User:WikiLinuz/Mathematics

< User:WikiLinuz

Mathematical logic

General

Theorems (list)
and paradoxes

Gödel's completeness and incompleteness theorems
Tarski's undefinability
Banach–Tarski paradox
Cantor's theorem, paradox and diagonal argument
Compactness
Halting problem
Lindström's
Löwenheim–Skolem
Russell's paradox

Traditional	Classical logic Logical truth Tautology Proposition Inference Logical equivalence Consistency Equiconsistency Argument Soundness Validity Syllogism Square of opposition Venn diagram
Propositional	Boolean algebra Boolean functions Logical connectives Propositional calculus Propositional formula Truth tables Many-valued logic 3 finite ∞
Predicate	First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus

Set hereditary Class (Ur-)Element Ordinal number Extensionality Forcing Relation equivalence partition Set operations: intersection union complement Cartesian product power set identities
Types of sets	Countable Uncountable Empty Inhabited Singleton Finite Infinite Transitive Ultrafilter Recursive Fuzzy Universal Universe constructible Grothendieck Von Neumann
Maps and cardinality	Function/Map domain codomain image In/Sur/Bi-jection Schröder–Bernstein theorem Isomorphism Gödel numbering Enumeration Large cardinal inaccessible Aleph number Operation binary
Set theories	Zermelo–Fraenkel axiom of choice continuum hypothesis General Kripke–Platek Morse–Kelley Naive New Foundations Tarski–Grothendieck Von Neumann–Bernays–Gödel Ackermann Constructive

Formal systems (list),
language and syntax

Alphabet
Arity
Automata
Axiom schema
Expression
- ground
Extension
- by definition
- conservative
Relation
Formation rule
Grammar
Formula
- atomic
- closed
- ground
- open
Free/bound variable
Language
Metalanguage
Logical connective
- ¬
- ∨
- ∧
- →
- ↔
- =
Predicate
- functional
- variable
- propositional variable
Proof
Quantifier
- ∃
- !
- ∀
- rank
Sentence
- atomic
- spectrum
Signature
String
Substitution
Symbol
- function
- logical/constant
- non-logical
- variable
Term
Theory
- list

Example axiomatic
systems (list)

of arithmetic:
of the real numbers
- Tarski's axiomatization
of Boolean algebras
- canonical
- minimal axioms
of geometry:
- Euclidean:
- non-Euclidean

Principia Mathematica

Computability theory

Related

Mathematics portal

Classical logic

General

Classical logics

Principles

Rules

Introduction	Negation Double negation Existential Universal Biconditional Conjunction Disjunction
Elimination	Double negation Existential Universal Biconditional Conjunction Disjunction

People

Works

Ancient Greek mathematics

Mathematicians
(timeline)

Treatises

Problems

Concepts
and definitions

Results

In Elements	Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Intersecting chords theorem Intersecting secants theorem Law of cosines Pons asinorum Pythagorean theorem Tangent-secant theorem Thales's theorem Theorem of the gnomon
Apollonius	Apollonius's theorem
Other	Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Law of sines Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus

Centers

Related

Ancient Greek astronomy Attic numerals Greek numerals Latin translations of the 12th century Non-Euclidean geometry Philosophy of mathematics Neusis construction
History of	A History of Greek Mathematics by Thomas Heath algebra timeline arithmetic timeline calculus timeline geometry timeline logic timeline mathematics timeline numbers prehistoric counting numeral systems list
Other cultures	Arabian/Islamic Babylonian Chinese Egyptian Incan Indian Japanese

Ancient Greece portal • Mathematics portal

v t e Algebra
Outline History
Areas	Abstract algebra Algebraic geometry Algebraic variety Scheme Algebraic number theory Category theory Commutative algebra Elementary algebra Homological algebra K-theory Linear algebra Multilinear algebra Noncommutative algebra Order theory Representation theory Universal algebra
Basic concepts	Algebraic expression Equation (Linear equation, Quadratic equation) Function (Polynomial function) Inequality (Linear inequality) Operation (Addition, Multiplication) Relation (Equivalence relation) Variable
Algebraic structures	Field (theory) Group (theory) Module (theory) Ring (theory) Vector space (Vector)
Linear and multilinear algebra	Basis Determinant Eigenvalues and eigenvectors Inner product space (Dot product) Hilbert space Linear map (Matrix) Linear subspace (Affine space) Norm (Euclidean norm) Orthogonality (Orthogonal complement) Rank Trace
Algebraic constructions	Composition algebra Exterior algebra Free object (Free group, ...) Geometric algebra (Multivector) Polynomial ring (Polynomial) Quotient object (Quotient group, ...) Symmetric algebra Tensor algebra
Topic lists	Algebraic structures
Glossaries	Field theory Linear algebra Order theory Ring theory
Category

v t e Major mathematics areas
History Timeline Future Lists Glossary
Foundations	Category theory Information theory Mathematical logic Philosophy of mathematics Set theory Type theory
Algebra	Abstract Commutative Elementary Group theory Linear Multilinear Universal Homological
Analysis	Calculus Real analysis Complex analysis Hypercomplex analysis Differential equations Functional analysis Harmonic analysis Measure theory
Discrete	Combinatorics Graph theory Order theory
Geometry	Algebraic Analytic Arithmetic Differential Discrete Euclidean Finite
Number theory	Arithmetic Algebraic number theory Analytic number theory Diophantine geometry
Topology	General Algebraic Differential Geometric Homotopy theory
Applied	Engineering mathematics Mathematical biology Mathematical chemistry Mathematical economics Mathematical finance Mathematical physics Mathematical psychology Mathematical sociology Mathematical statistics Probability Statistics Systems science Control theory Game theory Operations research
Computational	Computer science Theory of computation Computational complexity theory Numerical analysis Optimization Computer algebra
Related topics	Mathematicians lists Informal mathematics Films about mathematicians Recreational mathematics Mathematics and art Mathematics education
Mathematics portal Category Commons WikiProject

Retrieved from "https://en.wikipedia.org/w/index.php?title=User:WikiLinuz/Mathematics&oldid=1244887911"