Class Information

Course Title Math 454: Axiomatic Set Theory

Instructor Kameryn Williams


Email kamerynw [ at ] hawaii ( period ) edu

Class Hours Tuesday/Thursday 12:00–13:15

Room Keller 413

Office Hours Tuesday/Wednesday/Thursday 10:30–11:30, or by appointment

Office Physical Science Building 305

Textbook A Course on Set Theory, Ernest Schimmerling, 2011 edition. (ISBN 978-1-107-40048-1)

Course Description Sets, relations, ordinal arithmetic, cardinal arithmetic, axiomatic set theory, axiom of choice, and the continuum hypothesis.

Prerequisite Math 321, graduate standing in a related field, or consent.

Grading Policy

Your grade in this course will be based on homework and two exams. Each assignment will be given a letter grade (A through F), from which your final grade in the class will be calculated. I reserve the right to give pluses/minuses for borderline cases. The meanings of the letter grades are as follows.

  • A: Demonstrated mastery of the material. Proofs are largely correct, with any errors being minor. Arguments are presented clearly, showing competency at mathematical communication.

  • B: Demonstrated strong understanding of the material. Proofs are mostly correct, but may have some significant gaps. The presentation is decent, but could use improvement.

  • C: Demonstrated understanding of the material. Attempted most problems and made non-trivial progress, but may not have full arguments. The presentation is lacking in clarity.

  • D: Demonstrated some understanding of the material. May have skipped many problems, or failed to make significant progress on the problems attempted. The presentation is unclear and difficult to follow.

  • F: Demonstrated negligible understanding of the material. Attempted few problems, and did not make meaningful progress. The presentation does not demonstrate an understanding of the logical structure of mathematical arguments.

I will assign homework through the course website, aiming at weekly to bi-weekly assignments. Please make sure you regularly check the website so you don’t miss anything. Most problems will be proof-based, but you may also be asked to perform some calculations. Some of the problems will be routine, while others will be more challenging. A few will be marked as “reach exercises”. These are optional, more difficult problems. You are encouraged to attempt them, but it will not hurt your grade if you don’t do them. On the other hand, successfully completing them is a good way to get extra credit :)

Collaboration is both allowed and encouraged. However, you should write your own solutions. It is okay to discuss the ideas with your fellow classmates, but simply copying their solution constitutes cheating. If you do collaborate on a problem, state so at the beginning of your solution. If you consult additional references or books, you should list them as well. It may happen that while reading a different book you stumble upon a solution to a homework problem. That is fine, so long as it is not done intentionally and you are up-front about it. I trust your honest in this regard. For some problems, I may specify that no collaboration nor outside references are allowed.

Problem sets will not be accepted past their deadline. If you will not be in class, then arrange to turn in your homework by email or through a classmate, or get it to me earlier. If you do not fully finish, then turn in your partial solutions. It may be that you do not see how to completely solve a problem, but you see how it could be solved if you could prove an intermediate result, or you can prove a special case of the problem. In this case, clearly indicate the nature of your partial solution. This may result in partial credit or, for the really tricky problems, full credit. On the other hand, just writing something does not guarantee credit. You must demonstrate understanding of the material.

You are encouraged to look beyond the scope of the problems. For example, if a problem asks you to prove a result and you find a proof of a stronger statement, this may result in extra credit.

When grading I will pay attention not only to the correctness of your arguments, but also to your presentation. Your work should be clear and readable, and I should be able to follow your arguments without difficulty. I do not require you typeset your homework (i.e. use LaTeX) but you should not be turning in scratch work. Part of the point of the homework assignments is to give you practice in writing mathematics. You should follow standard mathematical conventions, and fully state the problem you are solving before giving your solution.

Here is a short example of how I would like to see homework written up. In case you want to use it as a template, here is the .tex source file. (This work would receive an A; although the second problem was not answered in full generality, it was very difficult problem—a euphemism for impossible :P—and so the partial work demonstrates sufficient mastery of the material.)

The format for exams is to be announced later.

Academic Honesty

Cheating, plagiarism, and other forms of academic dishonesty will not be tolerated.

KOKUA Program

Students with disabilities are legally entitled to reasonable accommodations to ensure equal access to education. Any student who feels they may need accommodation based on the impact of a disability should contact the KOKUA Program, the UH Mānoa office for students with disabilities. I am committed to providing students with equal access to this class, and am happy to work with you and KOKUA to ensure reasonable accommodations in my course. Because the accommodations offered are usually forward-looking modifications rather than mitigating poor grades you may have already received due to your disability, it is important to get in touch with the KOKUA Program as soon as you can. Further information and contact details can be found on their website.

The ADA defines a disability as a medical condition that substantially limits one or more major life activities—including things like walking sleeping, taking care of yourself, learning, and regulating your emotions—or major bodily functions. If you have a medical condition—including mental health conditions—that significantly interferes with your schoolwork, you probably qualify. You do not need to disclose your condition to your instructors to receive accommodations.

Counseling and Student Development Center

The Counseling and Student Development Center offers confidential counseling services to support students with personal, academic, or career concerns.

Food Vault Hawaiʻi

Groups on campus have organized a food pantry, free to use for students at UH Mānoa. All registered students with a valid student ID may access the food pantry. Further information, including location and schedule, can be found here or on this facebook page.