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.

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/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.

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 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/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.

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.