By Carl Pomerance. Slides for the ICERM meeting "Seventy-five years of Mathematics of Computation", 1–3 November 2018.

Online text: math.dartmouth.edu/~carlp/mathcomptalk2.pdf

Cited passages: slide 14 states Pépin's test and outlines its proof; slides 15–16 describe Fermat numbers and their role in integer factorization; slide 18 gives the Gauss-Wantzel theorem and distinguishes Gauss's construction result from Wantzel's necessity proof. Numerical records elsewhere in these 2018 slides are historical records, not claims about current records.

By Leonhard Euler; English translation by Jordan Bell. Presented to the St Petersburg Academy on 26 September 1732; the original Latin paper, "Observationes de theoremate quodam Fermatiano aliisque ad numeros primos spectantibus", appeared in Commentarii academiae scientiarum Petropolitanae 6 (1738), pp. 103–107. The publication note on page one of the translation distinguishes presentation from publication. The linked translation is version three, dated 15 April 2008.

English translation: arxiv.org/pdf/math/0501118

Catalogue record: arxiv.org/abs/math/0501118

Cited passages: pp. 1–2, Euler's account of Fermat's proposed prime pattern and the factor $641$ of $2^{32}+1$; p. 1 publication and translator note. The short modular check in Fermat number is presented as a modern verification, not a historical reconstruction of Euler's search.

By Joseph Fourier.

Official website: fr.wikisource.org/wiki/Livre:Fourier_-_Théorie_analytique_de_la_chaleur,_1822.djvu

By Glenn Shafer, Vladimir Vovk.

Online text: probabilityandfinance.com/articles/STS154.pdf

Cited passages: introduction, page 70; section 5.1.1, page 87.

By Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science.

Online text: ocw.mit.edu/courses/6-438-algorithms-for-inference-fall-2014/176d4c3a360b7ee4a32169f551b0722d_MIT6_438F14_rec8.pdf

6.438 Algorithms For Inference, Fall 2014, recitation notes; institutional authorship.

Cited passages: §1, The Junction Tree Algorithm; §6, Relationship between chordal graphs and junction trees.

By Durham Statistics and Probability teaching team.

Online text: www.maths.dur.ac.uk/users/clare.wallace/Prob1/01-axioms.html

Cited passages: 1.4-1.6, especially consequence C9.

By Achi Brandt.

Online text: www.stat.uchicago.edu/~lekheng/courses/302/classics/brandt.pdf

Cited passages: Achi Brandt, Multi-Level Adaptive Solutions to Boundary-Value Problems, Mathematics of Computation 31(138), April 1977, pp. 333–390, abstract and introduction.

By John Tsitsiklis, Patrick Jaillet.

Online text: ocw.mit.edu/courses/res-6-012-introduction-to-probability-spring-2018/91864c7642a58e216e8baa8fcb4a5cb5_MITRES_6_012S18_L01.pdf

Cited passages: slides 6-10 and 17-18.

By Long Chen.

Online text: webapps.math.uci.edu/~chenlong/226/Ch6MG.pdf

Cited passages: Long Chen, Introduction to Multigrid Methods, 17 December 2011, section 2: plain Jacobi retains both extreme sine modes; Long Chen, Introduction to Multigrid Methods, 17 December 2011, sections 4–5: energy projection, transfer matrices, and Galerkin triple product; the displayed cancellation identities follow by direct substitution.

By Andrei N. Kolmogorov.

Publication details and the original axioms are discussed in The Sources of Kolmogorov’s Grundbegriffe by Glenn Shafer and others.

By James Demmel.

Online text: people.eecs.berkeley.edu/~demmel/cs267/lecture25/lecture25a.html

Cited passages: James Demmel, CS267 supplemental notes, 12 March 1996, How Multigrid Damps High Frequencies: sine eigenvectors and the one-third high-frequency bound.

Additional cited passages: diagonal-2 tridiagonal Poisson matrix, error eigenvector expansion, weighted-iteration multiplier, and concluding attenuation statement. The heading dates the lecture to 12 March 1996.

By Gilbert Strang.

Official website: math.mit.edu/~gs/cse/

By Lieven Vandenberghe, Martin S. Andersen.

Online text: www.seas.ucla.edu/~vandenbe/publications/chordalsdp.pdf

Foundations and Trends in Optimization 1(4), 241–433; DOI 10.1561/2400000006. PDF lists the volume issue year as 2014 and copyright as 2015; author-hosted course reference and institutional publication record identify 2015.

Cited passages: §4.1–4.2, Algorithm 4.2; §9.1, equation 9.2 and Theorem 9.1.

By Jean R. S. Blair, Barry W. Peyton.

Online text: digital.library.unt.edu/ark:/67531/metadc1319152/m2/1/high_res_d/10145949.pdf

Oak Ridge National Laboratory technical report ORNL/TM-12203, November 1992.

Cited passages: §2.2, Lemma 1 and Theorem 2.2; §3.1–3.2, Theorems 3.1–3.3.

By Donald J. Rose, R. Endre Tarjan, George S. Lueker.

Online text: epubs.siam.org/doi/10.1137/0205021

SIAM Journal on Computing 5(2), June 1976, pp. 266–283; DOI 10.1137/0205021. R. Endre Tarjan is Robert Endre Tarjan.

Cited passages: Abstract; Information & Authors: volume 5, issue 2, June 1976.

By William L. Briggs.

Online text: math.nyu.edu/inmemoriam/donev/Teaching/NMII/Lectures/MultigridTutorial_Briggs.pdf

Cited passages: William L. Briggs, A Multigrid Tutorial, presented by Van Emden Henson, slides 59–63: correction and recursive V-cycle.

The verified instructor and personal-site host for MIT 18.901 topology notes from Fall 2024. The hosted PDF has no named byline, so the instructor and hosting credit is kept distinct from an unverified claim of sole authorship.^[ref]

William Rowan Hamilton introduced quaternions as a number system extending complex arithmetic. Their noncommutative multiplication encodes geometric structure useful for spatial rotations, while also showing that familiar real-number algebraic rules need not all survive an extension.^[ref]

Coauthor with George B. Dantzig and Delbert Ray Fulkerson of a 1954 study solving a large traveling salesman problem. The work links a specific route computation with a proof that no cheaper route exists.^[ref]

Peter J. Huber developed robust estimation methods that limit sensitivity to unusually large observations. The cited location-estimation work balances efficiency near a specified model against stability when the data depart from it.^[ref]