I'm a graduate student in the Logic & Methodology of Science group at the University of Berkeley, California . This mainly involves working in the Math department, with occasional sojourns with the philosophers. I'm advanced to candidacy and am working with John Steel on some problems in inner model theory.
My office is currently 845 Evans (note change as of 9/19/05) and you can email at [my surname]@math.berkley.edu if you correct the typo in the domain name [hint: second word]. A first approximation to where I am at any given point in time this semester may be found by looking at this schedule.
The above is what I look like, or atleast, what I looked like three
years ago.
I'm selling books.
In Spring '08, I will be teaching section one of Math 74 (Transition to upper division math) MWF 3-4 in 85 Evans. Math 74 exists for people who have completed the lower division requirements for the math major / minor, but still don't feel ready to start taking proof-intensive upper division classes. As such there's no specific `content' for us to cover; this is definitely a skills-based class. The skills are in one sense very abstract: thinking about math and communicating that thinking with other people. That communicating needs to be done formally and informally, in writing and in speech, and must include composition and comprehension. More concretely, we will study some basic logic before looking at proof techniques and then apply our knowledge to understanding some na\"ive\footnote{``Na\"ive" in this context means ``not axiomatic".} set theory. Running alongside this, we will be taking `peaks' into other areas of math, via readings and talks.
(The above paragraph might look a little strange -- it's written as LaTeX source code. I did this by mistake (forgetting I was meant to be writing html, not LaTeX) but I thought I'd leave it there for the benefit of any students learning LaTeX (which, by the way, I recommend). Also, if you'd like to see the LaTeX source code for any other document I put up, just ask.)
More content will go up here as it gets produced (including homework assignments), but here's the Syllabus which contains all the information about the book, schedule, assessment, etc.
Some advice for the oral presentation, and the homework assigment for the rest of the course. Here are Solutions for all the homework problems.
Here's a Practice midterm for the first midterm (Solutions for the
real MT I), and
here's practice for the second (and solutions for the real one)
. Note: they're twice the
length of the real midterm. Here's the practice questions for the final.
[There were a few errors on the practice questions: [Orderings] 2(b) "minimal" should be "smallest";
[Equivalence relations] 2(c) the second sentence should read "One should have infinitely
many equivalence relations classes when..."; [Functions] 1 (a) "...define f[X
A] and f-1(Y B", (b) "XA", (c) "XB"; [Induction]
2. "F_n := F_0n-2 + F_"1n-1"". These have now been fixed as of 3:15 5/11/08.]
Here are sample Solutions.
--
As one of my students correctly observed on my mid-semester evaluation, "[I] enjoy teaching." If I get depressed, I may write some other comments from my evaluations up here as an ego trip. I keep an archive of past course announcements, etc, here.
I passed my qual in the Summer of 2006. I'll put my syllabus up here soon. In the mean time, you can hop around the MGSA Qual questions wiki to see what I was asked (may require you to create an account in order to see it).
My main job here as a doctoral student is to learn how to write about math in such a way that real mathematicians want to read it. Here's a selection of (unpublished) stuff I've already written:
2007: I gave a talk for MCF entitles Some Models have Bigger
Ones than Others, on the large cardinal program. I'm giving a talk
for SLC called I embed, periodically on results of the relevance
of very large cardinal axioms (I_0) to purely combinatorial / algebraic
questions about left-distributive algebras.
2006: I'm giving a talk for SLC on Independence Results
in Homological Algebra for Dummies.
2005: I wrote a paper on how
to choose between Non-Indexical Contextualism and Hidden Indexicalism
for my philosophy seminar, under the guidance of John
MacFarlane. After finishing it, he gave me some
helpful comments which I should respond to at some point.
Responsibility for the mis-spelling in the title is entirely mine!
I
also wrote some Model Theory for both 225A
and the model theory half of the prelim. There are many
things I'm not happy about with them, but some people said they were
useful so I thought I'd put them up.
Also, I have given two talks
on Freiling's family of proposed axioms for set theory and spoken at
a panel discussion on philosophy of math.
2004: An
evaluation of the accuracy of Godel's 1947 predictions concerning the
continuum hypothesis. This was my fourth year
dissertation at Oxford, which received first class honours from the
examiners. I wrote it under the most excellent supervision of
Robin Knight .
I
also wrote revision notes on the following topics: axiomatic
set theory , analytic topology ,
model theory and Godel's
incompleteness theorems .
2003: In Oxford, Finals come
but twice in your life (once if you're lucky) and examine a year or
two's material at a time. Having finals is a big deal. I
had finals in 2003, hence I didn't write anything for public use.
However, I did learn LaTeX. This is why recent stuff is in
beautifully typeset pdf and less recent stuff isn't. I also
wrote lots of revision notes. I wrote them on the following
topics: linear algebra and differential
equations , complex analysis and geometry
, groups, rings and fields ,
Lebesgue integration and topology ,
non-physical applications of maths ,
foundations , algebraic
structures and Galois theory , functional
analysis .
2002: Baire
classes . This was an essay I wrote under the guidance of
Andrew Dancer, my personal tutor at Oxford (this is the man who
taught me to write a good proof). It won the Junior Vaughan
essay prize. I gave a talk on it to the Invariant
Society (undergraduate Oxford maths colloquium). You
can read about it here .
2001:
Is a mathematician an inventor or a
discoverer? . This was an essay I wrote under the guidance
of Fiona Ellis, then a philosophy tutor at Jesus College, Oxford (I
believe she's now at Wadham College, Oxford. Regardless,
she appears not to have a web presence). This won the R. Aled
Davies Prize.
I apologize for the oldest two essays being in Word. What can I say... the errors of youth!?
In pursuit of my main job , I spend a lot of time listening to people talk about math.
Some times, when people are talking about math, they say silly things. I collect a list of some of the silly things they say here . Most of these are from Oxford. People at Berkeley don't tend to say as many silly things. Feel free to send me extra examples.
You may think it weird, but I actually like math... including the bits I'm not sufficiently motivated to actually study. Listening to people speaking about those bits is fun. Speaking about the bits I try to pretend I know something about can be fun too. To facilitate this, during 2005 I co-organized Many Cheerful Facts with David Brown (one of my then office-mates). MCF is a series of talks given by grad students for a general mathematical audience (mostly other grad students, though faculty and undergrads have been known to attend sporadically).
Believe it or not, I have a life outside math. I am a Catholic. My parish is Newman Hall. I love choral music, both singing it (I'm a baritone who tries to pretend to be a bass) and listening to it. I especially like "early" music (eg. Palestrina and earlier), Russian music (though I can't get the low notes the Russian composers like to give basses) and "modern" stuff (people like Kenneth Leighton).
I used to do lots of drama, both on stage and behind the scenes. Lighting design was a real love of mine. Unfortunately, I don't do much anymore. This is for no real reason for this except lack of time. I would like to do some more.
I also used to write poetry and short stories (got full marks in my high school creative writing class), but haven't done much of that recently apart from a few parodies. I have had a sonnet published in an Oxford literary review, but can't find an online copy to link to. I aim to try and put that up here soon.
Other random facts: I am a Brit, in particular an Englishman; I do knitting; my birthday was the day before the Superbowl this year; and I'm currently feeling slightly nostalgic as people from my secondary school seem to be just now discovering Facebook.