User:Alec
From Maths
Hi, I'm Alec Teal; the admin of this site and creator of most of the content. Write a note on my talk page for requests!
- Don't forget about: Category:Finished notes
- Or User:Alec/BookTemplate
- Or User:Alec/NewTodoTemplate
- Or Characteristic property of the disjoint union topology/Proof
- Or User:Alec/ParametricPages
- Or /Modules
- Or /Unnamed inequality
- Or /Exam Qs
- Or /Questions to do
- Or /Pages to do
- Or /Goals
- Or /Manifolds pages
- Or /Link templates added: Alec (talk) 02:07, 31 December 2017 (UTC)
- Or /Template redirect test added Alec (talk) 19:26, 31 December 2017 (UTC)
Contents
Noticeboard
As of Wednesday, 21/Feb/2018 at 01:35:
- All pages marked for refactoring - count: 33
- Grade A refactoring - count: 17
- Grade B refactoring - count: 1
- Refactoring pages pending final review - count: 3
- All stub pages - count: 371
- Grade A* stubs - count: 90
- Grade A stubs - count: 116
- Grade B stubs - count: 43
- Stub pages pending final review - count: 2
- All pages requiring references - count: 84
- Grade A requiring references - count: 19
- Grade B requiring references - count: 10
- Pages requiring references pending final review - count: 0
- Pages requiring proofs - count: 128
- Grade A* requiring proofs - count: 8
- Grade A requiring proofs - count: 30
- Grade B requiring proofs - count: 14
- Grade C requiring proofs - count: 32
Watchdogs
- Warning:There are pages (12) in Category:Refactoring (unknown grade)
- Warning:There are pages (46) in Category:Stub pages of unknown grade
- Warning:There are pages (28) in Category:Pages requiring references of unknown grade
- Warning:There are pages (25) in Category:Pages requiring proofs of unknown grade
Things not to forget
- Ensure a sigma-algebra is at the forefront of the readers' minds when dealing with measures and such @ Alec (talk) 17:45, 8 April 2016 (UTC)
- Isotonic - define a special case of monotonic where the relation is facing the same way Alec (talk) 08:44, 9 April 2016 (UTC)
- Possibly sorted now. See Talk:Monotonic Alec (talk) 21:19, 9 April 2016 (UTC)
- User:Alec/Things not to forget/Order theory notes Alec (talk) 20:48, 9 April 2016 (UTC)
- Greater than or equal to - I made a (non-destructive) mistake in the proof, meaning my result is too concrete (as opposed to abstract). Don't forget to fix Alec (talk) 21:19, 9 April 2016 (UTC)
- Work on Ordered pair (lacks references) and
- Work on Cardinality (incomplete, not marked as stub....)
- Create some notion of urgency with regards to requiring references or proofs. Also maybe tag "low-hanging fruit" (easy proofs) so a new-comer has something they can do.
- Add that new Order Theory book.
- Bounded (ordering)
- The fundamental group of the product of a finite number of topological spaces is the product of the fundamental groups of each
- Investigate the arbitrary and countably infinite cases. I suspect the product of groups drops to the direct sum of the groups.
- An [ilmath]\epsilon[/ilmath]-[ilmath]\delta[/ilmath] form of continuity is missing.
- Partial orderings are to total orderings what partial function is to total function. That's where the partial comes from!
- Semi-ring pre-measure vs Pre-measure on a semi-ring Alec (talk) 00:31, 20 August 2016 (UTC)
- "Universal Mapping Property" = Group homomorphism theorem according to McCoy, Algebra: Groups, rings, and other topics - page 69 - Alec (talk) 20:29, 4 October 2016 (UTC)
- User:Alec/Things not to forget/Q9 wreckage
Pages being worked on
- Outer-measure @ Alec (talk) 17:45, 8 April 2016 (UTC)
Notation
Symbol | Command |
---|---|
[ilmath]\trianglelefteq[/ilmath] | \trianglelefteq |
[ilmath]\triangleq[/ilmath] | \triangleq |
[ilmath]\ntrianglelefteq[/ilmath] | \ntrianglelefteq |
Current projects
Currently ensuring that all existing measure theory articles are "up to a decent standard" and working on Measure Theory, following Halmos' example (rings).
- Notes:Halmos measure theory skeleton - notes for plan on definitions
- Site projects:Patrolling measure theory - "patrol" being the "decent standard" project.
- Site projects:Measure theory plan - implementation of plan.
- Site projects:Split set theory into elementary set theory - some things classified as "set theory" (like set subtraction) would be best classified as "elementary set theory". This project endeavorers to do that.
- Site projects:Patrolling topology - "patrol" being the "decent standard" project.
Notes
Diagram for Characteristic property of the product topology:
Diagram |
---|
Characteristic property of the subspace topology:
- [math]\forall S\in\mathcal{P}(X)\left[\forall Y\forall\mathcal{K}\in\mathcal{P}(\mathcal{P}(Y))\left(\overbrace{\mathcal{T}(Y,\mathcal{K})\implies}^{\text{if }(Y,\mathcal{K})\text{ is a topology then} }\Big[\underbrace{\forall f\in\mathcal{P}(Y\times X)}_{\text{relations from }X\text{ to }Y}\big(\overbrace{\mathcal{F}(f)\implies}^{\begin{array}{c}\text{if }f\text{ is a}\\\text{function then} \end{array} }[\mathcal{C}(f)\iff\mathcal{C}(\iota_S\circ f)]\big)\Big]\right)\right][/math]
Things I want to use
Linked list documentation diagram:
/*
* B is the node to be removed.
* We do this by binding A forward to C
*
* BEFORE:
* ---> +---+---------> +---+---------> +---+-----
*.... | A | | B | | C | ....
* -----+---+ <---------+---+ <---------+---+ <---
*
* AFTER: ,------------------.
* ---> +---+--' +---+-------'-> +---+-----
*.... | A | | B | | C | ....
* -----+---+ <-.-------+---+ ,--+---+ <---
* `------------------'
*
* Note that B.previous.bindForwards(B.next) is the same
* as B.next.bindBackwards(B.previous)
* A nice side-effect of this is that provided one has a
* ref counting scheme in place (which you need basically
* need for safe multi-threaded schemes anyway) any iterators
* "pointing" to B remain valid.
* Make sure that this "rail-road" situation where going
* forward and back MIGHT not be inverses is well documented
* and expected.
*/