Math 6337 Real Analysis



                                                                                                                        Instructor: Michael Loss
                                                                            email: loss@math.gatech.edu
                                                                                                                    Lectures: TTh 9:30-10:45
                                                                                                                             Location: Skiles 254


                                                                                  Office hours: TTh 12:05-12:55 or by appointment


                                  Text book: Introduction to Real Analysis by Chris Heil, Graduate Texts in Mathematics, Springer
                               A copy of the book is available for you on the Springer website, Springer.com .
                                 You have to be logged in into Georgia Tech in order to download the book.

                        This book is copyrighted and for your personal use only. You are not to copy nor distribute
                                                          the book as a whole or in part to other parties.

                   
                     
                        
                               The goal of this course is to give you a solid introduction into measure theory. Originally, this theory grew out of the desire to be able
                               to integrate non-continuous functions. The key advantage of this theory, however, is that this theory leads to an integral that behaves
                               very nicely under pointwise limits. The advance is that the finite additivity of volumes is replaced by the countable additivity of measures.
                               We shall construct Lebesgue measure, talk about measurable function and develop an integration theory for such functions. Important
                               theorems will be the `Dominated convergence theorem' and the `Monotone convergence theorem'. A consequence is that we will
                               be able to construct a space of square integrable functions which will be a Hilbert space, i.e., it will be complete.


                                                                                                                     Course outline


                                                                                           

                                  Academic Dishonesty: All students are expected to comply with the Georgia Tech Honor Code. Any evidence of cheating  or other
                                  violations of the Georgia Tech Honor Code will be submitted directly to the Dean of Students. The institute honor code is available at

                                                                                                                 http://www.honor.gatech.edu

                                 
                                  Exams and Homework:  There will be a midterm exam, a final exam and 10 homeworks.  Seven of these homeworks will count.
                                                                         Seven homeworks, 28 points each = 196 points
                                                                          Midterm exam                                    40 points
                                                                          Final exam                                          60 points

                                                                          Total                                                 296 points

                                  Grades: 270-300 points = A, 240-269 points = B, 210-239 points = C, 180-209 points = D and below 180 points = F

                                  I might deviate from this scheme but only in your favor. This depends on the difficulty of the homework and the exams.

                                  Homework: I'll post the homework on this web page. Each homework has a due date and late homework will not be accepted.
                                                                  Write only on the front side of the page only and staple the pages together, not forgetting to write your name.
                                                                  Write legibly. If the grader cannot read what you wrote no credit will be given.  Write clearly and concisely. 
                                                                  I encourage you to submit your solutions typed, preferably in TeX or LaTeX. You may discuss and work 
                                                                  together but you have to write independently your solutions to the homework in your own words.


                                                         
                                                                                           Here is the link to the Homework     


                                                                                            Here is a link to the Practice Tests