Maths
Jump to navigation
Jump to search
huge 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.
Philosophy
- http://en.wikipedia.org/wiki/Constructivism_(mathematics)
- http://en.wikipedia.org/wiki/Intuitionism - maths is purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality
- http://en.wikipedia.org/wiki/Finitism - accepts the existence only of finite mathematical objects
- http://en.wikipedia.org/wiki/Constructive_analysis
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/Boolean_algebra
- https://en.wikipedia.org/wiki/Boolean_algebras_canonically_defined
Linear 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/
Abstract algebra
Group theory
Ring theory
Combinatorics
Trigonometry
Calculus
- https://en.wikipedia.org/wiki/Calculus is the mathematical study of change
Logic
- 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
Leibniz;
- https://en.wikipedia.org/wiki/Characteristica_universalis
- https://en.wikipedia.org/wiki/Calculus_ratiocinator
- https://en.wikipedia.org/wiki/Gottlob_Frege - sense and reference, connotation and denotation
- https://en.wikipedia.org/wiki/Formal_language - well-defined vocabulary and grammar
- https://en.wikipedia.org/wiki/Formal_system
- https://en.wikipedia.org/wiki/Axiom
- https://en.wikipedia.org/wiki/Axiomatic_system
- https://en.wikipedia.org/wiki/Formal_methods
- YouTube: Introduction to Logic series
- Chico Jones - Logic
- https://en.wikipedia.org/wiki/Propositional_calculus - 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/Propositional_formula
- https://en.wikipedia.org/wiki/Propositional_variable
- https://en.wikipedia.org/wiki/Proposition
- https://en.wikipedia.org/wiki/Clause_(grammar)
- https://en.wikipedia.org/wiki/Copula_(linguistics) - are, is
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) Quantity: How much? Quality: Affirmative, negative
- https://en.wikipedia.org/wiki/Syntax_(logic)
- 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/Formal_proof - or derivation, is a finite sequence of sentences, each of which is an axiom or follows from the preceding sentences in the sequence by a rule of inference
- https://en.wikipedia.org/wiki/Well-formed_formula - proof in a formal system
- https://en.wikipedia.org/wiki/Proposition - refers to the meaning, basic semantics
- https://en.wikipedia.org/wiki/Antecedent_(logic) - first half of a proposition
- https://en.wikipedia.org/wiki/Consequent - second half of a proposition
- https://en.wikipedia.org/wiki/Argument#Formal_and_informal_arguments
- https://en.wikipedia.org/wiki/Predicate_(mathematical_logic) - a statement that may be true or false depending on the values of its variables.
- https://en.wikipedia.org/wiki/Boolean_algebra - primary: sets, secondary;
- https://en.wikipedia.org/wiki/Principle_of_bivalence - states that every declarative sentence expressing a proposition (of a theory under inspection) has exactly one truth value, either true or false
- https://en.wikipedia.org/wiki/False_(logic)
- https://en.wikipedia.org/wiki/Truth_value
- https://en.wikipedia.org/wiki/Logical_truth
- https://en.wikipedia.org/wiki/Truth_table
- https://en.wikipedia.org/wiki/Tautology_(logic) - always true
- https://en.wikipedia.org/wiki/Tautology_(rule_of_inference)
- https://en.wikipedia.org/wiki/Inference
- https://en.wikipedia.org/wiki/Interpretation_(logic)
- https://en.wikipedia.org/wiki/Logical_consequence - conclusion
- https://en.wikipedia.org/wiki/Validity
- https://en.wikipedia.org/wiki/Rule_of_inference - the act of drawing a conclusion based on the form of premises interpreted as a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions)
- https://en.wikipedia.org/wiki/Modus_ponens - "P implies Q; P is asserted to be true, so therefore Q must be true."
- "P implies Q; P is asserted to be true, so therefore Q must be true."
- 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 - precisely or exactly implies
- https://en.wikipedia.org/wiki/If_and_only_if - equivalent (or materially equivalent) implication - ↔ ⇔ ≡
- https://en.wikipedia.org/wiki/Corresponding_conditional - a valid/truthful argument. negation of its corresponding conditional is a contradiction.
- https://en.wikipedia.org/wiki/Negation - not, logical compliment
- https://en.wikipedia.org/wiki/Logical_conjunction - and
- https://en.wikipedia.org/wiki/Logical_disjunction - or
- https://en.wikipedia.org/wiki/Exclusive_or
- https://en.wikipedia.org/wiki/Assignment_(mathematical_logic)
- https://en.wikipedia.org/wiki/T-schema
- 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. formal system is distinguished from other systems in that its formulae contain variables which can be quantified.
- https://en.wikipedia.org/wiki/Zeroth-order_logic - first-order logic without quantifiers. finitely axiomatizable zeroth-order logic is isomorphic to a propositional logic.
- https://en.wikipedia.org/wiki/Second-order_logic - see frege's first predicate logic. quantifies over relations.
- https://en.wikipedia.org/wiki/Higher-order_logic - from first-order logic by additional quantifiers and a stronger semantics
- https://en.wikipedia.org/wiki/Many-sorted_logic
- https://en.wikipedia.org/wiki/Quantification#Logic
- https://en.wikipedia.org/wiki/Universal_quantification - all or any - universal - ∀
- https://en.wikipedia.org/wiki/Existential_quantification - there exists - particular - ∃
- https://en.wikipedia.org/wiki/Term_(logic)
- https://en.wikipedia.org/wiki/Formulation_(logic)
- https://en.wikipedia.org/wiki/Formula
- https://en.wikipedia.org/wiki/Variable_(mathematics)
- https://en.wikipedia.org/wiki/Free_variables_and_bound_variables - symbol that will later be replaced by some literal string
- https://en.wikipedia.org/wiki/Domain_of_discourse
- https://en.wikipedia.org/wiki/Universe_(mathematics)
- https://en.wikipedia.org/wiki/Interpretation_(logic)
- https://en.wikipedia.org/wiki/Formal_semantics_(logic)
- https://en.wikipedia.org/wiki/Categorical_logic - represents both syntax and semantics by a category, and an interpretation by a functor
- https://en.wikipedia.org/wiki/Mathematical_induction - an inference rule, not inductive reasoning
- https://en.wikipedia.org/wiki/Combinatorial_logic - a notation to eliminate the need for variables in mathematical logic
- https://en.wikipedia.org/wiki/Sequent_calculus
- Interactive Tutorial of the Sequent Calculus - This interactive tutorial will teach you how to use the sequent calculus, a simple set of rules with which you can use to show the truth of statements in first order logic. It is geared towards anyone with some background in writing software for computers, with knowledge of basic boolean logic.
See also Computing#Computation, Semantic web
Non-classical
all nc?
- https://en.wikipedia.org/wiki/Pure_type_systems
- https://en.wikipedia.org/wiki/Calculus_of_constructions
- https://en.wikipedia.org/wiki/Categorial_grammar - Lambek calculus
Software
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.
- universal algebra + logic = model theory
- model theory = algebraic geometry − fields
- 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]