User:Siddharthist References

Userboxes

a²+b²=c²

This user is a mathematics tutor.

This user has an account on GitHub.

This user develops free software.

This user has been on Wikipedia for 8 years and 11 days.

Welcome! I'm an editor interested in computer science, especially program analysis. You can find some statistics about my editing on XTools.

Significant contributions

These are pages and sections I've written at least half of.

Pages

Sections

Templates

Drafts

TODO

The following are some edits I'd like to make but haven't yet.

Simple

These should take ten minutes or less.

Improve hash consing
Add more properties to Opposite category
Replace diagrams on initial topology and final topology with SVGs
Add a citation to Awodey for the diagonal functor
Add weak higher groupoid associator to the examples on Coherence condition
Add examples of generated groups to Generating set of a group and Finitely generated group
Maybe note that all examples in "Finitely generated" are examples of "Generating set" and all examples of presentations on Presentation of a group are also examples of generating sets?
Add Lambek's Lemma to Initial algebra

Middling

These should take a half hour or less.

Create Property-based testing (see Software testing#Property testing)
Create page on Hypothesis Python library
Clean up /info/en/?search=Symbolic_execution#Tools
Add examples to Initial algebra and Final coalgebra
Add the weighted approximation to Set cover problem
Add the example of vertex cover to Linear programming relaxation
Expand Real representation with Liebeck
Add the application to mere propositions to subterminal object, add properties from nLab ( subterminal object at the nLab), add Johnstone's topos theory as a reference.
More fully split top type from singly rooted hierarchy. The former should contain information on type theoretical subtyping, whereas the latter should contain information on inheritance. They should both have paragraphs in their introductions distinguishing between the two.
Semi-streaming algorithms
Improve Calculus of constructions with descriptions of CIC, C(co)IC, pCuIC, etc.
Add Misra-Gries to Element distinctness problem
Improve Complex conjugate representation. Is it related to the dual representation?
Add a "History" section to Betti number, based on Emmy Noether
Add a "Formal definition" section to Free abelian group
Create Draft:Path space, based on Glossary of algebraic topology#path space, https://ncatlab.org/nlab/show/path+space, and Homotopy type theory
Add citations to Section (category theory)
Read Lee's definition of Reduced homology and possibly add it as a reference on that page
Verify the ring axioms in the definition of Group ring
Expand coinduction (reference: Coqart)
(After the new year 2018): Merge Category algebra into higher-dimensional algebra, or delete it.

Category Theory

There are many pages on category theory that are extremely short, but I am not very familiar with the concepts.

Anafunctor
Category of categories
2-functor
Tensor-hom adjunction
Natural number object
Improve the end of Direct sum
Investigate the relationship between Congruence (abstract algebra) and equalizers.
Justify Top as a Distributive category
Add properties to Distributive category
Add a section on the free groupoid to the Free category page. References on nLab.^[1]
Add the fundamental groupoid of a path-connected space as an example of a Connected category
Simpler examples of Isomorphism of categories
Add section "In homotopy type theory" to Category (mathematics), discussing the difference between "precategories" and univalent categories.
Rewrite the definition of a Group object to be less steeped in category theoretical vocabulary and conventions
Improve Church–Rosser theorem

Intensive

One hour

Create a section on Pointer analysis with CFL reachability: https://ieeexplore.ieee.org/abstract/document/6957254
Create SV-COMP
Create a section about decidability on Separation logic
Create a page on Bi-abduction
Move Constrained Horn clauses to a section of Constraint logic programming
Create C Bounded Model Checker
Create Univalence axiom
Add a "Motivation" section to Group representation based on the action of the dihedral group on the plane
Add citation to the HoTT book to n-connected, rewrite and add examples. Add section on the fundamental groupoid.
Proof irrelevance

Universes

I'm partiularly interested in the concept of a mathematical universe. Here are some ways I'd like to improve the discussion on Wikipedia, with the goal of a complete overhaul of Universe (mathematics).

Improve top type
- Split the "Implementation" section of top type to singly rooted hierarchy
- Do research and find out more about the top type in subtyped systems
Add a Universes section to Calculus of Constructions. Use this paper or this one.
Create Girard's Paradox (see also Category:Mathematical paradoxes, List of paradoxes#Mathematics)
Overhaul Universe (mathematics)
- An outline of the sections:
  - Set theory
    - A universal set and Russell's Paradox
    - Motivation (model theory)
    - Set-theoretic universes
  - Category theory
    - Motivation (category of categories)
    - Lawvere's work: Elementary theory of the category of categories
    - Universes in topos theory
    - Cosmoses as a setting for category theory https://ncatlab.org/nlab/show/cosmos
  - Type theory
    - Motivation (dependent types)
    - Motivation (formalization of mathematics)
    - Universes in the Calculus of (co)Inductive Constructions
    - Universes in Homotopy Type Theory

The Stanford Encyclopedia of Philosophy and Springer EOM should come in handy for the page creation aspects.

More

Create computational type theory
Understand Preadditive category enough to add a categorical definition to Endomorphism ring
Understand Monad (category theory) enough to improve it and add examples
Create Algebraic category
Merge braid theory into braid group, add the formal definition from Configuration space (mathematics)
Distinguish and/or blend Homology (mathematics) with Chain (algebraic topology)
Improve the "Intuition" section of Fundamental group, possibly adding figures.
Add a section (or just a note) on the algorithmic complexity of choosing an optimal Morse function to Discrete morse theory
Research Topological complexity to get that article to non-stub status
Make sense of the definition of 2-group
Explain the Common string reference model better
Create a page on Cubical homology
Rethink and expand the Introduction section of Homotopy group
Improve the definition of Homotopy group, especially the spherical version (read Hatcher and Lee)
Page on globular sets? See Awodey survey on HoTT, which has more references
Create Homotopy n-type^[2], with subsection on h-level
Create Path space, improve Path space fibration (which assumes all spaces are compactly generated Hausdorff... in a note??)
Add alternative definition to Natural equivalence from Topology and Groupoids^[3]
Research and rethink the Subobject classifier

Less Serious

Create a Userbox for Reed College
Create a Userbox for NixOS

References

^ "free groupoid in nLab". ncatlab.org. Retrieved 2017-09-13.
^ "homotopy n-type in nLab". ncatlab.org. Retrieved 2017-09-14.
^ Ronald,, Brown, (June 2006). Topology and Groupoids. Academic Search Complete. North Charleston: CreateSpace. ISBN 1419627228. OCLC 712629429.{{ cite book}}: CS1 maint: extra punctuation ( link) CS1 maint: multiple names: authors list ( link)

[1] "free groupoid in nLab". ncatlab.org. Retrieved 2017-09-13.

[2] "homotopy n-type in nLab". ncatlab.org. Retrieved 2017-09-14.

[3] Ronald,, Brown, (June 2006). Topology and Groupoids. Academic Search Complete. North Charleston: CreateSpace. ISBN 1419627228. OCLC 712629429.{{ cite book}}: CS1 maint: extra punctuation ( link) CS1 maint: multiple names: authors list ( link)

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