Maths
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total mess. also working back from computation on computing
General
to sort
- https://en.wikipedia.org/wiki/Outline_of_mathematics
- https://en.wikipedia.org/wiki/Foundations_of_mathematics
- https://en.wikipedia.org/wiki/Areas_of_mathematics
- https://en.wikipedia.org/wiki/Mathematics_Subject_Classification
- https://en.wikipedia.org/wiki/Linear_system
- https://en.wikipedia.org/wiki/Superposition_principle
- https://en.wikipedia.org/wiki/Nonlinear_system
- 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.
Social
- http://michaelnielsen.org/polymath1/index.php?title=Main_Page - massively collaborative online mathematical projects
Books
Arithmetic
- http://en.wikipedia.org/wiki/Radix
- http://threesixty360.wordpress.com/2009/06/09/ethiopian-multiplication/ [2]
Number theory
- https://en.wikipedia.org/wiki/Algebraic_number_theory
- https://en.wikipedia.org/wiki/Algebraic_integer
Prime
Geometry
- https://en.wikipedia.org/wiki/Differential_geometry
- https://en.wikipedia.org/wiki/Discrete_geometry
- https://en.wikipedia.org/wiki/Convex_geometry
Topology
- https://en.wikipedia.org/wiki/Topos
- https://en.wikipedia.org/wiki/Topology
- https://en.wikipedia.org/wiki/Topological_space
- https://en.wikipedia.org/wiki/Metric_space
Algebra
- https://en.wikipedia.org/wiki/Linear_algebra
- https://en.wikipedia.org/wiki/List_of_linear_algebra_topics
- http://minireference.com/blog/linear-algebra-tutorial/
- http://betterexplained.com/articles/linear-algebra-guide/
Group theory
Ring theory
Combinatorics
Trigonometry
Calculus
- https://en.wikipedia.org/wiki/Calculus is the mathematical study of change
Logic
See also Computing#Computation
- YouTube: Introduction to Logic series
- Chico Jones - Logic
- https://en.wikipedia.org/wiki/Classical_logic
- https://en.wikipedia.org/wiki/Informal_logic - content
- https://en.wikipedia.org/wiki/Mathematical_logic - form
- https://en.wikipedia.org/wiki/Premise
- https://en.wikipedia.org/wiki/Statement_(logic) - refers to the wording
- https://en.wikipedia.org/wiki/Sentence_(mathematical_logic) - grammar
- https://en.wikipedia.org/wiki/Proposition - refers to the meaning
- https://en.wikipedia.org/wiki/Argument#Formal_and_informal_arguments
- https://en.wikipedia.org/wiki/Inference
- https://en.wikipedia.org/wiki/Logical_consequence - conclusion
- https://en.wikipedia.org/wiki/Logical_connective - or logical operator, a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the sense of the compound sentence produced depends only on the original sentences.
- https://en.wikipedia.org/wiki/Material_conditional
- https://en.wikipedia.org/wiki/Corresponding_conditional
- https://en.wikipedia.org/wiki/Logical_disjunction
- https://en.wikipedia.org/wiki/Logical_conjunction
- https://en.wikipedia.org/wiki/Logical_form
- https://en.wikipedia.org/wiki/Validity - valid form
- https://en.wikipedia.org/wiki/Soundness - valid form and true proposition
- https://en.wikipedia.org/wiki/Hypothetical_syllogism
- https://en.wikipedia.org/wiki/Propositional_calculus
- https://en.wikipedia.org/wiki/Truth_function
- https://en.wikipedia.org/wiki/Mathematical_proof
proposition;
- https://en.wikipedia.org/wiki/Logical_reasoning
- https://en.wikipedia.org/wiki/Deductive_reasoning - proposition that reasons by necessity - valid/true or invalid/false
- https://en.wikipedia.org/wiki/Inductive_reasoning - proposition that reasons by probability - strong or weak likelihood
- https://en.wikipedia.org/wiki/Abductive_reasoning - guessing
- https://en.wikipedia.org/wiki/Defeasible_reasoning
- https://en.wikipedia.org/wiki/Probabilistic_reasoning
- https://en.wikipedia.org/wiki/Formulation_(logic)
- https://en.wikipedia.org/wiki/Quantifier#Logic
- https://en.wikipedia.org/wiki/Quantification
- https://en.wikipedia.org/wiki/Variable_(mathematics)
- https://en.wikipedia.org/wiki/Free_variables_and_bound_variables
- https://en.wikipedia.org/wiki/Domain_of_discourse
- https://en.wikipedia.org/wiki/Interpretation_(logic)
- https://en.wikipedia.org/wiki/Formal_semantics_(logic)
- https://en.wikipedia.org/wiki/Propositional_logic - propositional calculus or logic (also called sentential calculus or sentential logic) is a formal system in which formulas of a formal language may be interpreted to represent propositions. A system of inference rules and axioms allows certain formulas to be derived. These derived formulas are called theorems and may be interpreted to be true propositions.
- https://en.wikipedia.org/wiki/Zeroth-order_logic - propositional
- https://en.wikipedia.org/wiki/Predicate_logic - generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic, or infinitary logic
- https://en.wikipedia.org/wiki/First-order_logic
- https://en.wikipedia.org/wiki/Second-order_logic
- https://en.wikipedia.org/wiki/Higher-order_logic
- https://en.wikipedia.org/wiki/Many-sorted_logic
- https://en.wikipedia.org/wiki/Formal_system
- https://en.wikipedia.org/wiki/Axiomatic_system
- https://en.wikipedia.org/wiki/Formal_methods
- https://en.wikipedia.org/wiki/Formal_language
- https://en.wikipedia.org/wiki/Mathematical_induction - an inference rule, not inductive reasoning
- https://en.wikipedia.org/wiki/Natural_deduction
- https://en.wikipedia.org/wiki/Mathematical_induction
- https://en.wikipedia.org/wiki/Fuzzy_logic
- https://en.wikipedia.org/wiki/Intuitionistic_logic
- https://en.wikipedia.org/wiki/Linear_logic
- https://en.wikipedia.org/wiki/Modal_logic
- https://en.wikipedia.org/wiki/Paraconsistent_logic
- https://en.wikipedia.org/wiki/Pure_type_systems
- https://en.wikipedia.org/wiki/Calculus_of_constructions
Software
Set theory
- https://en.wikipedia.org/wiki/Set_theory
- https://en.wikipedia.org/wiki/Set_(mathematics)
- https://en.wikipedia.org/wiki/Class_(set_theory)
- https://en.wikipedia.org/wiki/Element_(mathematics)
- https://en.wikipedia.org/wiki/Subset
- https://en.wikipedia.org/wiki/Power_set
- https://en.wikipedia.org/wiki/Family_of_sets
- https://en.wikipedia.org/wiki/Algebraic_structures
- https://en.wikipedia.org/wiki/Constructible_universe
- https://en.wikipedia.org/wiki/Naive_set_theory
- https://en.wikipedia.org/wiki/Axiomatic_set_theory
Type theory
- https://en.wikipedia.org/wiki/Category:Homotopy_theory
- https://en.wikipedia.org/wiki/Homotopy_group
- http://homotopytypetheory.org/
- https://github.com/HoTT/book
Field theory
- https://en.wikipedia.org/wiki/Field_theory_(mathematics)
- https://en.wikipedia.org/wiki/Field_(mathematics)
Category theory
- https://en.wikipedia.org/wiki/Category_theory
- https://en.wikipedia.org/wiki/Morphism
- https://en.wikipedia.org/wiki/Cartesian_closed_categories
Model theory
The study of interpretation of formal systems is the branch of mathematical logic that is known as model theory.
- 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
Order theory
Domain theory
Proof theory
Analysis
Statistics
- https://github.com/mavam/stat-cookbook
- https://normaldeviate.wordpress.com/2012/11/17/what-is-bayesianfrequentist-inference
- http://www.greenteapress.com/thinkbayes
Information theory
Cellular automaton
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
Visualisation
to find those prime vis things again
Gephi
- Gephi is an interactive visualization and exploration platform for all kinds of networks and complex systems, dynamic and hierarchical graphs.
- https://wiki.gephi.org
- http://en.wikipedia.org/wiki/Gephi
Fractals
- 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
Other
Informatics
to sort
- 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.evanmiller.org/mathematical-hacker.html]