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- 21:18, 21 May 2023 Quotients (Topology) (hist) [1,861 bytes] Kfagerstrom (talk | contribs) (Created page with "The quotient of $$X$$ with respect to $$∼$$, $$X/∼$$ denotes the set of equivalence classes The function $$q:X → X/∼$$ defined by $$q(p) := [p]$$ for all $$p ∈ X$$...")
- 20:59, 21 May 2023 Path Connected (hist) [1,782 bytes] Kfagerstrom (talk | contribs) (Created page with "Definition: A space $$X$$ is path-connected, or PC, if for all $$p,q ∈ X$$, there is a continuous function $$f: I → X $$ such that $$f(0) = p$$ and $$f(1) = q$$ (that is,...")
- 20:46, 21 May 2023 Topology Qualifying Syllabus (hist) [1,344 bytes] Kfagerstrom (talk | contribs) (Created page with "==Point-set Topology:== ===Topological spaces and continuous functions:=== Topology, open and closed sets, basis, subbasis; continuous function, homeomorphism; closure, limit...")
- 22:26, 25 March 2023 Jordan Canonical Form (hist) [760 bytes] Kfagerstrom (talk | contribs) (Created page with "$F$ field, $V$ finite dim vector space, $V\xrightarrow{t} V$ linear transforamtion. Assume that the charateristic polynomial of $t$ compleately factor into linear forms (so th...")
- 18:03, 10 March 2023 Cayley-Hamilton Theorem (hist) [1,953 bytes] Kfagerstrom (talk | contribs) (Created page with "Let <math>F</math> be a field, and let <math>V</math> be a finite dimensional <math>F</math>-vector space. If <math>t : V → V</math> is a linear transformation, then <math>m...")
- 21:41, 9 March 2023 Uniqueness of Rank of Free Modules Over Commutative Rings (hist) [295 bytes] Kfagerstrom (talk | contribs) (Created page with "Let <math>R</math> be a commutative ring with <math>1 \ne 0</math> and let M be a free R-module. If A and B are both bases for M, then A and B have the same cardinality, meani...")
- 22:07, 8 March 2023 Category (hist) [391 bytes] Kfagerstrom (talk | contribs) (Created page with "Let <math>R</math> be a ring with <math>1\neq0</math>. A ''Left'' <math>R</math>-mod is an abelian group <math>(M,+)</math> together with an action of <math>R</math> on <mat...")
- 17:17, 8 March 2023 UMP for Free Modules (hist) [1,641 bytes] Kfagerstrom (talk | contribs) (Created page with "UMP for free modules Let <math>R</math> be a ring, <math>M</math> a free <math>R</math>-module with basis <math>B</math>, <math>N</math> an <math>R</math>-module, <math>j:B\...")
- 05:54, 8 March 2023 Free Modules (hist) [2,606 bytes] Kfagerstrom (talk | contribs) (Created page with " '''Definition:''' A subset A of an R-module M is a basis of M if A is linearly independent and generates M. An R-module M is a '''free''' R-module if M has a basis.")
- 01:30, 8 March 2023 Modules (hist) [341 bytes] Kfagerstrom (talk | contribs) (Created page with "Definition and examples: matrices, free modules, and bases over arbitrary commutative rings, Structure Theorem for finitely generated modules over PIDs, applications to linear...")
- 01:11, 8 March 2023 Isomorphism Theorems (hist) [28 bytes] Kfagerstrom (talk | contribs) (Created page with " Category: Group Theory")
- 01:03, 8 March 2023 Algebra Qualifying Syllabus (hist) [3,079 bytes] Kfagerstrom (talk | contribs) (Created page with "'''Group Theory:''' Groups, subgroups, homomorphisms, cosets, quotients, isomorphism theorems, direct and semidirect products, solvable groups, structure of cyclic, symmetric...")
