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| ]. This proof shows that the set of all real numbers is uncountable, but this proof is '''not''' a diagonal argument! | ]. This proof shows that the set of all real numbers is uncountable, but this proof is '''not''' a diagonal argument! | ||
| ], ], ], ], ], ], ], ], ], ], ], ], ] (not the same as an "iterated integral"; see the article), ], ], ], ], ], ], ], ], ], ], ], ] (that article needs more work), ] (that needs ''a lot'' more work; it's barely a definition and two or three more-or-less obvious examples), ], ], ], ], ], ] (a disambiguation page), | ], ], ], ], ], ], ], ], ], ], ], ], ] (not the same as an "iterated integral"; see the article), ], ], ], ], ], ], ], ], ], ], ], ] (that article needs more work), ] (that needs ''a lot'' more work; it's barely a definition and two or three more-or-less obvious examples), ], ], ], ], ], ] (a disambiguation page), | ||
| ] -- I think this topic may be one of the best ways for any ] who is ignorant of statistical inference to get an impression of the flavor of that subject. | ] -- I think this topic may be one of the best ways for any ] who is ignorant of statistical inference to get an impression of the flavor of that subject. | ||
Revision as of 21:04, 23 July 2004
Style tip:
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I am a statistician and mathematician interested in foundational issues in probability and statistical inference. The image is a driver's license photograph of me taken in August 1999.
Among pages I have initiated (some of which have since been substantially edited by others) are these:
incidence algebra, Ladislaus Bortkiewicz, Euler characteristic, stereographic projection, Gauss-Markov theorem, common logarithm, Dirichlet kernel, 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 that 0 is almost always 1, and should be taken to be 1 for the purposes of set theory, combinatorics, probability, and power series.
binomial type, Sheffer sequence, umbral calculus, John Gillespie Magee, Junior, Bell numbers, Hermite polynomials, Chebyshev polynomials, Bernoulli polynomials, Completeness (statistics), Sufficiency (statistics), logit, Kolmogorov's zero-one law, self-evidence, Gian-Carlo Rota
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;
How Archimedes used infinitesimals, Archimedean property, tidal resonance, martingale, margin of error, zeta distribution, Zipf's law, confidence interval, Bruno de Finetti, Woods Hole Oceanographic Institution, Eric Temple Bell, Arthur Cayley, Maxwell's theorem, law of total probability, law of total expectation, law of total variance, Riemann-Stieltjes integral, bounded variation, Fall of Constantinople (I wrote a short stubby article; much has been added by others), Ferdinand von Lindemann, Charles Hermite,
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
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, list of religious topics, list of optical topics, Fellowship of Reason, Foundation for the Advancement of Art, 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, cumulant, parallelogram law, canonical correlation, Wishart distribution, Hamel basis, iridescence, König's theorem, Schur complement (that article needs more work), combinatorial species (that needs a lot more work; it's barely a definition and two or three more-or-less obvious examples), A simple proof that 22/7 exceeds Pi, Putnam Competition, Stone's representation theorem for Boolean algebras, Separation of variables, Elisha Otis, moment (a disambiguation page),
Rao-Blackwell theorem -- I think this topic may be one of the best ways for any probabilist who is ignorant of statistical inference to get an impression of the flavor of that subject.
list of mathematical examples (still in its infancy)
Möbius transform, cross-ratio, Morera's theorem, Mahler's theorem, Cauchy principal value, Student's t-distribution, 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, initial-stress-derived noun
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, Wiener process, errors and residuals in statistics, proof that holomorphic functions are analytic, branch point, Seymour Geisser, prediction interval, rankit, Bell polynomials, continuity correction, Pedoe's inequality, Studentized residual, Hadwiger's theorem, Francis Ysidro Edgeworth (a stub; if it's a long article when you read this, then someone else has contributed), ancillary statistic, defect (geometry) (a fairly terse article so far....), Roman Republic (19th century), Dandelin spheres, Matrix exponential (others have added material to that one), The Devil's Dictionary (and that one), noncrossing partition, empirical Bayes method, Herbert Robbins, What is trigonometry used for?, memorylessness, Bohr-Mollerup theorem, characterization (mathematics), examples of contour integration, factorial moment, list of Boolean algebra topics, germ (mathematics), rule of succession, conditional independence, Lissajous curve -- someone has since edited that one by adding illustrations, pairwise independence , prior probability distribution