.1:  1, 2, 3, 4, 16
 8/29
8/27 - 31
 Pr. 1:  2, 5, 7    Ex.1:  24, 30, 33, 34, 38
Ex.1:   8, 9,10, 11, 28, 29
 9/5
    9/3 - 7
 Pr. 1: 4     Ex. 1:  31, 35, 36, 39
 Ex. 1: 17, 18, 21, 22, 23
 9/12
9/10 -14
Ex. 2:  1, 3, 6, 10, 11
 9/19
9/17-21
 Pr.2: 1, 2, 4          Ex. 2:  5, 15, 22
 Ex. 2:  4, 9,12, 14 a,b,  16, 19
 9/26
10/8 - 12
 Pr.2: 3, 5     Ex. 2:  22, 23, 24, 25
Ex. 2: 2, 7, 8, 20, 21,
9/19
10/15 -19
 Pr.2:  2, 4, 7, 8
 Ex. 3:  2, 3, 4, 5, 11, 17
 10/26
10/22 - 10/26
Ex. 3:  12, 13,  14, 16
 11/9
11/12 - 11/16

Ex. 4:  2, 3, 4, 8, 11, 13 11/19
11/26 - 11/30
  
 Ex. 4:  10, 12, 15, 18, 20   Ex. 6: 3, 8, 9
 12/5


Midterm (with Solutions)

Make up Midterm