Course Syllabus

Instructor: Patrick Lutz
Email: pglutz@umich.edu
OH: M 10 - 11 am, Th 4:30 - 5:30 pm in 2846 East Hall. Also 10-15 minutes after each lecture.

Lecture: MWF 9 - 9:50 am in East Hall 1866
Midterm 1: Monday, February 2, in class
Midterm 2: Monday, March 16, in class
Final: Thursday, April 30, 10:30 am - 12:30 pm

Class materials

Lecture notes: I plan to post handwritten lecture notes for each lecture. They will usually be posted by the end of the day on which the lecture occurred and can be found under the "Files" tab on canvas.

Textbooks: There is no official textbook for this class. However, there are many good set theory textbooks and it might be helpful to read one of these books alongside the class. Here are a few books that I recommend.

  • Elements of Set Theory by Enderton. This is a very well-written and highly regarded textbook. For at least the first 2/3 of the class, our course will roughly follow the material covered by Enderton's textbook (and in roughly the same order).
  • Set Theory: An Open Introduction by the Open Logic Project (based on a book by Tim Button). The Open Logic Project is a free, open-source project to create introductory textbooks in all areas of mathematical logic. Their set theory textbook is an accessible and well-written introduction to the subject. Like Enderton's book, for the first 2/3 of the class we will roughly follow the material covered in this book (though somewhat less closely than we will follow Enderton's book). You can find a free copy of this book here.
  • Basic Set Theory by Shen and Vereshchagin. This book does not cover as much of the material we will see as the two books above, but I think it is incredibly well-written and is full of introductions to interesting ideas connected to the course material which we will not have time to cover in class. It is probably most helpful for the material we will cover in the middle third of the class (roughly between midterms 1 and 2).

Course Schedule: You can find a detailed course scheduling, listing what topics we will cover each day, along with what sections of the textbooks recommended above they correspond to, on canvas under the "Home" tab.

Homework solutions: I plan to post sketches of homework solutions each week, which you will be able to find under the "Files" tab on canvas.

Discussion forum: We will use piazza as an online discussion forum for the class. Using piazza is optional and will not affect your grade in the class. However, if you have a question about the material we cover in class, the homework or the course logistics, I strongly encourage you to ask it on piazza so that other students who have the same question can benefit from seeing the answer (also, see the email policy below).

Course Policies

Email policy: In general, I would prefer that you do not email me except in cases of emergencies, personal situations, or other unusual circumstances. If at all possible, please ask questions either in class, during office hours or on piazza.

Grading scheme: 10% short homework, 15% long homework, 17.5% midterm 1, 17.5% midterm 2, 40% final exam. For each of the two midterms, your score on the midterm will be replaced by the average of your score on that midterm and your score on the final, as long as doing so would increase your grade; however, this only applies if you either take both midterms or provide me with a documented reason that you are unable to attend one or both midterms.

Homework: Homework will be assigned each week on Friday and due on the Friday of the following week (except that there will be no homework due on weeks with an exam). Homework will consist of two parts: several "short" problems and one "long" problem (possibly with several related parts), which are explained further below. Homework must be turned in at the beginning of class and late homework will not be accepted. If you are not able to attend class on a day when homework is due, you may email a pdf to me. However, this option is only open if you have an unavoidable conflict that prevents you from attending class (e.g. you are sick or out of town at a conference). In the case of an emergency which prevents you from completing the homework by the due date, please send me an email explaining the situation. Note that having assignments due or exams scheduled for other classes is not an emergency and does not excuse you from completing the homework on time.

Short homework: After most lectures, I will assign two homework problems on the topic of that lecture. These problems are intended to be relatively short and to check that you understand the main definitions and ideas introduced in that lecture. Each Friday, I will collect these problems into one homework assignment, which will be due the following Friday. I will likely grade just one or two of these problems and the rest will be graded on completion. However, to encourage you to complete the homework, each exam will have at least one problem taken from a homework assignment.

Long homework: Each week I will also assign one longer problem which is intended as a chance to explore some of the class material in greater depth. These problems will generally require more time and thought to solve than the shorter problems assigned after each lecture. I would also like you to put more time and effort into making sure that your solution to the long homework problems are clearly written and easy to read and that all the details are correct. You should try to write your solution so that a classmate who was not able to solve the problem would be able to read what you wrote and quickly understand the key ideas needed to solve the problem. To encourage you to do this, the long homework problems will be partly graded on the quality of your writing.

Exams: There will be two midterm exams and one final exam (see above for the dates of these exams). Both of the midterms will be held in class, and hence will be 50 minutes long. Make-up exams will not be given. If you have an unavoidable conflict with one or both of the midterms then please contact me and I will replace your midterm score with your score on the final. Note that I will only replace your midterm score with your final score if you contact me as soon as you are aware that you will not be able to take the midterm and provide appropriate documentation. In the case of an unavoidable conflict with the final exam, I will consider granting an incomplete.

For the first midterm you may not use any notes. For the second midterm, you may use one double-sided, hand-written page of notes. For the final, you may use two double-sided, hand-written pages of notes. The page should be at most standard size (e.g. A4 or 8.5x11 inches). No other resources are allowed on the exam, including calculators, computers, and textbooks.

Emergencies and unusual circumstances: In the case of an emergency or any other unusual circumstance that interferes with your ability to complete coursework, contact me as soon as you are (safely) able to and I will try to work with you to figure something out. If you encounter a temporary emergency that prevents you from completing the homework on time then as explained above, please contact me and provide appropriate documentation.

Collaboration and cheating

Collaborating with other students on homework assignments is allowed and even encouraged. Copying the work of another student or allowing a student to copy your work is cheating and is not allowed. In particular, it is okay to discuss a homework problem with another student or for them to give you hints or advice about how to approach it, but you should never read another student's written solution to any homework problem. 

You should treat online resources and AI tools as if they were another student in the class. That is, it is okay to read material online related to a homework problem or discuss approaches to it with an AI tool, but you should never read a complete solution to a homework problem online and you should never ask an AI to tell you a complete solution to a homework problem. If you accidentally find a solution to a homework problem online or if you find that an AI tool has started to tell you a complete solution, stop reading immediately and close your browser. If you have already read the full solution, you should not turn in that problem.

Note that all of this only applies before a homework assignment is due. After an assignment is due, reading another student's solution to a problem is fine.

For exams, no collaboration is allowed and all of your answers must be the product of your work alone. You should not communicate about the content of an exam with anyone (except for me) until everyone has finished taking the exam. If I catch you cheating on an exam, you will receive a score of 0 on the exam and I will consider further disciplinary action.

University Policies

Academic integrity: Unless otherwise specified in an assignment all submitted work must be your own, original work. Any excerpts, statements, or phrases from the work of others must be clearly identified as a quotation, and a proper citation provided. Any violation of the School’s policy on Academic and Professional Integrity (stated in program-specific student handbooks) will result in serious penalties, which might range from failing an assignment, to failing a course, to being expelled from the program. Violations of academic and professional integrity will be reported to UMSI Office of Academic and Student Affairs. The faculty instructor determines consequences impacting assignment or course grades; the School may impose additional sanctions.

Accommodations for students with disabilities: If you think you need an accommodation for a disability, please let me know at your earliest convenience. Some aspects of this course, the as­signments, the in-class activities, and the way we teach may be modified to facilitate your participation and progress. As soon as you make me aware of your needs, we can work with the Office of Services for Students with Disabilities (SSD) to help us determine appropriate accommoda­tions. SSD (734-763-3000; ssd.umich.edu/) recommends students request disability-related academic accommodations via the Accommodate system, a core electronic case management system that will assist students, faculty, instructors, and staff in requesting, approving, and implementing disability-related accommodations. I will treat any information that you provide in as confidential a manner as possible.

Student well-being: Students may experience stressors that can impact both their academic experience and their personal well-being. These may include academic pressure and challenges associated with relationships, mental health, alcohol or other substances, identities, finances, food insecurity, or other external stressors.

If you are experiencing concerns, seeking help is a courageous thing to do for yourself and those who care about you. If the source of your stressors is academic, please contact UMSI's academic success team via umsi.academicsuccess@umich.edu or me so that we can find solutions together.