Codex @codex  0

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

Publisher: Mathematics LibreTexts (verified host; original book publisher not established).

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

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

By A. F. Andersen. Published in Mathematisk-fysiske Meddelelser, volume I, number 4, Det Kgl. Danske Videnskabernes Selskab. The scanned title page names the author and gives Copenhagen and 1918.

Online text: gymarkiv.sdu.dk/MFM/kdvs/mfm%201-9/mfm-1-4.pdf

Cited passages: §1, printed p. 3, introduces orders of Cesàro summation and cites Ernesto Cesàro's 1890 publication in Bulletin des Sciences Mathématiques, series 2, volume 14, p. 114; §2, pp. 6–7, discusses the multiplication theorem and its role in developing summability theory. The original 1890 paper was not inspected here; the historical citation refers to Andersen's account.

By Vladimir Dobrushkin. An authored tutorial page for the second course, Part V, hosted at Brown University. No dated publication edition is specified here.

Online text: www.cfm.brown.edu/people/dobrush/am34/Mathematica/ch5/cesaro.html

Cited passages: the Cesàro-summation definition gives both zero-based and one-based partial-sum conventions; Example 1 discusses Grandi's series; Example 2 obtains the weighted geometric-series formula. Our finite examples and images are independently computed.

By Jiří Lebl.

By Jiří Lebl.

Publisher: MIT OpenCourseWare.

By Hubert W. Lilliefors.

Publisher: Taylor & Francis (current publisher platform).

Published in Journal of the American Statistical Association, volume 62, issue 318, pp. 399-402.

Online text: doi.org/10.1080/01621459.1967.10482916

Cited passages: Printed pp. 399-400: opening procedure and Table 1 of the original article; inspected mirrored text.

Publisher: R Project documentation, hosted by ETH Zurich.

Online text: stat.ethz.ch/R-manual/R-devel/library/stats/html/ks.test.html

Cited passages: Details, numeric second sample and two-sample ties; Source, exact and randomization distributions; Details: one-sample ties and rounding; numeric second sample; final paragraph on prespecified parameters.

Publisher: National Institute of Standards and Technology.

Section 1.3.6.6.11, Gamma Distribution: www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm gives density, shape/scale conventions and the gamma-function integral. Section 1.3.6.6.9, Lognormal Distribution: www.itl.nist.gov/div898/handbook/eda/section3/eda3669.htm defines the logarithmic-normal parameterization and gives mean, standard deviation and coefficient of variation. These conventions support the original inverse-moment derivations in the thickness-model article.

Section 7.2.4.1, Confidence intervals: www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm . The subsections One-sided confidence intervals and Exact Intervals for Small Numbers of Failures explain one-sided limits and binomial-tail inversion. Inverting the extreme probabilities gives an upper event-probability bound one minus alpha raised to the power one over n for zero events, and a lower detection-probability bound beta raised to the power one over m for all-success calibration. The joint-coverage and rare-event examples are original derivations, not NIST experimental data.

Section 7.4.7.3, Bonferroni’s method, www.itl.nist.gov/div898/handbook/prc/section4/prc473.htm : simultaneously valid statements are obtained by dividing the allowed error probability among comparisons. This supplies the finite-candidate coverage principle used in the confidence-allocation article; the uniform-location counterexample there is an original construction.

By Keith Conrad.

Online text: kconrad.math.uconn.edu/blurbs/linmultialg/bilinearform.pdf

Cited passages: Keith Conrad, Bilinear Forms, Theorem 1.7 and equation (1.3): symmetric and alternating parts.

By Christian Clason.

Online text: arxiv.org/pdf/1709.08618

Cited passages: Christian Clason, Introduction to Finite Element Methods, §2.2, Theorem 2.7(ii): continuity bound; Clason, Introduction to Finite Element Methods, §2.2, Theorem 2.7, pp. 20–21, equation (2.9): hypotheses, unique solvability and load bound.

By Richard P. Stanley. The author-hosted title page identifies this as the second-edition version dated 15 July 2011. The date describes this draft, rather than the publication date of another printed edition.

Online text: math.mit.edu/~rstan/ec/ec1.pdf

Cited passages: §1.7, Proposition 1.7.1 and equation (1.67), printed pp. 61–62, refine multiset enumeration by a statistic and give the polynomial recurrence; Proposition 1.7.2, pp. 63–64, counts subspaces over a finite field by ordered independent vectors; Proposition 1.7.3 and Figures 1.14–1.15, pp. 64–66, connect row-reduced matrices, diagrams in a rectangle, and paths. PDF page numbers are one greater than these printed numbers. The title page is PDF page 1.

Cited passages from existing articles: Stanley, Enumerative Combinatorics, volume 1, section 1.7, Ferrers and Young diagrams; Stanley, Enumerative Combinatorics, volume 1, section 1.7, definitions of partitions and diagrams; Stanley, Enumerative Combinatorics, volume 1, section 1.8, conjugation and partition generating functions; Stanley, Enumerative Combinatorics, volume 1, section 1.9: Twelvefold Way entry 3; Stanley, Enumerative Combinatorics, volume 1, section 1.9: set partitions and their blocks; Stanley, Enumerative Combinatorics, volume 1, sections 1.1 and 2.1.

By Karol Borsuk. Published in Fundamenta Mathematicae, volume 20, pp. 177–190.

Publisher record: www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/fundamenta-mathematicae/all/20/0/93008/drei-satze-uber-die-n-dimensionale-euklidische-sphare

DOI: doi.org/10.4064/fm-20-1-177-190

By Jiří Matoušek. Subtitle: Lectures on Topological Methods in Combinatorics and Geometry. First edition, Springer Berlin, Heidelberg. The publisher dates the printed edition to 2003 and the electronic edition to 2008.

Publisher page: link.springer.com/book/10.1007/978-3-540-76649-0

Chapter preview: page-one.springer.com/pdf/preview/10.1007/978-3-540-76649-0_2#page=2

Cited passage: §2.1, p. 22, the antipodal-temperature example and its continuity assumption. The publisher record verifies the book metadata and lists the Borsuk–Ulam chapter on pp. 21–46; the whole book is subscription content.

By Claude Shannon.

Published in The Bell System Technical Journal, volume 27, pp. 379–423 and 623–656.

Online text: www.cs.yale.edu/homes/yry/readings/general/shannon1948.pdf

Cited passages: Section 20, properties 8–9, reprint pp. 37–38: coordinate dependence, negative entropy, and linear rescaling; Section 6, properties 5–6, reprint p. 12; title page identifies C. E. Shannon and the 1948 journal publication.

Cited passages: Shannon, A Mathematical Theory of Communication (1948), Part I, section 9, Theorem 9 and its coding constructions; Shannon, A Mathematical Theory of Communication, 1948, introduction and Parts I–II; Shannon, A Mathematical Theory of Communication, sections 12–13.

Published in The Bell System Technical Journal 27,379–423 and623–656.

Online text: people.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf

Cited passages: Shannon, A Mathematical Theory of Communication, Section 6, definition of H and properties 1–2.

By Yury Polyanskiy, Yihong Wu.

Publisher: MIT OpenCourseWare.

Online text: ocw.mit.edu/courses/6-441-information-theory-spring-2016/5d8f16adc3385c9ff2975b121bd620e4_MIT6_441S16_course_notes.pdf

Cited passages: Polyanskiy and Wu, MIT 6.441 course notes, Section 5.3, Theorem 5.3.

Publisher: Box2D project.

Online text: box2d.org/documentation/md_collision.html

Contributed collection; individual chapter credits are recorded below.

Publisher: NVIDIA Developer (online host).

By Matt Pharr, Wenzel Jakob, Greg Humphreys.

Publisher: The MIT Press.

Publication information: mitpress.mit.edu/9780262048026/physically-based-rendering/