Maths

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General

http://en.wikipedia.org/wiki/Maths

http://www.gutenberg.org/wiki/Mathematics_%28Bookshelf%29

http://en.wikipedia.org/wiki/Foundations_of_mathematics

http://en.wikipedia.org/wiki/History_of_mathematics
- http://en.wikipedia.org/wiki/Indian_mathematics

mathematical object - an abstract object arising in philosophy of mathematics and mathematics. Commonly encountered mathematical objects include numbers, permutations, partitions, matrices, sets, functions, and relations. Geometry as a branch of mathematics has such objects as hexagons, points, lines, triangles, circles, spheres, polyhedra, topological spaces and manifolds. Algebra, another branch, has groups, rings, fields, group-theoretic lattices, and order-theoretic lattices. Categories are simultaneously homes to mathematical objects and mathematical objects in their own right.

http://en.wikipedia.org/wiki/Formal_system

https://gist.github.com/stoutbeard/4158578

http://functionspace.org/
- http://functionspace.org/articles/6/Understanding-the-most-beautiful-equation-in-Mathematics

Arithmetic

http://en.wikipedia.org/wiki/Arithmetic

http://en.wikipedia.org/wiki/Number_theory

http://blog.stata.com/2011/03/03/understanding-matrices-intuitively-part-1/

Algebra

Geometry

http://en.wikipedia.org/wiki/Geometry

Model

[https://gist.github.com/4158578 Mathematics: What do grad students in math do all day?]

[http://cstheory.stackexchange.com/questions/14811/what-is-the-enlightenment-im-supposed-to-attain-after-studying-finite-automata What is the enlightenment I'm supposed to attain after studying finite automata?]

http://news.ycombinator.com/item?id=4875770

http://en.wikipedia.org/wiki/Dedekind_eta_function

http://junfukuyama.wordpress.com/
- http://news.ycombinator.com/item?id=4901849

http://esciencecommons.blogspot.co.uk/2012/12/math-formula-gives-new-glimpse-into.html

http://www.empiricalzeal.com/2012/12/21/what-does-randomness-look-like/

http://jeremykun.com/2013/02/08/why-there-is-no-hitchhikers-guide-to-mathematics-for-programmers/

http://en.wikipedia.org/wiki/Denotational_semantics

http://jeremykun.com/primers/

http://archive.org/stream/BrainfillingCurves-AFractalBestiary/BrainFilling#page/n0/mode/2up

Statistics

Information theory

http://en.wikipedia.org/wiki/Information_theory

http://en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication

Books

http://minireference.com/

Social

http://functionspace.org/

Computing

Mathics is a free, general-purpose online computer algebra system featuring Mathematica-compatible syntax and functions. It is backed by highly extensible Python code, relying on SymPy for most mathematical tasks and, optionally, Sage for more advanced stuff.