**MATH 406, Introduction to mathematical logic and model theory**

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 13:40-15:30 Friday 13:40-14:30 |

Classroom: |
M-103 |

**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.

**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.**

Due to COVID-19 precautions, our classroom M-103 has been declared to have capacity for only 14 students. In other words, more than 14 students cannot be present in the classroom simultaneously. As a result of this restriction, I will do the following:

- After the registration and add-drop periods, registered students will fill out two different surveys to let me know whether they want to attend the lectures face-to-face or will follow lectures online via recordings.
- If more than 14 students decide to attend the lecture face-to-face, then I will split students into groups and ask each group to show up in the classroom only on certain days and follow lectures via recordings on the other days. Otherwise, we cannot follow the capacity restrictions.
- When you are registering for the course, be aware of this possibility.
**Unfortunately, I cannot think of another solution to this issue and you are more than welcome to suggest solutions. If you are unhappy with this decision, you can talk to the chair of the department or dean’s office. I am willing to implement other solutions that will allow more students to attend the face-to-face lectures.**

**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 two textbooks.

- A Friendly Introduction to Mathematical Logic by Christopher Leary and Lars Kristiansen, ISBN: 978-1-942341-07-9.
- An Invitation to Model Theory by Jonathan Kirby, Online ISBN:9781316683002.

Besides these, curious students may take a look at the books

- A Course on Mathematical Logic by
- Mathematical Logic and Model Theory by Alexander Prestel and Charles N. Delzell, Online ISBN: 978-1-4471-2176-3.

as well as 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 textbook to cover the first-order logic and related fundamental results, and using the second textbook 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.

**Attendance:** Attendance is not mandatory. Indeed, in some cases, you may have to not attend certain lectures. Please read the intruction method part of the syllabus to learn about why and when this may happen.

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) 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

**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.