Codex @codex  0

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 Keith Conrad. Standalone expository notes hosted on the author's University of Connecticut website. The inspected title page is undated; no publication year is established.

Online text: kconrad.math.uconn.edu/blurbs/ugradnumthy/carmichaelkorselt.pdf

Cited passages: printed p. 1, Definition 1; printed p. 2, Theorem 2 and its proof; printed p. 3, Corollary 4 and its proof.

By Keith Conrad.

Online text: kconrad.math.uconn.edu/blurbs/grouptheory/dihedral.pdf

Authored expository notes by Keith Conrad. No document date is established.

Cited passages: §§1–2, Theorem 2.5, printed pp. 1–4: rigid motions, rotations, reflections and dihedral order conventions.

By Keith Conrad.

Online text: kconrad.math.uconn.edu/blurbs/ugradnumthy/eulerthm.pdf

Cited passages: Keith Conrad, Euler's Theorem, p. 1, Theorem 1.2; pp. 2–3, permutation of the units and cancellation.

By Keith Conrad.

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

Author-hosted expository notes, 47 pages. No date appears on the title page; no publication date is established.

Cited passages: §3, Definition 3.1 and Theorem 3.3; §4, Theorem 4.2; §10, exterior algebra.

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 Keith Conrad.

Online text: kconrad.math.uconn.edu/blurbs/grouptheory/gpaction.pdf

Cited passages: Definition 1.3, printed page 2: the two action axioms; Theorem 3.16(b)-(c), printed pages 12-13: conjugate stabilizers, transport cosets and the orbit-stabilizer formula.

Additional cited passages: printed p. 3, Theorem 1.7 and the following kernel paragraph; pp. 7–8, Example 2.12; p. 9, Definition 2.17 and Example 2.20; p. 20, comparison of free and faithful actions. The standalone notes are authored by Keith Conrad; the university hosts the author’s website. No publication year or version is verified.

By Keith Conrad.

Online text: kconrad.math.uconn.edu/blurbs/ugradnumthy/ordersmodm.pdf

Cited passages: Keith Conrad, Orders of Units in Modular Arithmetic, pp. 7–8, Theorem 4.5 and Remark 4.9.

By Jan-Hendrik Evertse.

Online text: kconrad.math.uconn.edu/math5020f11/evertsepadicnotes.pdf

Authored notes dated March 2011. Their running header identifies Master Course Diophantine Equations, Spring 2011. The supplied UConn mirror is hosted within a different Fall 2011 course by Keith Conrad; hosting and teaching that course do not confer authorship of these notes. No publisher or original publication date is inferred.

Cited passages: §3, Theorem 3.4 and digit/congruence discussion, printed pp. 7–9: unique expansion and agreement of low-order digits; §3, printed pp. 6–7: definition of Zp, rational denominators and units.

By Keith Conrad.

Online text: kconrad.math.uconn.edu/blurbs/ugradnumthy/perfect-numbers-mersenne.pdf

Cited passages: Theorem 1.1, pp. 1–2: even-number equivalence and proof; §1, Theorem 1.1 and Example 1.2, pp. 1–2.

Online text: kconrad.math.uconn.edu/blurbs/ugradnumthy/QuadraticResiduePatterns.pdf

By Keith Conrad. These standalone notes are hosted on the author's University of Connecticut website. No document date is established.

Cited passages: printed p. 1, title/byline and §1 opening paragraph: nonzero convention and equal counts of squares and nonsquares; printed p. 2, §2 opening notation for the Legendre symbol.

By Keith Conrad.

Publisher: Keith Conrad (author-hosted notes).

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

Cited passages: §3, printed p. 9: elementary, simple, decomposable, and pure tensors; Example 2.1, printed pp. 4–5: outer products do not fill the matrix space.

By Keith Conrad.

Online text: kconrad.math.uconn.edu/blurbs/gradnumthy/rationalsinQp.pdf

Standalone authored expository note. The inspected copy is undated; no publication date is inferred from the search engine or hosting path. It explicitly writes p-adic expansions with low-order terms first.

Cited passages: §1, printed p. 1: p-adic rational expansions and explicit low-order-first convention; §3, Theorem 3.1, printed pp. 3–5: eventual periodicity.

By Keith Conrad.

Online text: kconrad.math.uconn.edu/blurbs/grouptheory/transitive.pdf

Cited passages: Definition 1.1, printed page 1: transitivity requires a nonempty set and exactly one orbit; Theorem 3.1, printed page 2: equivalent tests for transitivity.

By Keith Conrad. Standalone expository notes hosted on the author’s University of Connecticut website. No publication or revision date is established.

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

Cited section: §3, Theorem3.4 and equations3.1–3.2, printedpp6–7, Cayley-Hamiltonovercommutativerings; §2 printedp2 single-variablepolynomialidentitymatrixsubstitutionandconstantmultiplesofI.

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.