The course will meet Monday, Wednesday, and Friday at 10am, online. Zoom links can be found on Canvas. Lectures will be recorded, as many students have said it can be useful to be able to go back and re-watch parts of the lectures. Students are nonetheless encouraged to attend 'live', as that is what makes asking questions possible. I may not respond well to students who want to ask questions outside of class because they didn't bother to attend the lectures.
I will lecture a fair bit, as there will be material in our readings I need to explain, and material not in our readings I'd like to introduce. It is my hope, however, that there will be a good bit of discussion during our meetings, as well. It will be particularly important, therefore, that everyone come to class prepared not just to listen but to participate, every time, and of course that means reading in advance the material we will be discussing. I will talk some the first day about how to read mathematics.
I've activated the "Ed Discussion" platform for this class (which replaces Piazza). Please feel free to ask questions there, make comments, and start discussions. You can access it through Canvas.
There are no formal prerequisites for this course, though it will be helpful to have had some prior exposure to logic (PHIL 0540 or 1630, say). Mostly what you will need to know is what something like ∀x∃y(x < y) might mean, and how it would differ from ∃y∀x(x < y). (For one thing: The former is true, but the latter is false.) And you will need to understand what it means to say that the latter implies the former, but not conversely, and how this could be shown. I'll spend some time at the beginning of the course reviewing this material. See this page for some good online resources.
There is some overlap between the material covered in this course and the material covered in PHIL 1880, but the way we approach the common material will be very different. That said, it would not be a bad idea to have a copy of the text from that course, Computability and Logic, by Boolos, Burgess, and Jeffrey, to use as a reference for some of what we shall be reading.
What will be most important, though, is that students should have a degree of mathematical sophistication. The course will be very mathematical in content. It will be especially helpful if that students have a solid understanding of what it is to prove something mathematically, though this course will also, to some extent, teach that.
The only required book for the course is Undecidable Theories, by Tarski, Mostowski, and Robinson. It should be available at the bookstore. It is also readily available from the usual outlets, such as ABE Books, Amazon, and Barnes and Noble. You may also wish to purchase a copy of The Undecidable, edited by Martin Davis (ABE Books, Amazon, Barnes and Noble). This has Gödel's paper in it and several other things you should read, such as Turing's original paper on computability, though we will not be reading them in this class. If you just want a copy of Gödel's paper, you can buy it too from Amazon, Barnes and Noble, or ABE Books. Note that all three of the books I've just mentioned are Dover editions, so they are quite cheap.
Other readings will be distributed electronically. Some of these are available online through Brown's digital journal holdings; others will be scans of articles, or chapters from books, that are not otherwise available digitally.
To view PDFs, you will of course need a PDF reader. For the DjVu files, you will need a DjVu reader. Free browser plugins for Windows and Mac OSX are available from Caminova; Linux users can likely just install the djviewlibre package using their distro's package management system. Another option is Okular, which was originally written for Linux's KDE Desktop Environment but which can now be run, experimentally, on Windows and OSX, as well. A list of other DjVu resources is maintained at djvu.org.
The program I use to convert PDFs to DjVu is
a simple Bash script
I wrote myself, pdf2djvu. It relies upon other programs to do the real work and should run on OSX as well as on Linux.
There will be seven problem sets, connected with our readings, due about every couple weeks. There will also be a take-home final exam during the final exam period.
The exercises will mostly involve filling in the details of proofs from the readings or proving results that are similar to ones we discuss in class. As I will emphasize as we go, however, students should really be doing more of this kind of work than will be assigned. It is impossible to learn mathematics without doing mathematics, and in this case doing very often means: working out details the author leaves unstated, proving results for which the author does not give a proof, and so forth.
Students are encouraged to work on the problems together, though submitted material should be one's own work. That means you should feel free to discuss the problem sets with others, but your answers should be your own. Do not come up with a "group answer" and then each submit it. Indeed, I'd suggest you not come up with a group answer in the first place. If you do, destroy it, and then re-do the problem by yourself. This is what you need to be able to do, anyway.
You are welcome to do your problem sets by hand or on a computer. But if you are going to do the latter, then I would strongly recommend that you not use a traditional 'word processor' to do so. They are simply not optimized for mathematics, and their output is awful. A much better option is LaTeX, and if you want to use LaTeX in an environment that feels a lot like a word processor, then you can use LyX, which can be downloaded for free from http://lyx.org/. (I am one of the lead developers of LyX, so you should feel free to ask me any questions you may have about it.) Especially if you have any intention of ever doing serious technical writing, you should start using LaTeX sooner rather than later. In the sciences, especially, it is the standard tool. Many scientific journals do not accept submissions in any other form.
Final grades will be determined by a variety of factors.
There is a Canvas site for the course. It will mostly be used for submission of problem sets and to to record grades. Please do not pay any attention to any 'grade average' that Canvas might report. These are useless.
Problem sets should be submitted on Canvas on the day specified, by 10am. I will not accept late problem sets. On the other hand, you will find that I am quite prepared to grant extensions, so long as they are requested in advance, that is, at least one day prior to the due-date. Extensions will not be granted after that time except in very unusual and unfortunate circumstancess.
Because I am so reasonable, exploitation of my reasonableness will be taken badly.
You should thus expect your total time commitment for this class to be about 181 hours.
Brown University is committed to full inclusion of all students. Please inform the instructor early in the term if you have a disability or other condition that might require accommodations or modification of any of the course procedures. For more information, please contact the Office of Student and Employee Accessibility Services. Students in need of short-term academic advice or support can contact one of the deans in the Dean of the College's office.