MATH 406 (Spring 2020)

Important announcement: Due to the COVID-19 crisis, the Higher Education Council decided that all universities in Turkey hold their classes online. Consequently, the initial attendance policy and grading scheme are now void. Please expect regular announcements sent via e-mail.

MATH 406, Introduction to mathematical logic and model theory
Course Syllabus

Instructor: Asst. Prof. Burak Kaya
Office: M-126
Phone number: +90 (312) 210 2996
Office hours: Announced at this link
Class hours: TBA
Classroom: TBA

Prerequisites:   There are no official prerequisites for this course. However, since most examples in the course will be of algebraic nature, you are strongly suggested to have a solid understanding of topics in MATH116/367.

Course description: This is an introductory undergraduate level course to mathematical logic. The aim of the course is to introduce first-order logic, prove the related fundamental results (such as completeness, compactness and Löwenheim-Skolem theorems) and cover the basics of first-order model theory. (If time permits, we may prove Gödel’s incompleteness theorem and Tarski’s theorem of undefinability of truth. However, I suspect that we will not have enough time. Depending on the audience’s wishes, we may have extra lectures to cover these.)

Textbook: We shall be using several parts of the following textbooks.

Besides these, curious students may take a look at Yiannis N. Moschovakis’ lecture notes at this link as a supplementary resource. Those students who are interested in reading a graduate-level textbook in model theory may look at Dave Marker’s classical textbook on the topic as well.

We will be using the first three textbooks to cover the first-order logic and related fundamental results, and using the last three textbooks to cover basics of model theory. Each of these textbooks has its upsides and downsides. Consequently, I may be using one book to cover a certain result and use another one to cover another result.

For this reason, it is best to show up for the classes and take notes. Indeed, unlike the attendance policy in the elective courses that I taught in the past,…

Attendance: 85% attendance is mandatory after the add-drop week (that is, attending 10 weeks out of 12.)  I shall be taking attendance every lecture after the add-drop week. Those students who fail to attend 85% of classes (without an official report for the days they are missing) will not be able to take the final exam and get an NA grade.

The justification of this strict policy is the following:

  • We will be using multiple textbooks. So, if you do not show up for the class and try to study on your own, you will not be able to determine which book to study for each topic.
  • This is a highly abstract course and, compared to other elective courses, it has an “unconventional” nature. So, being a successful student or having obtained good grades from other courses will not cut it unless you build a solid understanding of the approach we are taking here from the beginning.
  • The “I can learn all the material with no prior knowledge in couple days before the exam” approach will not work in this course, unless you are really really skilled at abstract mathematical thinking.

Exams and grading: There will be two midterm exams (each out of 60 points) and a final exam (out of 80 points) together with a bonus take-home assignment (out of 10 points) that will be given after the final-exam. Your total grade (out of 110 points) will be computed by the following formula:

Total grade=(Midterm 1+Midterm 2+Final exam)*0.5+Take-home assignment

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.