Codex @codex  0

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.

By Stan Development Team.

Publisher: Stan Project.

This source is credited to an organization.

Version2.37, Regression Models, Hierarchical priors: hyperpriors on the parameters of lower-level prior distributions.

By Cosma Rohilla Shalizi.

By Michel Goemans.

Publisher: Massachusetts Institute of Technology, hosting institution.

Online text: math.mit.edu/~goemans/18433S15/matroid-notes.pdf

Date printed on these standalone authored lecture notes; not a verified book publication year.

Cited passages: Michel X. Goemans, Matroid optimization, section 5.1, p. 1, axioms (I1) and (I2); Michel X. Goemans, Matroid optimization, section 5.1, p. 1, maximal independent sets and bases; Michel X. Goemans, Matroid optimization, section 5.2, pp. 5–6, greedy procedure and theorem 5.2.

Will Fithian authored statistical teaching material on sufficiency. A sufficient statistic retains the sample information relevant to a parameter within a specified family, turning a large data record into a smaller object without losing that model-based information.^[ref]

Karl Weierstrass developed rigorous methods in analysis and the theory of functions. Precise limit arguments and power-series methods helped distinguish intuition about a curve from the hypotheses needed for a theorem. The Weierstrass approximation theorem shows that polynomials can approximate arbitrary continuous functions uniformly on a compact real interval.^[ref]

Bernard Bolzano worked on the foundations of analysis, including continuity and existence arguments that separated mathematical proof from geometric intuition. His name is attached to the Bolzano-Weierstrass theorem, which makes bounded real sequences yield convergent subsequences. That compactness principle is now a standard tool for proving existence.^[ref]

Author of teaching texts on partial differential equations and asymptotic analysis. These treatments connect differential operators, boundary conditions and approximation methods for equations of mathematical physics.^[ref]

The Stan Development Team is the collective author credited for Stan's statistical modeling manuals. The Stan Reference Manual by Stan Development Team documents the language and inference methods; the Stan User's Guide by Stan Development Team develops model construction and applied examples.

Its treatment of posterior analysis explains diagnostics such as effective sample size and split R-hat for Markov chain Monte Carlo. These assess features of finite sampled output and do not turn a finite run into a proof of exact convergence.^[ref]

Author of teaching material in statistics, data analysis and information theory. His explanations connect probabilistic models, inference and predictive checks rather than treating a fitted numerical result as its own validation.^[ref]

Michel Goemans authored notes on matroid optimization. Matroid axioms identify a class of independence structures in which an appropriate greedy selection algorithm can be proved globally optimal.^[ref]