By Richard P. Stanley.

Online text: math.mit.edu/~rstan/bij.pdf

Authored problem collection. The inspected cover is dated 18 August 2009; this identifies the supplied version rather than a book publication date. The Catalan interpretations occur in §5, printed pp. 38–39, Problems 153–159.

Cited passages: §5, Problem 154, printed p. 38: binary parenthesizations of n+1 letters; §5, printed pp. 38–39, formula (7) and Problems 154–159: Catalan counts, binary parenthesizations, binary trees and Dyck paths.

By Charles M. Grinstead and J. Laurie Snell.

Publisher of the underlying book: American Mathematical Society.

Online text: math.dartmouth.edu/~prob/prob/prob.pdf

The linked CHANCE Project version is dated 4 July 2006. Its cover identifies the underlying second-edition book as copyright 2003 by the two authors, and this version as copyright 2006 by Peter G. Doyle. The version credit does not identify Doyle as an original-book coauthor or formal editor. These dates describe copyrights and a version, rather than a claim about first publication.

Cited passages: §3.1, Example 3.3 and Table 3.1, printed pp. 77–78: uniform-calendar assumptions, distinct-label product and threshold.

Section 6.1, Definition 6.1, printed p. 226, defines finite discrete expectation by summing values weighted by their probabilities. This is the discrete calculation used in nonnegative random variable. Online text: math.dartmouth.edu/~prob/prob/prob.pdf .

By Refael Hassin, Nimrod Megiddo.

Publisher: Elsevier Science Publishing Co., Inc.

Published in Linear Algebra and Its Applications 114/115, 589–602.

Online text: theory.stanford.edu/~megiddo/pdf/orientat.pdf

Cited passages: Hassin and Megiddo (1989), Theorem 2.6 proof, printed p. 592: cycle orientation and contraction, explicitly described as a different constructive proof from Robbins's; Hassin and Megiddo, On Orientations and Shortest Paths (1989), printed pp. 591–592: bridge-connectedness, strong connectivity and Theorem 2.6 (Robbins).

Original work by Euclid. The linked English adaptation and guide are by David E. Joyce, drawing on Thomas Little Heath and other translations. About the Text describes this adaptation; it is not unmodified Heath.

By Keith Conrad.

Online text: kconrad.math.uconn.edu/blurbs/ugradnumthy/perfect-numbers-mersenne.pdf

Cited passages: Theorem 1.1, pp. 1–2: even-number equivalence and proof; §1, Theorem 1.1 and Example 1.2, pp. 1–2.

By Godfrey Harold Hardy, John Edensor Littlewood, George Pólya.

Publisher: Cambridge University Press.

Online text: djvu.online/file/CjwWRpwExRE7j

Cited passages: Inequalities, second edition, §9.8(ii), truncation and integration by parts, printed pp. 242–243; Inequalities, second edition, §9.8, Theorem 327, equation (9.8.2), printed p. 240; Inequalities, second edition, §9.8, Theorem 327, printed p. 240, and sharpness argument on printed p. 243.

First published in 1934; second edition published in 1952.

By Claude Berge.

Publisher: National Academy of Sciences.

Publication information: pubmed.ncbi.nlm.nih.gov/16590096/

Published in Proceedings of the National Academy of Sciences of the United States of America.

Online text: acm.math.spbu.ru/~sk1/download/books/roma/Other/pnas00700-0060.pdf

Cited passages: Claude Berge, Two theorems in graph theory, printed p. 842: finite unoriented graph and Problem 3; printed p. 843, Theorem 1: maximum matching and absence of an alternating chain between neutral points.

Proceedings of the National Academy of Sciences 43(9), pp. 842–844; published 15 September 1957. The paper was communicated on 8 July 1957.

By Leonhard Euler; English translation by Jordan Bell.

Presented to the St Petersburg Academy on 5 December 1735. Published as "De summis serierum reciprocarum" in Commentarii academiae scientiarum Petropolitanae 7 (1740), pp. 123–134. The linked translation is arXiv version 2, dated 5 February 2008.

Online text: arxiv.org/pdf/math/0506415

Cited passages: English translation, p. 1, §2 and publication note; pp. 3–4, §§3–8: sine series, roots and coefficients.

By Jean Gallier.

Online text: www.cis.upenn.edu/~jean/geomcs-v2.pdf

Author-hosted version dated 9 October 2025. This version date is distinct from first publication.

Cited passages: §2.4, Lemma 2.4.1, pp. 23–24; §2.7, Definition 2.7.1, p. 37; §2.7, Definition 2.7.1 and linear-map construction, pp. 37–38.

By Francis Galton.

Published in Journal of the Anthropological Institute of Great Britain and Ireland, volume 15, pp. 246-263.

Online text: galton.org/essays/1880-1889/galton-1886-jaigi-regression-stature.pdf

Cited passages: Printed p. 252: shoes-on versus shoes-off uncertainty and the average two-thirds height-deviation claim; Printed pp. 247-248, Table I; pp. 261-262, explanation of Plate IX(a): adjusted heights, counts, grouped medians and 2:3 deviation ratio.

By Terence Tao.

Course context: 246B, complex analysis. These notes were posted on 23 December 2020.

Publisher: Terence Tao, What's new (author website).

Online text: terrytao.wordpress.com/2020/12/23/246b-notes-1-zeroes-poles-and-factorisation-of-meromorphic-functions/

Cited passages: §1, Theorem 2 and equation (6): neighbourhood of the closed disk, zeros counted with multiplicity, holomorphic special case.

By K. I. Dickson, C. T. Kelley, Ilse Ipsen, Yannis G. Kevrekidis.

Publisher: Society for Industrial and Applied Mathematics.

Published in SIAM Journal on Numerical Analysis, volume 45, number 1, pp. 263–276.

Online text: ipsen.math.ncsu.edu/ps/sinum65438.pdf

Cited passages: §2.1, Corollary 2.1, printed pp. 264–265: Lipschitz continuously differentiable map, nonsingular state Jacobian, and a sufficiently small parameter increment; §2.2, Definition 2.2, printed p. 265: one-dimensional kernel of the state Jacobian and parameter derivative outside its range; §2.2, equations (2.2)–(2.5), printed pp. 265–266: unit tangent and hyperplane normalization; Corollary 2.3 gives local Newton convergence for sufficiently small steps.

By Gerald Teschl.

Publisher: American Mathematical Society.

Online text: www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf

Author-hosted preliminary version. The printed book was published by the American Mathematical Society in 2012; the author page’s last-modified date is not a PDF revision date.

Cited passages: Gerald Teschl, Ordinary Differential Equations and Dynamical Systems, §2.7, Theorem 2.19, printed p. 56: forward existence and the analogous backward result; Teschl, Theorem 2.17, p. 53; Teschl, §2.7, printed pp. 54–56, equations (2.69), (2.71)–(2.76): polygon bounds, compactness, and vanishing integral defect.

By Emre Yolcu, Xinyu Wu, Marijn Heule.

In Theory and Applications of Satisfiability Testing – SAT 2020, Lecture Notes in Computer Science 12178, pp. 201–217.

Publisher: Springer.

Published in 23rd Conference on Theory and Applications of Satisfiability Testing, SAT 2020.

Online text: emreyolcu.com/research/mycielski-graphs-pr-proofs.pdf

Cited passages: §4.1, Proposition 1 and proof, manuscript pp. 6–7; §4.1, manuscript pp. 5–6, construction steps 1–3.

By Keith Conrad.

Online text: kconrad.math.uconn.edu/blurbs/ugradnumthy/fermattest.pdf

Cited passages: Keith Conrad, Fermat's Test, p. 2, Definition 2.4 and footnote 3 on the two witness conventions; Keith Conrad, Fermat's Test, pp. 5–6, Definition 4.1 and the list beginning with 561.

By Will Fithian.

Online text: stat210a.berkeley.edu/fall-2025/reader/sufficiency.html

Explicitly authored standalone online lecture. Fall 2025 identifies the course offering, not a separately verified publication or revision date.

Cited passages: Sufficiency, Will Fithian, “Factorization theorem”: common dominating measure and almost-everywhere factorization; Sufficiency, Will Fithian, “Independent Bernoulli sequence”: conditional pmf; Sufficiency, Will Fithian, “Sufficiency”: definition.

By David R. MacIver.

Publisher: David R. MacIver's Blog.

Online text: drmaciver.com/notebook/2022/08/notes-on-the-design-of-a-conference-scheduler/

Online text: www.stat.cmu.edu/~cshalizi/dm/20/lectures/09/lecture-09.html

Lecture dated 11 February 2020 for Statistics 36-462/662, Spring 2020. The course page identifies Cosma Rohilla Shalizi as professor, without providing a separate slide byline.

Cited passages: Information Theory I — Scene Setting and Statistical Applications, Lecture 9, section Conditional independence and conditional mutual information: conditional factorization and predictive irrelevance.

By Victor Ivrii.

By Victor Ivrii.