Maths

mess. working back from computation on coding

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

• http://en.wikipedia.org/wiki/Mathematical_objects 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://mathwithbaddrawings.com/
• http://www.mathsisfun.com/index.htm

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

• https://en.wikipedia.org/wiki/Linear_system
• https://en.wikipedia.org/wiki/Superposition_principle
• https://en.wikipedia.org/wiki/Nonlinear_system

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

• http://en.wikipedia.org/wiki/Philosophy_of_mathematics
• http://en.wikipedia.org/wiki/Metalogic

• http://en.wikipedia.org/wiki/Areas_of_mathematics
• http://en.wikipedia.org/wiki/Discrete_mathematics

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

• http://www-history.mcs.st-andrews.ac.uk/Extras/Poincare_Intuition.html

• http://terrytao.wordpress.com/

• http://www.arsmathematica.net/

• http://tutorial.math.lamar.edu/

• http://mathoverflow.net/questions/54430/video-lectures-of-mathematics-courses-available-online-for-free

• http://www.reddit.com/r/askscience/comments/1kt88j/is_0_halfway_between_positive_infinity_and/

• http://web.stonehill.edu/compsci//History_Math/math-read.htm

• http://www.ams.org/notices/200501/fea-dundes.pdf

• http://afp.sourceforge.net/

• http://blogs.scientificamerican.com/roots-of-unity/2013/09/12/10-trig-functions-youve-never-heard-of/?WT_mc_id=SA_DD_20130913

• https://sites.google.com/site/numberopedia/

Arithmetic

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

• http://en.wikipedia.org/wiki/Radix
• http://threesixty360.wordpress.com/2009/06/09/ethiopian-multiplication/ [2]

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

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

• http://blog.ram.rachum.com/post/54747783932/indescribable-numbers-the-theorem-that-made-me-fall-in

• https://news.ycombinator.com/item?id=6187014

• http://www.uh.edu/engines/epi504.htm

Algebra

• http://en.wikipedia.org/wiki/Algebra
• http://en.wikipedia.org/wiki/Elementary_algebra
• http://en.wikipedia.org/wiki/Equation

• http://profkeithdevlin.org/2011/11/20/what-is-algebra/

• http://en.wikipedia.org/wiki/Abstract_algebra
• http://en.wikipedia.org/wiki/Algebraic_structures
• http://en.wikipedia.org/wiki/Boolean_algebra

Geometry

• Geometry

• http://www.mathsisfun.com/geometry/platonic-solids-why-five.html

• http://fleetinbeing.net/hypersolid/examples/24cell-construction.html

• http://sciencevsmagic.net/geo

• http://en.wikipedia.org/wiki/Polytope
  • http://en.wikipedia.org/wiki/Polygon
  • http://en.wikipedia.org/wiki/Polyhedron
  • http://en.wikipedia.org/wiki/Polychoron

• http://en.wikipedia.org/wiki/Aperiodic_tiling
• http://en.wikipedia.org/wiki/Girih_tiles

• http://en.wikipedia.org/wiki/Icosahedral_symmetry

Model

• http://en.wikipedia.org/wiki/Model_theory
• http://en.wikipedia.org/wiki/Mathematical_structure
• http://en.wikipedia.org/wiki/Morphism
• http://en.wikipedia.org/wiki/Space_%28mathematics%29

• https://en.wikipedia.org/wiki/Alloy_(specification_language)

Category

• http://en.wikipedia.org/wiki/Category_theory
• http://en.wikipedia.org/wiki/Cartesian_closed_categories

• Category Theoretic Foundation Systems

• http://yogsototh.github.io/Category-Theory-Presentation

Set

• http://en.wikipedia.org/wiki/Set_theory
• http://en.wikipedia.org/wiki/Set_(mathematics)
• http://en.wikipedia.org/wiki/Class_(set_theory)
• http://en.wikipedia.org/wiki/Element_(mathematics)

• http://en.wikipedia.org/wiki/Structure_(mathematical_logic)

• https://en.wikipedia.org/wiki/Finitary_relation

• http://en.wikipedia.org/wiki/Algebraic_structures
• http://en.wikipedia.org/wiki/Constructible_universe
• http://en.wikipedia.org/wiki/Naive_set_theory
• http://en.wikipedia.org/wiki/Axiomatic_set_theory
• http://en.wikipedia.org/wiki/Type_theory

• http://en.wikipedia.org/wiki/Topos
• http://en.wikipedia.org/wiki/Topology
• http://en.wikipedia.org/wiki/Topological_space
• http://en.wikipedia.org/wiki/Metric_space

Group

• http://en.wikipedia.org/wiki/Group_theory
• http://en.wikipedia.org/wiki/Element_(mathematics)

Proof

• http://en.wikipedia.org/wiki/Proof_theory

• http://www.proofwiki.org/wiki/Main_Page

Logic

• http://en.wikipedia.org/wiki/Classical_logic
• http://en.wikipedia.org/wiki/Mathematical_logic

• https://en.wikipedia.org/wiki/Peano_axioms

• http://coq.inria.fr/
  • https://en.wikipedia.org/wiki/Coq

• http://en.wikipedia.org/wiki/Combinatorial_logic
• http://en.wikipedia.org/wiki/Sequential_logic

• http://logitext.mit.edu/logitext.fcgi/tutorial?

• http://en.wikipedia.org/wiki/Non-classical_logic
• http://en.wikipedia.org/wiki/Intuitionistic_logic
• http://en.wikipedia.org/wiki/Categorical_logic
• http://en.wikipedia.org/wiki/Modal_logic

• http://en.wikipedia.org/wiki/Computational_logic
• http://en.wikipedia.org/wiki/Computability_logic

• http://en.wikipedia.org/wiki/Natural_deduction

• http://en.wikipedia.org/wiki/Mathematical_induction

• http://en.wikipedia.org/wiki/Zeroth-order_logic - propositional
• http://en.wikipedia.org/wiki/Predicate_logic
• http://en.wikipedia.org/wiki/First-order_logic
• http://en.wikipedia.org/wiki/Second-order_logic
• http://en.wikipedia.org/wiki/Higher-order_logic
• http://en.wikipedia.org/wiki/Many-sorted_logic

• http://en.wikipedia.org/wiki/Pure_type_systems
• http://en.wikipedia.org/wiki/Calculus_of_constructions

• http://en.wikipedia.org/wiki/Lambda_cube
• http://www.scribd.com/doc/2384893/barendregt92lambda

• https://news.ycombinator.com/item?id=6119414

• http://skibinsky.com/godel-turing-and-cantor-the-math/

• http://www.logicmatters.net/resources/pdfs/TextbooksOnLogic.pdf

Computation

See Coding#Computation

• http://www.youtube.com/watch?v=foITiYYu2bc

• http://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
• http://existentialtype.wordpress.com/2011/03/27/the-holy-trinity/

• http://en.wikipedia.org/wiki/Combinatorics
  • http://en.wikipedia.org/wiki/Thue-Morse_sequence - !!!

Calculus

• http://en.wikipedia.org/wiki/Calculus is the mathematical study of change

• http://en.wikipedia.org/wiki/Formula
• http://en.wikipedia.org/wiki/Well-formed_formula
• http://en.wikipedia.org/wiki/Propositional_calculus

• http://en.wikipedia.org/wiki/Partial_function
• http://en.wikipedia.org/wiki/Domain_of_a_function

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

Analysis

• http://en.wikipedia.org/wiki/Mathematical_analysis

to sort

• http://en.wikipedia.org/wiki/Theory_of_relations

• http://www.ams.org/notices/201201/rtx120100031p.pdf [1]

• http://betterexplained.com/articles/linear-algebra-guide/

• http://www.wisdomandwonder.com/link/6582/some-thoughts-on-mathematics
• http://news.ycombinator.com/item?id=4839881
• http://www.evanmiller.org/mathematical-hacker.html

• http://www.altdevblogaday.com/2011/05/17/understanding-the-fourier-transform/
• http://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/

• [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

• http://homotopytypetheory.org/
• https://github.com/HoTT/book
  • https://news.ycombinator.com/item?id=5914395

• http://3.14-pi.net/

Statistics

• https://en.wikipedia.org/wiki/Mathematical_statistics

• https://en.wikipedia.org/wiki/Median

• https://github.com/mavam/stat-cookbook
• https://normaldeviate.wordpress.com/2012/11/17/what-is-bayesianfrequentist-inference
• http://www.greenteapress.com/thinkbayes

• https://en.wikipedia.org/wiki/Principal_component_analysis
  • http://stats.stackexchange.com/questions/2691/making-sense-of-principal-component-analysis-eigenvectors-eigenvalues

Information theory

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

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

Books

http://minireference.com/

Cellular automaton

• http://en.wikipedia.org/wiki/Cellular_automaton

• http://sciencevsmagic.net/eca/#150

Social

• http://functionspace.org/

• http://michaelnielsen.org/polymath1/index.php?title=Main_Page - massively collaborative online mathematical projects
  • http://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/

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.

• http://www.p-value.info/2012/11/free-datascience-books.html
• How to implement an algorithm from a scientific paper

• http://www.scilab.org/

• http://www.linuxbsdos.com/2013/07/14/2-free-software-alternatives-to-matlab/

Visualisation

• http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/#

to find those prime vis things again

• http://acko.net/blog/making-mathbox/

Gephi

• https://gephi.org/
• https://wiki.gephi.org
• http://en.wikipedia.org/wiki/Gephi

• http://gephi.org/2011/forceatlas2-the-new-version-of-our-home-brew-layout/

Tools

• http://oeis.org/

Prime

• http://www.sievesofchaos.com/
  • http://infosthetics.com/archives/2009/12/visualizing_prime_numbers.html

• http://www.jasondavies.com/primos/

• http://www.numbersimulation.com/

Fractals

• http://www.oftenpaper.net/sierpinski.htm

• http://en.wikipedia.org/wiki/Julia_set
• http://acko.net/blog/how-to-fold-a-julia-fractal/
• http://sprott.physics.wisc.edu/carlson/dragons.html

• http://en.wikipedia.org/wiki/Mandelbulb

• https://code.google.com/p/mandelstir/

• http://syntopia.github.io/Fragmentarium/

• http://en.wikipedia.org/wiki/L-system

• http://forums.tigsource.com/index.php?topic=33260.msg885099#msg885099

• http://www.openprocessing.org/sketch/105510

Informatics

• http://hypertextbook.com/chaos/