# User:Michael Hardy

## Barnstars

 The Barnstar of Diligence Your endless devotion to wikipedia is amazing. Keep it up! Memming (talk) 12:57, 2 April 2010 (UTC)

 The Minor Barnstar A Barnstar for minor edits, but not a minor Barnstar! Thank you for your tireless work: you wikify tons of articles, and explain wikipedia' standards to tons of users! gala.martin (what?) 00:20, 8 April 2006 (UTC)

 The Original Barnstar This barnstar is given to recognize particularly fine contributions to Wikipedia, and to let you know that your hard work is seen and appreciated. evrik 23:15, 10 August 2006 (UTC)

 The E=MC² Barnstar For making mathematical and statistical articles readable for the layperson. Specifically, I ran across Second-order logic on random article and was extremely impressed by your work. Keep it up! Teke 18:37, 25 August 2006 (UTC)

Thank you! Michael Hardy 19:24, 25 August 2006 (UTC)

 The Original Barnstar I award you this barnstar in recognition of your continued work on statistics articles. Just about every statistics article I look at has some important contributions by you. Keep up the good work! Zvika 08:13, 5 January 2007 (UTC)
Thank you. Michael Hardy 22:49, 5 January 2007 (UTC)

 The Original Barnstar To Michael Hardy, on the occasion of Minneapolis, Minnesota reaching featured article. With thanks -Susanlesch 23:23, 28 June 2007 (UTC)
Thank you. Michael Hardy 06:08, 29 June 2007 (UTC)

 The Original Barnstar To Michael Hardy, on the occasion of Laplace transform and many other mathematics articles in which he showed his skill and vast knowledge of HTML, TeX and Wiki details. I learned a lot from your edits. With thanks --Lantonov 06:19, 1 September 2007 (UTC)

Thank you. Michael Hardy 18:06, 2 September 2007 (UTC)

## The climate has changed here

Is it just me, or does one no longer frequently encounter illiterate legalistically inclined Wikipedians who angrily order around anyone claiming professional expertise in the topic of articles that said illiterate legalistically inclined Wikipedians want to work on for no reason? I haven't seen much of that for the past year or so.

## Some normative comments on editing Wikipedia articles

### 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."

Here's another example (fictitious---a composite of several actual instances).

### Keep links simple when possible

Writing [[hyphen]]ated, [[logic]]al, [[cat]]s, [[evolution]]ary, [[rabbi]]nical, [[Egypt]]ian, [[dogma]]tic, [[apocrypha]]l, [[fur trade]]r, [[antagonist]]ic, [[algebra]]ic, [[legend]]ary etc., makes the whole word, not just the part in the brackets, appear as a clickable link, which links to the article whose title is in the brackets. The more complicated form can be used for things like [[philosophy|philosophies]].

Also, one does not need underscores as in [[prime_number_theorem]] or [[prime_number_theorem|prime number theorem]].

### a useful TeXnicality

${\displaystyle Y\ {\stackrel {\mathrm {def} }{=}}\ 1(y^{*}>0).}$

### NEVER NEVER NEVER use \mbox within Wikipedia

This was a temporary workaround when we didn't have better things available and produces inferior results in some cases. Worse: In standard TeX usage (as opposed to the way TeX is used in Wikipedia and similar web sites) \mbox has a completely different function, so its use within Wikipedia just misleads people about what it's for.

## How many times was a particular Wikipedia article viewed in a particular month?

Find out from this site.

## 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.

Lévy process, Wigner semicircle distribution, multinomial distribution, Ewens's sampling formula, imputation (statistics), law of total cumulance, copula (statistics) (incorporating some material from Sklar's theorem, which was created by User:Oo64eva and is now a redirect page), normally distributed and uncorrelated does not imply independent, list of stochastic processes topics, method of moments (statistics), method of moments (probability theory)

Eduard Helly, David Blackwell (both stub articles; if they're more than stubs when you see them, then more recent edits have been done)

### 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.),

pointwise convergence, Bernstein polynomial, George Boolos, Cantor's theorem, Löwenheim–Skolem theorem, second-order logic (much expanded by others since I started it)

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! This article has since been sweepingly revised by user:RJGray, who added material on a dispute over whether the proof is constructive and material derived from letters between Cantor and colleagues.

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.

## Puzzle

See if you can spot the difference between this:

${\displaystyle a+b+c+d\,}$
${\displaystyle +e+f+g+h\,}$

and this:

${\displaystyle a+b+c+d\,}$
${\displaystyle {}+e+f+g+h\,}$

Without looking at the TeX code, and guess how and—perhaps more subtly—why the difference was achieved.

That's subtle! Here is a cruder way of achieving the same effect:
${\displaystyle +\,e+f+g+h\,}$
--RockMagnetist (talk) 04:53, 29 September 2010 (UTC)
Actually this latter version by RockMagnetist is incorrect. The correct version, however, doesn't seem to work with our maths module, so I must show it in the commented spoiler below.
• Yea, I got the visual difference quickly but am uncertain what RockMagnetist is perceiving. I was going to put my observation up here and then realized when I saw the spoiler notes, that it would in fact be a spoiler. For those of us non-mathematicians, we certainly take some things for granted... Regards, Steve... Stevenmitchell (talk) 05:24, 8 March 2011 (UTC)
b_jonas 12:23, 7 December 2010 (UTC)
Actually I think the version using the curly brackets is better and more logical. However I normally put the dangling sign at the end of the first line and indent the second. Dmcq (talk) 17:37, 10 November 2011 (UTC)

My answer to the question above is this: When "+" is a binary operator, there is a space on each side of it, thus: 3 + 5. But when it is a unary operator, there isn't, thus: +5. In TeX, when you write +5 at the beginning of a line, the software construes it as unary since nothing comes before it (on the same line). But if you want it to be read as binary, you write {} +5, and then there's something (albeit invisible) before it, so it gets rendered as + 5. Michael Hardy (talk) 19:49, 12 May 2012 (UTC)