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/

By Tuukka Korhonen, Michał Pilipczuk, Giannos Stamoulis.

Publisher: arXiv (repository).

Online text: arxiv.org/html/2404.03958v1

Cited passages: Section 1, Introduction, opening two paragraphs: deletion/contraction definition and minor-model conditions (i)–(iii).

By Reinhard Diestel.

Publisher: Springer (book); University of Hamburg author site (preview host).

Online text: diestel-graph-theory.com/Sample.pdf

Cited passages: Diestel, Graph Theory, Chapter 2, Exercise 23; Diestel, Graph Theory, Section 2.1, Theorem 2.1.1 and its lower-bound argument; Diestel, Graph Theory, fourth electronic edition, Section 2.1, definition of vertex cover.

Published in Springer, Graduate Texts in Mathematics 173.

Online text: webhomes.maths.ed.ac.uk/~v1ranick/papers/diestel1.pdf

The linked University of Edinburgh mirror is the third electronic edition, 2005. Supporting locators here refer to printed pp. 165–167 of that edition, rather than to differently paginated author-hosted previews or later editions.

Third electronic edition (2005), §1.5, Trees and forests, pp.13–15: unique paths in trees, rooted-tree order and leaves.

By Günter Last, Mathew Penrose.

Publisher: Cambridge University Press.

Online text: stoch.math.kit.edu/img/Last/lastpenrose2017.pdf

Cited passages: Section 7.1, Theorem 7.2, printed p. 59: interval theorem characterizing independent exponential gaps; Sections 5.2-5.3, Definition 5.7, Proposition 5.5, Theorem 5.8 and Corollary 5.9, printed pp. 42-44: location-dependent independent marking, intensities, and independence of the split processes.

By Robert Gallager.

Publisher: MIT OpenCourseWare (host of the author’s draft).

By Nicomachus; translated by Martin Luther D'Ooge in 1926, and revised for classroom use by Nathanael Hahn in 2025. The editor's note distinguishes the translated text from added headings, introductions, footnotes, images and exercises. Our citations refer to the translated mathematical passages.

Online text: stoicheiamath.com/wp-content/uploads/2025/09/Nicomachus-Introduction-to-Arithmetic-Teacher-Edition.pdf

Cited passages: Book II, Chapter 8, printed pp. 63–64 (PDF pages 68–69), describes triangular rows; Chapter 12, §§1–2, printed p. 70 (PDF page 75), combines consecutive triangular counts into squares; Chapter 20, §5, printed p. 75 (PDF page 80), groups consecutive odd integers into cubes. Publication and contributor credits appear on PDF page 2; notes distinguishing editorial additions appear on PDF page 3.

Additional cited passages: Book II, Chapter 23, §§1 and 3, printed p. 80 (PDF p. 85). The citation concerns translated mathematical paragraphs; the classroom editor’s introductions, footnotes and exercises are not used.

Student notes by Andrew Lin; course taught by Casey Rodriguez.

Publisher: MIT OpenCourseWare.

By Jiří Lebl.

Online text: www.jirka.org/ra/

Additional inspected sections: 3.4 Uniform continuity and 7.5 Continuous functions.

Whole-book author: Jiří Lebl; no separately credited chapter author is established. These HTML sections are undated. The author landing page dates the downloadable PDF version 6.3 to 15 May 2026; that version date is not assigned to the HTML.

Cited passages: §3.4.1, Definition 3.4.1 and Theorem 3.4.4; §3.4.2, Lemma 3.4.5; §3.4.3, Proposition 3.4.8 and Example 3.4.10; §7.5.4, Definition 7.5.10 and Theorem 7.5.11.

By Gilbert Strang, Edwin “Jed” Herman.

Publisher: OpenStax, Rice University.

By Tom Leinster.

Online text: webhomes.maths.ed.ac.uk/~tl/topology/topology_notes.pdf

Cited passages: Tom Leinster, General Topology, Example C3.6, p. 78, and the discussion after Lemma C4.12, p. 84: the sine-curve obstruction and nonclosed path components; here the positive graph is restricted to $0<x\le 1$; Tom Leinster, General Topology, Lemma C1.8, p. 70: a continuous image is connected; Tom Leinster, General Topology, Lemma C4.12 and the following definition, p. 84: path equivalence and maximal path-connected subsets; Tom Leinster, General Topology, Remark C1.2, p. 68, and Proposition C2.6, p. 73: the nonempty convention and the interval characterization.

By Romyar Sharifi.