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`