MATH 535 (Fall 2020)

Below you will find the PDF and TeX files of the homework assignments given this semester. These files are also posted on the ODTU Class course web page.

MATH 535, Topology
Course Syllabus

Instructor: Asst. Prof. Burak Kaya
E-mail: burakk@metu.edu.tr
Website: http://blog.metu.edu.tr/burakk
Office: M-126
Phone number: +90 (312) 210 2996
Office hours: TBA
Class hours: Monday 15.30-17.40, Friday 15.30-16.40.
(Friday 16.40-17.30 is also reserved if we need extra lectures.)
Classroom: Lectures will be held online. Before each lecture, you will receive a Zoom link over e-mail.

Prerequisites:   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 MATH349 or MATH251 and be satisfying requirements in the department’s policy for undergraduates taking graduate courses.

Course description: This is an introductory graduate level-course to general topology. You can reach the official catalog description of the course from this web page.

Textbook: We will be following the textbook

We are planning to cover Munkres’ book from Chapter 2 to Chapter 8, possibly with some omissions. Depending on our progress, we may cover additional material which I think are of importance.

Those students who wish to have supplementary resources besides Munkres’ book and the lecture notes may also take a look at General Topology by Willard, General Topology by Kelley and Topology by Waldmann. Finally, I should note that, though not a textbook to follow for this course, Counterexamples in Topology by Steen and Seebach is an excellent source of examples and problems.

Attendance: Attendance is not mandatory, however, is strongly suggested.

Assignments and grading: There will be five homework assignments each out of 10(+2 bonus) points, a final take-home exam out of 100 points and a subsequent oral exam out of 50 points. Your overall score will be calculated by the following function of three variables.

Overall score = (Homework assignments+Final Exam+Oral Exam) x 0.5

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 final exam, 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.

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.

Final exam and oral exam: Your final exam will be a take-home exam for which you will have ~96 hours to submit. Unlike the homework assignments, there will be no bonus points for TeXing. That said, you are free to submit solutions typed in TeX if you wish.

After the final exam, each student will reserve a time period to take an oral exam. The oral exam will be conducted as an (individually taken) interview over a video-conferencing software of your choice (such as Zoom, Webex etc.) and last approximately 20 minutes for each student. In order to comply with regulations, the oral exam will be recorded and stored at the department for two years as an electronic video file. In order to take the oral exam, you will have to officially give consent to being recorded.

If you wish to take this course and do not want to give consent for being recorded over such video-conferencing software for the oral exam, then you have the option to come to campus and take a written in-person exam to replace your online oral exam. Should there be such students, the written replacement exam time will be announced towards the end of the semester.

The questions in the oral exam will be of more conceptual nature compared to homework assignments and the final exam. For example, I may ask about some definitions, basic examples and counterexamples, and some easy proofs. However, there will be no proof questions that may require involved and long arguments.

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.