User:Lord Farin/Long-Term Projects

This page contains a list of things I have encountered and take considerable time.


 * Processing of Conway's 'A Course in Functional Analysis'.
 * Progress kept at User:Lord_Farin/Long-Term Projects/Conway Course
 * Currently on hold since the basis is missing


 * Processing of Schilling's 'Measures, Integrals and Martingales'
 * Progress at User:Lord_Farin/Long-Term Projects/Schilling
 * Currently on hold since I don't master the theory on martingales (yet)


 * Processing of Awodey's 'Category Theory'
 * Progress at User:Lord_Farin/Long-Term Projects/Awodey


 * Processing of Halmos/Givant's 'Introduction to Boolean Algebras'
 * Progress at User:Lord_Farin/Long-Term Projects/Givant-Halmos


 * Develop the rigid foundations for Category:Complex Analysis.
 * Properly use the about template on every page linked to a disambiguation/combined (definition) page.
 * Establish connections between the results on matrices and those on operators on Hilbert/Banach space (the former are the finite-dimensional versions of the latter).
 * Introduce and properly use 'Example' namespace.
 * Develop the rigid foundations of logic and axiomatic set theory further (zeroth, first order logic).
 * Creating a MediaWiki extension tailored to ProofWiki
 * Progress kept at User:Lord_Farin/Long-Term Projects/Extension


 * Establish the relations between all the kinds of set systems, similar to Sequence of Implications of Separation Axioms.
 * Develop the notion of a "partial operation" and its theory.
 * Various sources suggest that there is a viable approach possible granting Hilbert spaces over the quaternions. Vector spaces over the quaternions could constitute the first proper example of a vsp. over a division ring that is truly not commutative on PW.
 * Employ category theory to help cutting down tedious forests of similar theorems.
 * Introduce a 'Duality' section for category theory, so as to universalize the 'two-for-one' nature implicit in it.
 * Proper categorization of the category theory section