MATH 452 (Fall 2021)

MATH 452, Introduction to functional analysis
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: Announced at this link
Class hours: Wednesday 10:40-12:30
Friday 14:40-15:30
Classroom: M-13

Prerequisites:   There are no official prerequisites for this course. However, by nature of the topic, you are expected to have a good understanding of topology of metric spaces as covered in MATH349 and fundamental results regarding vector spaces and functionals as covered in MATH261.

Instruction method: Although the instruction method for this course has been announced as “hybrid”, 100% of the lectures will be held face-to-face. I would like to point out that this possibility (that all lectures are held face-to-face) was stated in the relevant announcement.

I will be holding lectures online only in the case that I have to be quarantined due to COVID-19 precautions. I am hoping that I stay not infected and this situation never occurs.

While the lectures will be held face-to-face, I will also be recording each lecture and the recordings will be available each week on ODTU Class and YouTube. Consequently, students who do not want to show up for the class can watch the lecture videos online.

Course description: This is an introductory undergraduate level course to functional analysis. The aim of the course is to introduce the basic theory of Banach spaces and cover some classical results such as the Hahn-Banach theorem, the uniform boundedness principle, the open mapping and closed graph theorems, as well as, their applications.  (If time permits, we may cover some basic results regarding Hilbert spaces, though, there is a separate course MATH497 for this topic.)

Textbook: I am going to TeX lecture notes for this course, which will mostly be based on Prof. Dr. Zafer Nurlu’s past lecture notes for this class. These TeXed lecture notes will be available in the teaching material section of my departmental web site every week before the lectures. (You may check out my previously TeXed lecture notes for MATH320 and MATH501 to get a sense of what you should expect.) Besides these lecture notes, students who wish to have a textbook may take a look at the following textbook.

A copy of this textbook is available in the library. Actually, the course material that we will cover is pretty classical and consequently, any standard textbook on functional analysis should be fine, as long as you pay attention to potential minor differences in notation and some definitions.

Attendance: Attendance is not mandatory.

Based on a note by the Dean’s Office which is forwarded to the faculty members of department, no student is going to be admitted to the classroom without registering their HES code to the university’s system via portal.metu.edu.tr.

Recall also that the university administration announced on September 3, 2021 that

“Yüz yüze eğitim yapılan ders ve uygulama mekanlarında ve tüm kapalı alanlarda maske takma zorunluluğu getirilecektir. Bu şartı yerine getirmek istemeyenler dersliklere ve ilgili alanlara alınmayacak; bu konudaki takip, uygulama ve sorumluluklar ilgili akademik ve idari birim yöneticilerine verilecektir.”

and that

“Bütün öğrencilerin ve tüm personelin dersliklere, ortak çalışma ve kullanım alanlarına girebilmeleri için e-Nabız koşullarına göre aşı süreçlerini tamamlamış olmaları; henüz aşılarını tamamlamamış olan öğrencilerin ve personelin ise beyan edilen gün dahil en fazla 3 gün önce alınmış negatif sonuçlu PCR testi sunmaları gereklidir.”

You can find English versions of these announcements following this link in Academic Procedures Item 9 and Administrative Procedures Item 1.

For this reason, any student who refuses to wear a mask in the classroom will be reported to the chair of the department and will be physically removed from the classroom by the authorities, if necessary. Your vaccination status or PCR tests may also be checked while entering the classroom.

Exams and grading: There will be two midterm exams (each out of 60 points) and a final exam (out of 80 points). Your total grade (out of 100 points) will be computed by the following formula:

Total grade=(Midterm 1+Midterm 2+Final exam)*0.5

Both midterms and the final exam are planned to be held in-person and are NOT online exams.

Let me now talk about some imaginary scenarios which hopefully are not going to not take place. If at any point during the semester, the Council of Higher Education or the university administration decides that we cannot hold face-to-face exams due to new COVID-19 restrictions, then

  • the remaining exams will be conduced as webcam-proctored online exams via Zoom or BigBlueButton and these remaining exams will be worth 80% of what they are originally planned to be worth. In this case, there will be an oral exam that is worth the remaining points (excluding the bonus take-home assignment).
  • For example, suppose that before we conduct the first midterm, the university decides that there will be no more in-person exams due to new COVID-19 restrictions. In that case, the two midterms and the final exam will be worth 48 points, 48 points and 64 points respectively. Then the exams add up to (48+48+64)*0.5=80 points. This means that the oral exam will be worth 20 points.
  • Now, suppose that after we conduct the first midterm as an in-person exam, the university decides that there will be no more in-person exams due to new COVID-19 restrictions. In that case, the second midterm and the final exam will be worth 48 points and 64 points respectively. Then the exams add up to (60+48+64)*0.5=86 points. This means that the oral exam will be worth 14 points.
  • Finally, suppose that we conduct both midterms as in-person exams and then it is decided that there will be no more in-person exams due to new COVID-19 restrictions. In that case, the final is worth 64 points. Then the exams add up to (60+60+64)*0.5=92 points. This means that the oral exam will be worth 8 points.

While it may be obvious at this point, to avoid confusion, let me emphasize the following: There will not be an oral exam if we can have all exams held in-person.

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.