By Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis.

By Kyle Siegrist.

Online text: www.randomservices.org/random/prob/Events.html

The linked section discusses events and random variables. Its terminology includes a measurable structure with the sample space; this wiki names the underlying set and its sigma-algebra separately.

Additional section: Expected Value, 2 Additional Properties.

Cited passages: Right Distribution Function; A General Definition.

Additional section: Conditional Probability.

Cited passages: Probability Spaces, §4 Conditional Probability, Definitions and Interpretations, The Basic Definition; Basic Theory, The Multiplication Rule; Conditioning and Bayes’ Theorem, countable partition and weighted-average interpretation. Whole-textbook authorship is credited to Kyle Siegrist; no separate section byline or publication or revision date is established. The University of Alabama in Huntsville is an affiliation and project supporter, distinct from authorship; Random Services hosts the text.

Cited section: Expected Value, §6 Generating Functions, Basic Theory, The Probability Generating Function: definition, power-series expansion and absolute convergence on [-1,1]; Inversion formula f(k)=P^(k)(0)/k! and its termwise differentiation proof; Factorial moments and variance under the source’s stronger radius > 1 hypothesis; Independent-sum identity and expected-product factorization; The Moment Generating Function: M(t)=G(exp(t)) and finite-domain requirement.

Cited section: Definition: sequence of independent identically distributed jumps independent of the Poisson process; Properties: conditional mean/variance proof, generating-function conditioning proof, and PGF version; Compound Poisson Distributions: random count independent of the whole sequence; fixed-count-parameter definition.

By Keith Conrad.

Online text: kconrad.math.uconn.edu/blurbs/grouptheory/dihedral.pdf

Authored expository notes by Keith Conrad. No document date is established.

Cited passages: §§1–2, Theorem 2.5, printed pp. 1–4: rigid motions, rotations, reflections and dihedral order conventions.

By Gaston Floquet.

Source information: www.numdam.org/item/ASENS_1883_2_12__47_0/

Online text: www.numdam.org/article/ASENS_1883_2_12__47_0.pdf

Research article credited in print to G. Floquet, Gaston Floquet, published in 1883 in Annales scientifiques de l’École Normale Supérieure, series 2, volume 12, pp. 47–88. The linked scan and archive metadata identify the article; the historical citation does not assert priority for every modern matrix formulation.

Cited passages: Printed p. 48, definition of a function periodic of the second kind and its multiplier; p. 49, transformation of a fundamental solution system after one period.

By John M. Lee.

Source information: sites.math.washington.edu/~lee/Books/ITM/

Source information: www.math.toronto.edu/mgualt/courses/MAT1300F-2012/

Collection of sources; individual chapter authors and dates are recorded below.

Collection of sources; individual chapter authors and dates are recorded below.

Collection of sources; individual chapter authors and dates are recorded below.

Collection of sources; individual chapter authors and dates are recorded below.

By Terence Tao.

Online text: terrytao.wordpress.com/2009/04/06/the-fourier-transform/

Authored website post credited to Terence Tao and published 6 April 2009. Its course category is 245C, Real Analysis; the byline applies to this post, not to a separately published book of every course resource.

Cited passages: §3, Definition 32 and Exercise 54: Schwartz hypotheses and Poisson summation on the integer lattice; §3, Exercise 41: transform of a scaled Gaussian; put r=1/sqrt(a) and adjust its prefactor.

Additional locator: section 2, the constant character and Corollary 22, Fourier expansion on compact abelian groups with probability Haar measure. The zero coefficient is the average against the constant character. terrytao.wordpress.com/2009/04/06/the-fourier-transform/

By André Jürgen Massing.

Online text: www.math.ntnu.no/emner/TMA4130/2021h/lectures/ErrorAnalysisNuMeODE.pdf

Authored notes credited to André Massing, identified as André Jürgen Massing by the NTNU profile. Dated 3 October 2021, in the TMA4125/4130/4135 Mathematics 4N/D materials; the university is the host, rather than the author.

Cited passages: André Massing, Numerical solution of ordinary differential equations: One step methods, October 3, 2021, page 1, Example 1.1: Euler and Heun increment functions.

By Rodolfo Ruben Rosales.

Online text: math.mit.edu/classes/18.305/Notes/n00Branch_Points_B_Cuts.pdf

Standalone teaching notes credited to Rodolfo R. Rosales, identified as Rodolfo Ruben Rosales by the MIT profile. The title page says MIT 18.04 and is dated 11 October 1999; the hosting folder 18.305 does not identify its course or authorship of an entire course.

Cited passages: Rosales, Branch Points and Branch Cuts, section 1 and Example 2.4; Rosales, Branch Points and Branch Cuts, section 1, printed pp. 3–8, and Example 2.4, printed p. 15; Rosales, section 1, Definition 1.1 and its clarifications; Rosales, section 1, equation 1.3, and Example 2.4.

By Steven G. Krantz.

Online text: www.math.wustl.edu/~sk/books/guide.pdf

Author-hosted whole manuscript credited to Steven G. Krantz. The inspected title page is dated 14 October 2007; no first-publication or copyright year inferred. Citations use printed chapter pages, rather than the preliminary table-of-contents pagination.

Cited passages: Krantz, A Guide to Complex Variables, sections 9.3.4–9.3.5, printed pp. 158–159; Section 9.3.6, printed p. 159: globally defined holomorphic function; Sections 9.3.1–9.3.3, printed pp. 157–158: terminal elements and fixed endpoint homotopy.

By Arthur Pentland Dempster, Nan M. Laird, Donald B. Rubin.

Published in Journal of the Royal Statistical Society. Series B (Methodological), volume 39, number 1.

Online text: web.mit.edu/6.435/www/Dempster77.pdf

Joint article by Arthur Pentland Dempster, Nan M. Laird and Donald B. Rubin, printed with the byline A. P. Dempster, N. M. Laird and D. B. Rubin. Published in 1977 in Journal of the Royal Statistical Society, Series B, volume 39, number 1. The December 1976 presentation and later scan date are distinct from publication.

Cited passages: Section 1, printed pp. 1 and 3: naming of the two steps and earlier special cases; Section 2, printed p. 6, equation (2.17) and the general E-step/M-step definition; Section 2, printed p. 6: general maximization step; Section 3, printed pp. 6-7, Lemma 1 and Theorem 1, especially equation (3.10); Section 4.3, printed pp. 15-16, especially the paragraph following equation (4.3.3): conditional indicator probabilities and weighted counts.

By John K. Hunter.

Online text: math.ucdavis.edu/~hunter/notes/asy.pdf

The title page credits John K. Hunter and is dated February 2004; copyright 2004 is stated separately. The university is his affiliation and the notes host, rather than an author. No first-publication or online revision date inferred.

Cited passages: §1.1.2, p. 2: regular and singular perturbations; §4.3.5, p. 58: uniform solution and overlap subtraction; §§4.3.3–4.3.4, pp. 57–58: inner expansion and matching.

By Keith Conrad.

Online text: kconrad.math.uconn.edu/blurbs/gradnumthy/rationalsinQp.pdf

Standalone authored expository note. The inspected copy is undated; no publication date is inferred from the search engine or hosting path. It explicitly writes p-adic expansions with low-order terms first.

Cited passages: §1, printed p. 1: p-adic rational expansions and explicit low-order-first convention; §3, Theorem 3.1, printed pp. 3–5: eventual periodicity.

By Jan-Hendrik Evertse.

Online text: kconrad.math.uconn.edu/math5020f11/evertsepadicnotes.pdf

Authored notes dated March 2011. Their running header identifies Master Course Diophantine Equations, Spring 2011. The supplied UConn mirror is hosted within a different Fall 2011 course by Keith Conrad; hosting and teaching that course do not confer authorship of these notes. No publisher or original publication date is inferred.

Cited passages: §3, Theorem 3.4 and digit/congruence discussion, printed pp. 7–9: unique expansion and agreement of low-order digits; §3, printed pp. 6–7: definition of Zp, rational denominators and units.

By Robbert Fokkink.

Published in Nieuw Archief voor Wiskunde, series 5, volume 17, number 4, pp. 275–280.

Online text: www.nieuwarchief.nl/serie5/pdf/naw5-2016-17-4-275.pdf

Cited passages: Robbert Fokkink, Wie weet wie Willem Wijthoff was?, Nieuw Archief voor Wiskunde 5/17(4), December 2016, printed p. 279, Wythoffs bewijs van de stelling van Mantel: attribution of problem 28 in 1907.

By Igor Pak.

Online text: arxiv.org/pdf/1408.5711

Standalone historical preprint, arXiv:1408.5711. Version 1 was submitted on 25 August 2014; the inspected version 2 is dated 27 August 2014. Its cover says the account will appear as an appendix in a forthcoming book by Richard P. Stanley; the authorship here applies to this preprint, not to the whole book.

Cited passages: §§2–3 and §5, printed pp. 2–4: Euler correspondence, Segner recurrence and Catalan's bracketed products.