# User:Michael Hardy

## Style tip

"In ABCology, an X is a blah blah blah."

is superior to

"X is a term used by ABCologists to describe a blah blah blah."

## Hello

 File:Hardy.jpg

The image is a driver's license photograph of me taken in August 1999.

## Some Wikipedia articles I originated

### On probability, statistics, probabilists, and statisticians

Francis Ysidro Edgeworth (a stub; if it's a long article when you read this, then someone else has contributed),

ancillary statistic, empirical Bayes method, Herbert Robbins, memorylessness, factorial moment, rule of succession, conditional independence, pairwise independence, prior probability distribution, infinite divisibility, a term used in physics, probability theory, and several other disciplines, Schrödinger method, Vandermonde's identity, an inequality on location and scale parameters, compound Poisson distribution,

In estimation of covariance matrices, I describe what seems to me to be a surprisingly subtle and elegant application of linear algebra. I have no idea who originated it; I seem to recall that it is in Morris Eaton's book on multivariate statistics, and I suppose it is in lots of others. In that argument you find out why it is sometimes better to view a scalar as the trace of a 1×1 matrix than as a mere scalar and then to apply certain matrix decompositions to it.

[[L�vy process]], Wigner semicircle distribution, multinomial distribution,

### On other mathematical topics

exponential growth (a concept that "laymen" take to mean very fast growth, but which has a technical definition that need not imply great rapidity)

empty product This explains why, when you multiply no numbers at all, you get 1, and why 00 is almost always 1, and should be taken to be 1 for the purposes of set theory, combinatorics, probability, and power series.

Archimedes Palimpsest This one mentions ancient history, mathematics, physics, engineering, an art museum, a federal lawsuit, and a very old hierarchical religious organization, in a very short space, without undue cramming;

orthogonal polynomials (Do not move that article to "orthogonal polynomial" under a delusion that that would conform to the convention of titling an article "dog" rather than "dogs". That would be absurd. There is no such thing as an orthogonal polynomial; there is such a thing as orthogonal polynomials.),

Cantor's first uncountability proof. This proof shows that the set of all real numbers is uncountable, but this proof is not a diagonal argument!

inclusion-exclusion principle, linearly ordered group, Boolean prime ideal theorem, uniform norm, Galton-Watson process, coherence (philosophical gambling strategy), dominated convergence theorem, Robertson-Seymour theorem, double integral (not the same as an "iterated integral"; see the article), Fubini's theorem, mathematical logic, Girard Desargues, Desargues' theorem, parallelogram law, Hamel basis, König's theorem, Schur complement (that article needs more work), combinatorial species (I left this one a stubby article that was barely a definition and two or three more-or-less obvious examples; AlexG has since added an account of operations on combinatorial species and lots of essential facts), A simple proof that 22/7 exceeds pi, Putnam Competition, Stone's representation theorem for Boolean algebras, Separation of variables, moment (a disambiguation page), list of mathematical examples (still in its infancy) Möbius transform, cross-ratio, Morera's theorem, Mahler's theorem, Cauchy principal value, Pincherle derivative

Radius of convergence -- This article includes an example of the fact that complex numbers are sometimes simpler than real numbers; they allow us to quickly find the radius of convergence of a power series in which the coefficients are Bernoulli numbers. (As you see from the previous sentence, I firmly believe in splitting infinitives on occasion.) Faà di Bruno's formula,

I moved the anonymously written "absolutely continuous" page to absolute continuity and rewrote it from scratch, including both absolute continuity of real functions, and absolute continuity of measures and the Radon-Nykodym theorem.

An infinitely differentiable function that is not analytic -- Although this is merely the usual example, I explained (albeit tersely, so far) its relevance to Schwartz's theory of generalized functions: One can construct test functions (i.e., infinitely differentiable functions with bounded support) with prescribed behavior on an interval. The existence of such functions must be known before we can confidently say that Schwartz's whole theory is not vacuous.

Moreau's necklace-counting function, cyclotomic identity, proof that holomorphic functions are analytic, branch point, Bell polynomials, Pedoe's inequality, Hadwiger's theorem (a stub; if it's a long article when you read this, then someone else has contributed), defect (geometry) (a fairly terse article so far....), Dandelin spheres, Matrix exponential (others have added material to that one), noncrossing partition, uses of trigonometry, Bohr-Mollerup theorem, characterization (mathematics), list of Boolean algebra topics, germ (mathematics), Lissajous curve -- someone has since edited that one by adding illustrations, Cauchy product, Gibbs phenomenon -- a number of people have worked on this one Schrödinger method, Vandermonde's identity, list of Fourier analysis topics Muirhead's inequality, Stanley's reciprocity theorem