Online text: loss.math.gatech.edu/16FALLTEA/NOTES/weierstrassbernstein.pdf

Cited passages: The Weierstrass approximation theorem, Lemmas 0.1–0.2 and Theorem 0.3, printed pp. 1–2: weights, binomial moments and polynomial construction; The Weierstrass approximation theorem, Theorem 0.3, printed p. 2: uniform polynomial approximation on the unit interval.

Online text: www.arponr.com/files/f24-18.901/notes.pdf

Course offering: Fall 2024. Arpon Raksit is the verified instructor and personal-site host; the PDF has no named byline. The course page records a December 6 update, rather than a publication date.

Cited passages: Lecture 12, Exercise 12.1.2(1)-(2), printed page 43: box basis, comparison with the product topology, and finite-factor equality; Lecture 5, Proposition 5.3.2, printed page 21: continuity into a product is equivalent to continuity of all component functions.

Publisher: Trinity College Dublin (archive host).

Online text: www.maths.tcd.ie/pub/HistMath/People/Hamilton/Icosian/

Cited passages: The Icosian Calculus, Hamilton papers archive: opening historical introduction and quoted report of the 1857 British Association presentation: dodecahedron projection and ivory pins.

By George B. Dantzig, Delbert Ray Fulkerson, Selmer M. Johnson.

Publisher: Operations Research Society of America (original); INFORMS (current archive).

Published in Journal of the Operations Research Society of America 2(4), pp. 393–410.

Online text: pubsonline.informs.org/doi/abs/10.1287/opre.2.4.393?journalCode=jors

Cited passages: Solution of a Large-Scale Traveling-Salesman Problem by G. Dantzig, R. Fulkerson and S. Johnson, abstract; Journal of the Operations Research Society of America 2(4), pp. 393–410 (1954).

By Peter J. Huber.

Publisher: Institute of Mathematical Statistics.

Published in The Annals of Mathematical Statistics, volume 35, number 1, pp. 73-101.

Online text: doi.org/10.1214/aoms/1177703732

Cited passages: Peter J. Huber, Robust Estimation of a Location Parameter, §11, pp. 95-96: estimating location when normal-component scale and contamination fraction are unknown; Peter J. Huber, Robust Estimation of a Location Parameter, §3, p. 78: derivative normalization; §4(iii), p. 79: clipped location criterion and central-mass denominator.

Cited passages: original journal wrapper and byline, March 1964 publication; §1, printed pp. 73–75; §2, printed p. 76, minimizing set; §4(iii), printed p. 79, piecewise criterion and clipping about the fitted location. The manuscript receipt date, 4 June 1963, precedes publication.

Inspected mirrored scan transcription: www.scribd.com/document/861209215/Huber-RobustEstimationLocation-1964

By Frank R. Hampel.

Publisher: Taylor & Francis on behalf of the American Statistical Association (mirror wrapper metadata).

Published in Journal of the American Statistical Association, volume 69, number 346, pp. 383-393.

Online text: doi.org/10.1080/01621459.1974.10482962

Cited passages: Frank R. Hampel, The Influence Curve and Its Role in Robust Estimation, p. 383, §2: pointwise right-limit definition along mixtures with a point mass; Frank R. Hampel, The Influence Curve and Its Role in Robust Estimation, §4, p. 386: exact asymptotic curve supplemented by behavior at other distributions, especially empirical ones.

By Gordan Žitković.

By Timothy Gowers.

Publisher: Gowers’s Weblog (author-published; WordPress is host).

Online text: gowers.wordpress.com/2008/08/12/how-to-use-zorns-lemma/

Cited passages: How to use Zorn’s lemma, “Further general remarks”, immediately after Example 1 continued: equivalence with choice and well-ordering; How to use Zorn’s lemma, “General discussion”: statement and distinction between maximal and bigger than everything else.

By Keith Conrad.

Online text: kconrad.math.uconn.edu/blurbs/zorn1.pdf

Cited passages: Zorn’s Lemma and Some Applications, §1, p. 4, paragraph on the 1935 introduction to shorten algebraic proofs; Zorn’s Lemma and Some Applications, §4, pp. 18–19, Theorem 4.1 and Corollary 4.2; Zorn’s Lemma and Some Applications, §4, pp. 18–19, chain-union proof of Theorem 4.1 and extension argument of Corollary 4.2.

Additional cited passages: §4, printed p. 19, Corollary 4.2, extension of an independent subset to a basis; printed p. 20, Corollary 4.5 and the rational-basis construction. The inspected notes are undated.

By Janet Heine Barnett.

Online text: www.cs.nmsu.edu/historical-projects/Projects/Cayley.pdf

Cited passages: Abstract awakenings in algebra: Early group theory in the works of Lagrange, Cauchy, and Cayley by Janet Heine Barnett, Section 3.1, printed page 50: reproduced opening paragraph of Arthur Cayley's On the theory of groups, as depending on the symbolic equation theta^n = 1; reference 5, printed page 91: original publication in 1854.

Publisher: NPTEL.

Online text: archive.nptel.ac.in/content/storage2/courses/112104030/lecture13/13_4.htm

Cited passages: Lecture 13, Thomas algorithm: opening historical attribution and Crank Nicolson motivation.

By University of Tennessee, University of California Berkeley, University of Colorado Denver, NAG Ltd..

Publisher: LAPACK project (Netlib hosting).

This source is credited to an organization.

Online text: www.netlib.org/lapack/explore-html/d1/db3/dgtsv_8f_source.html

Cited passages: DGTSV, LAPACK 3.12.1, Fortran lines 175–180: multiplier and two updates without row interchange; DGTSV, Purpose lines 34–39; DL argument lines 63–69; adjacent interchange lines 188–199; back solve lines 295–305.

By Peter H. Westfall.

Published in The American Statistician.

Online text: pmc.ncbi.nlm.nih.gov/articles/PMC4321753/

Cited passages: §2, Terminology, definition of κ; §4, counterexamples with different peaks; §5, central and tail contributions; §5, Why Tails Mostly Determine Kurtosis, inequality (1) and following fixed-h argument.

By Nigel Hitchin.

Online text: people.maths.ox.ac.uk/~joyce/Nairobi2019/Hitchin-GeometryOfSurfaces.pdf

Cited passages: Section 3.2, Theorem 3.2 and its triangulation proof, printed pp. 38-39; Section 3.3, printed pp. 41-43: local coordinates at simple roots, two points at infinity for even polynomial degree, and ramification count.

By Constantin Teleman.

Online text: math.berkeley.edu/~teleman/math/Riemann.pdf

Cited passages: Lecture 5, Definition 5.16, printed p. 19: total branching index as the sum of fibre deficits; Lecture 5, Theorems 5.1 and 5.3; Definition 5.16 and Theorem 5.17, printed pp. 16-19.

By Kevin M. Lynch, Frank C. Park.

Publisher: Cambridge University Press.

Online text: hades.mech.northwestern.edu/images/2/25/MR-v2.pdf

Cited passages: Modern Robotics, §3.2.1, definition 3.1 and propositions 3.3–3.6, preprint pp. 67–69; Modern Robotics, §3.2.1.1, propositions 3.4–3.5, preprint p. 69: closure and the distinction between planar and spatial composition; Modern Robotics, §3.2.1.2, preprint p. 69: three uses of a rotation matrix; Modern Robotics, §3.2.1.2, preprint pp. 72–73: premultiplication uses fixed-frame axes; postmultiplication uses body-frame axes.

Author video supplement: modernrobotics.northwestern.edu/nu-gm-book-resource/4-1-1-product-of-exponentials-formula-in-the-space-frame/ . Section4.1.1 develops forward kinematics and the end-effector frame through the product-of-exponentials representation.

Author video supplement: modernrobotics.northwestern.edu/nu-gm-book-resource/inverse-kinematics-of-open-chains/ . Chapter 6 develops inverse kinematics for open kinematic chains.

Author video supplement: modernrobotics.northwestern.edu/nu-gm-book-resource/3-4-wrenches/ . Section 3.4, Wrenches, transcript: six-vector moment/force representation, changes of reference frame, and the frame-independent power pairing of a wrench with a rigid-body twist.

Additional author video supplement: modernrobotics.northwestern.edu/nu-gm-book-resource/3-3-2-twists-part-1-of-2/ . Section 3.3.2, Twists (Part 1 of 2), defines the ordered angular/linear six-vector, origin dependence of its linear component, normalized screw axis and pitch, and the distinct body/space reference-frame representations. The wiki's numerical twist example and velocity-field derivation are independent calculations.

§3.2.3, Exponential Coordinates of Rotation, Part 2: unit-axis rotation, matrix exponential and Rodrigues formula. The axis-direction uncertainty bound in the current article is derived explicitly rather than attributed to this source.

By Lieven Vandenberghe, Stephen Boyd.

Published in Mathematical Programming, Series B, 69(1), 205–236.

Online text: web.stanford.edu/~boyd/papers/pri_dual.html

Cited passages: Publication record and authored abstract: A Primal-Dual Potential Reduction Method for Problems Involving Matrix Inequalities, Mathematical Programming, Series B, 69(1), 205–236 (1995).

By Simo Särkkä, Arno Solin.

Publisher: Cambridge University Press.

Online text: users.aalto.fi/~asolin/sde-book/sde-book.pdf

Cited passages: Applied Stochastic Differential Equations, Example 6.2, printed p. 81, equations (6.27)–(6.30); centered model with diffusion constant q; Applied Stochastic Differential Equations, Example 6.8, printed pp. 91–92, equations (6.73)–(6.76): steady-state variance and covariance.

By G. E. Uhlenbeck, L. S. Ornstein.

Publisher: American Physical Society.

Published in Physical Review, volume 36, issue 5, starting p. 823.

Online text: journals.aps.org/pr/abstract/10.1103/PhysRev.36.823

Cited passages: On the Theory of the Brownian Motion, abstract: velocity minus its decaying initial contribution; friction coefficient divided by mass.

By University of Tennessee, University of California Berkeley, University of Colorado Denver, NAG Ltd..

Publisher: LAPACK project (Netlib hosting).

This source is credited to an organization.

Online text: www.netlib.org/lapack/explore-html/dc/d23/drot_8f_source.html

Cited passages: DROT source, lines 116–120 and 130–134: temporary first-row value and second-row update.