MATH 501, Analysis
|Instructor:||Asst. Prof. Burak Kaya|
|Phone number:||+90 (312) 210 2996|
|Office hours:||Announced at this link|
|Class hours:||Tuesdays: 11.40-13.30
- If you are a graduate student, then there are no prerequisites.
- If you are an undergraduate student, then, in order to take this course, you should have passed (or have a working knowledge of) MATH 349 and be satisfying requirements in the department’s policy for undergraduates taking graduate courses that are sent to you over e-mail at the beginning of each semester.
Course description: This is an introductory graduate level-course to measure theory and integration theory.
As far as I think, the topics that will be covered in this course is so fundamental to mathematics that any mathematician should know these basics, regardless of what field they specialize in.
Textbook: We shall be mainly following my lecture notes, which can be found at this link. I would like to note that I am planning to cover more than what is included in the lecture notes this semester, and hence there will be sections added to lecture notes towards the end of the semester. Besides my lecture notes, you can use the following excellent textbook
- Real Analysis: Modern Techniques and Their Applications, Second Edition,
by Gerald B. Folland ISBN: 978-0-471-31716-6.
copies of which are available in the library reserve collection. You should keep in mind that, while my lecture notes will be based on Folland’s book, some notational conventions and details in my lecture notes may differ from the book.
Those students who wish to have supplementary resources may also take a look at Measure Theory by Donald L. Cohn and Measure Theory by Vladimir I. Bogachev, both of which can be downloaded from Springer’s own site provided that you connect to through the campus.
Attendance: Attendance is not mandatory, however, is strongly suggested.
Assignments and grading: There will be 7 homework assignments each out of 10(+2 bonus) points, a midterm exam out of 50 points and a final exam out of 100 points. Your overall score will be calculated by the following function of three variables.
Overall score = Homework assignments x 0.60 + Midterm x 0.40 + Final x 0.40
Your final letter grades will be given based on your overall score.
Submission of homework assignments and bonus points: You will use Gradescope to submit your homework assignments electronically over the internet. I will grade your homework submissions, as well as your exams, through this system. Once the class roster is finalized after the add-drop period, you will get an e-mail which contains instructions for logging into Gradescope. If there are any students who, for any reason, want their homework assignments and exams not to be graded over Gradescope, then these students should contact me as soon as possible.
LaTeX has been a fundamental tool to the mathematical community over years. A mathematician who does not use LaTeX is like a fisherman who uses a wooden stick instead of a professional rod.
For this reason, any non-empty homework submission typed in LaTeX which contains at least one attempted-solution will automatically get +2 bonus points. You can ask others who use LaTeX about how to install a TeX distribution, such as MiKTeX, and a TeX editor, such as TeXmaker.
Academic dishonesty policy: You are expected to be familiar with the university’s academic integrity guide for students. No form of academic dishonesty is tolerated.