This page is still under construction. For more details on my research, go to this separate page.

Mathematical education: article by W.P. Thurston (originally appeared as Notices of the AMS 37:7 (Sept. 1990), 844--850. See [math.HO/0503081] for an online copy

A rummage through my bookmarks has turned up a 1990 article by Halmos for the American Mathematics Monthly, provocatively titled Has mathematics slowed down? For a slightly querulous commentary you can read the Math Review by Dieudonné.

- Math in the Movies
- Fast Fourier Analysis on Groups
- Part III 2004-05: lecture courses and essay topics
- Research at Lancaster: RM and related analysis

Barry Simon's 'The Case Against The Codes' has me convinced.

A preprint of Alberti, Csornyei, Pelczynski and Preiss shows that BV has BAP.

Some recent notes (104 pp.) of M. Khalkhali on "Very basic noncommutative geometry": [math.KT/0408416]. Material covered includes: examples of algebraic and analytic duality between geometry and algebra; several constructions of cyclic (co)homology with and without topology on the algebra; short appendices on Banach algebras and equivalence of categories.

Some day I hope to understand more of a talk given by Martin Bridson at the 2004 LMS meeting in Newcastle.

An extended index to Cartan and Eilenberg's 1956 book Homological Algebra can be found here.

The paper The OK Corral and the power of the law [MR 99d:60028] makes for interesting reading.

Division by three is a surprisingly interesting problem, quoted approvingly by John Baez (week 147).

Is Cambridge biased against state-school applicants? Read this articlette for an argument why this is not immediate from the observed statistics.

The quotient of a uniform algebra by a closed ideal can be isometrically embedded in B(H) for some Hilbert space (see § 50 of Bonsall and Duncan's 1973 Springer book). Some other references are:

- [MR 51 #1408] A. Bernard, Quotients of operator algebras, Seminar on uniform algebras (Univ. Aberdeen, 1973).
- [MR 48 #2779] A.M. Davie, Quotient algebras of uniform algebras, J. LMS (2) 7 (1973), 31--40.

Stats in action: interpreting poll leads using the margin of error. A similar point is made in this weblog post: CJR Campaign Desk: Margin of Ignorance.

- Distances between the winning numbers in Lottery
- An article/lecture by James Propp: Fermat's Last Theorem and the Fourth Dimension
- [math.CA/0502408] A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices

The title is self-explanatory; the article appeared in Amer. Math. Monthly, Vol 112, No. 2, Feb. 2005, page 118. - [math.FA/0502021] On the uniform convexity of L^p
We present a short, direct proof of the uniform convexity of L^p spaces for 1<p<\infty.

- [math.CO/0501170] Tilings

"Based on a Clay Public Lecture by the second author at the IAS/Park City Mathematics Institute in July, 2004" - [math.AG/0501146] Tropical geometry

4 pp. (from MSRI newsletter: intended for a general mathematical audience)

Ralph Howard has an exposition of Gunther's proof of the local Nash imbedding theorem, in DVI, gzipped PS and PDF formats.

Baez and Bunn have a very readable expository article on the meaning of Einstein's equation

- From Kevin Brown's MathPages: Determining the Galois Group of a Polynomial
- Ibid: Galois Groups

Helpful entries on Mathworld:

- (pho rem ??-02-06) In praise of exposition
- Michael McIntyre's LUCIDITY PRINCIPLES supplement
- Can We Make Mathematics Intelligible? -- a 1981 article by R.P. Boas for the American Mathematical Monthly
- Publish or Perish: Finding a Journal
- Shahn Majid's guide to writing papers
- advice from John Baez
- R. F. Streater on good courses
- Kline: Why the professor can't teach
- J.S. Milne's tips for authors
- Rota: 10 lessons I wish I had been taught
- Peter Cameron on the RAE

math full record search for 'sofic group' all years (1992-2004)

- Alexander Grothendieck
- Amenable group
- Atiyah-Singer index theorem
- Bicyclic semigroup
- Coherent sheaf
- Cohomology
- Comma category
- Combinatorial species
- Congruence relation
- Galois connection
- Group representation
- Hodge theory
- Kuratowski closure axioms
- Mikio Sato
- Non-standard analysis
- Scheme (mathematics)
- Stack (category theory)
- Tarski monster group
- Thompson groups
- Transfinite induction
- Wishart distribution

Some search results on MathSciNet:

- Matches for: Anywhere=agler AND Anywhere= model theory
- Matches for: Author/related=Atiyah, M* AND Anywhere=configuration space
- Matches for: Author/related=Barr, M* AND Anywhere=cohomology
- Matches for: Review text=Banach AND Anywhere=(cogebra OR coalgebra)
- Matches for: Author/related=Barr, M* AND Anywhere=cohomology
- Matches for: Anywhere=Barr and obstruction theory
- Matches for: Author/Related=bercovici AND Anywhere=free
- Matches for: Anywhere=decoupling inequality
- Matches for: Anywhere= derivative AND polynomial AND (Lucas' theorem)
- Matches for: Anywhere=elliptic AND Anywhere=reaction-diffusion AND Anywhere=logistic

(it seems that these kinds of modified heat equations are used to model population dynamics) - Matches for: Anywhere=( (Galois extension) OR (Galois theory) ) AND (Banach algebra)
- Matches for: Author/Related=(Hewitt AND Zuckerman) AND Anywhere=semigroup
- Matches for: Anywhere=hypercontractive inequality
- Matches for: Anywhere=idempotents AND group ring AND Kaplansky
- Matches for: Author/related=Manuilov AND Anywhere=asymptotic representations
- Matches for: Author/related=Mbekhta, M* AND Anywhere=generalized inverse
- Matches for: Anywhere= (Property T) AND cohomology
- Matches for: Anywhere=(Rips complex) OR (Rips construction)
- Matches for: Author/Related=Turowska AND anywhere=synthesis
- Matches for: Anywhere=zero divisor conjecture

Abstracts and details for some papers by R. F. Streater:

- Ito's formula is the chain rule with Wick ordering
- Classical and quantum probability
- Fock space decomposition of Levy processes

See also the following for interesting comments:

Expository bits:

- 20 pp. survey article on SCV (by R.M. Range)
- Galois connections primer by George Strecker
- Gröbner Basis Theory (a gentle introduction)
- ``Some motivating ideas in mathematical logic", by John Kirby
- Basic concepts in quantum information theory
- Zeilberger: Enumerative and algebraic combinatorics

My supervisor's neighbourhood of the Maths Genealogy looks like this, as far as I can work out.