# Jay Williams

Page Redirection Hey there! I'm no longer at Rutgers. If you are not redirected automatically, follow the link to my current website. I am a 5th-year Ph.D. student in mathematics at Rutgers. My research interests are in logic; mainly descriptive set theory and its application to problems in combinatorial/geometric group theory.

You can contact me at jaywil at math dot rutgers dot edu.

### Teaching info:

My office is room 512 in Hill Center on Busch Campus.

In the Fall 2011 semester I will be the recitation instructor for Math 151, Calculus I for the Mathematical and Physical Sciences. My office hours are from 1-2 PM Mondays and 4-5 PM Wednesdays, or by appointment.

### A few words on workshops

The workshops we do in this class are intended to sharpen not only your mathematical skills, but also your ability to communicate to others how you used math to solve a problem. This means when writing up a workshop problem, you need to do more than just show a few algebraic manipulations and underline an answer. The average person (even one who understood calculus) would look at that mystified as to what any of it means, and why the answer given has anything to do with the problem presented.

Think of it this way: if you were explaining how to do the problem to another student, you surely would not just recite a string of mathematical equations at them. You'd actually say why you did the steps you did, and how you got from one to the other. The writeups should be done in a similar spirit, although perhaps more polished and formal.

The workshops are worth 10 points each. My grading rubric for the workshops is as follows.

• 2 points for correct mathematical setup
• 2 points for correct work during the mathematical steps
• 1 point for the correct answer
• 3 points for clear and correct explanation of the work done and the answer found
• 1 point for correct spelling/grammar (yes, I'm serious)
• 1 point for clear, well-labelled pictures and figures (this is not always necessary, in which case the point will be part of the explanation points)

Quiz 1
Quiz 2

### Course Notes

• These are notes for Math 561, Math Logic. I have done several (but not nearly all) of the provided exercises as well. Please let me know if there are any typos, or unclear (or wrong!) proofs. Many thanks to Adrien Deloro, who helped me immensely with the formatting and lectured the class. There is a table of contents listing the topics covered; it is roughly 1/3 set theory and 2/3 model theory.
• These are notes for Math 566, Axiomatic Set Theory. This class was an introduction to the techniques of forcing. Again, there is a table of contents listing the individual topics covered. This has been revised to fix several typos, but please, let me know if you find any more.
• These are notes for Math 553, Topics in Group Theory. This class was an introduction to geometric group theory, covering quasi-isometries, amenable groups, the Grigorchuk group, and several other things. As always, if you find any typos please let me know.