Kleene's Second Recursion Theorem and more general advice

[jimbob_barnes]

Ok so here is a little context, this academic year I've been applying to graduate schools for a PhD in mathematics, particularly in logic. So far I have places in Cornell, CUNY and Illinois at Chicago and the deadline for picking places is coming up quickly.

Now my tutor informs me that Cornell is very strong in computability theory so if I wanted to do that I should go there. The problem is that I almost entirely unfamiliar with computability theory, to fix this my final year project is on Tennenbaum's theorem and I am almost done. However there a supplemental smaller project which my tutor also advised I did on some more pure recursion theory namely Kleene's Second Recursion Theorem and I need some filler for the essay. Thus I have two questions.

1) What is the significance of the recursion theorems (philosophical or mathematical)? In particular things which are important for someone which little familiarity with the subject matter.

2) More broadly do any of you know about the three schools above and could give a general description of any experiences you have with them? (Oh, I am British and therefore don't know much about the US)

[gorcee]

Well, for one, Cornell is in Upstate NY. It's pretty far from anything exciting, which is basically the opposite of CUNY. Also, Cornell gets cold. Really cold. You know that stretch of winter you blokes had this year that was pretty cold? That's what Cornell is typically like, all winter, from like, November to March. Chicago can be very similar.

CUNY and Illinois @ Chicago are all located in a big city, and Cornell is not. Upstate NY is a series of small to mid-sized cities that punctuate a rather rural landscape. Ithaca is very much the same way. It is, however, gorgeous in that part of the country. (I went to school in Upstate NY and although my experience was both good and awful, I would not trade it for the world, and I still have great nostalgia about the clear winter nights up there).

Beyond that, they're all very good schools with a strong reputation in your field. I can't say I know too much about the departments or curricula, per se. But I can say that graduate programs in the US are much more uniform across universities than some people would have you think.

If you have the opportunity to visit prior to deciding, spend time with the faculty, ideally the ones you'd be working most directly with. They'll be your lifeline into the rest of the world, no matter where you go, and a good relationship is worth a hell of a lot more, sometimes, than the name on the sign at the University's front gates.

[Tirian]

As a western New Yorker, I'd temper gorcee's comments a little. Winters in both Chicago and Ithaca cap out at the freezing point throughout January and February and are milder in December and March. You'll have a winter coat and a hat and gloves and you'll make it. Both cities are going to tend to get plenty of snow as well, but I prefer to winter in cities that know how to handle snow than cities that are paralyzed by a storm. On the other side of the calendar, I think that the climate the other nine months of the year is an enormous asset to Ithaca -- the Finger Lakes are simply one of the most beautiful places on Earth and if you have any interest in water sports or hiking, it has a lot to recommend. Chicago and New York aren't literally intolerable in the summertime, but they can get hot and humid.

It is true that Ithaca is not cosmopolitan with regards to its culture, but it's still the regional capital of a very rich and elite part of the nation as well as being a vibrant college town. I don't recall hearing complaints about the lack of culture from graduates unless someone's needs literally require living in a city like New York, Boston, Chicago, or San Francisco. (As a Briton, perhaps it is worth saying that Ithaca is about five hours by train from New York for the times when you do feel like having a getaway weekend and hitting up Broadway.) As far as major universities in New York state go, I feel nervous when people go to RPI sight unseen but spending a portion of your life in Ithaca shouldn't be a burden to you if you feel that it's the best program for you in an academic sense.

[gorcee]

As a western New Yorker, I'd temper gorcee's comments a little. Winters in both Chicago and Ithaca cap out at the freezing point throughout January and February and are milder in December and March. You'll have a winter coat and a hat and gloves and you'll make it. Both cities are going to tend to get plenty of snow as well, but I prefer to winter in cities that know how to handle snow than cities that are paralyzed by a storm. On the other side of the calendar, I think that the climate the other nine months of the year is an enormous asset to Ithaca -- the Finger Lakes are simply one of the most beautiful places on Earth and if you have any interest in water sports or hiking, it has a lot to recommend. Chicago and New York aren't literally intolerable in the summertime, but they can get hot and humid.

It is true that Ithaca is not cosmopolitan with regards to its culture, but it's still the regional capital of a very rich and elite part of the nation as well as being a vibrant college town. I don't recall hearing complaints about the lack of culture from graduates unless someone's needs literally require living in a city like New York, Boston, Chicago, or San Francisco. (As a Briton, perhaps it is worth saying that Ithaca is about five hours by train from New York for the times when you do feel like having a getaway weekend and hitting up Broadway.) As far as major universities in New York state go, I feel nervous when people go to RPI sight unseen but spending a portion of your life in Ithaca shouldn't be a burden to you if you feel that it's the best program for you in an academic sense.

To be fair, the challenge of spending time at RPI sight unseen is largely due to the fact that you grossly underestimate your chances of getting stabbed. Honestly, I always felt like my trips towards the western part of the state took me to colder territories than Troy, but that may just be random coincidence. I second the quality of the nature aspect of Cornell, though. Some of the most beautiful land in the whole of the US is in that region.