Maths

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Revision as of 03:10, 14 January 2014 by Milk (talk | contribs) (→‎Arithmetic)
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huge mess. also working back from computation on computing

General

to sort




  • 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.

History

Philosophy

Social

Books

Basics

Arithmetic



Numbers


Prime

Geometry

Algebra

Universal algebra

Linear algebra

Abstract algebra

Group theory

Ring theory

Scheme theory

Topology

Combinatorics

Trigonometry

Calculus


Logic

meeeess

All S are P. (A form)
All S are not P. (E form)
Some S are P. (I form)
Some S are not P. (O form)


  • https://en.wikipedia.org/wiki/Propositional_calculus - logic of sentences. 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.




Bacon;

Leibniz;





Quantity: How much?
Quality: Affirmative, negative





  • https://en.wikipedia.org/wiki/Predicate_logic - logic of objects. generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic, or infinitary logic. formal system is distinguished from other systems in that its formulae contain variables which can be quantified.





  • https://en.wikipedia.org/wiki/Natural_deduction - a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. This contrasts with the axiomatic systems which instead use axioms as much as possible to express the logical laws of deductive reasoning.

See also Computing#Computation, Semantic web

Non-classical

all nc?



Software


Set theory


Type theory

Homotopy theory

Field theory

Category theory

  • nLab is a wiki-lab for collaborative work on Mathematics, Physics and Philosophy — especially from the n-point of view: insofar as these subjects are usefully treated with tools and notions of category theory or higher category theory.

Model theory

The study of interpretation of formal systems is the branch of mathematical logic that is known as model theory.

  • universal algebra + logic = model theory
  • model theory = algebraic geometry − fields

Order theory

Domain theory

Proof theory

Analysis

Statistics

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.

Visualisation

to find those prime vis things again

Gephi

Fractals

Other

Informatics

to sort