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39 relations: Abstract algebra, Abstract algebraic logic, Abstract and concrete, Abstract logic, Abstract model theory, Abstract nonsense, Abstract structure, Abstraction, Affine geometry, Analytic geometry, Arithmetic, Axiomatic system, Bernhard Riemann, Bertrand Russell, Carl Friedrich Gauss, Cartesian coordinate system, Category theory, Constructivism (philosophy of education), Dimension, Erlangen program, Essence, Euclid's Elements, Felix Klein, Finite geometry, Generalization, Hippocrates of Chios, Invariant (mathematics), János Bolyai, Mathematical maturity, Mathematics, Model theory, Montessori education, Nikolai Lobachevsky, Non-Euclidean geometry, Phenomenon, Principle of abstraction, Projective geometry, René Descartes, Symmetry.
Abstract algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
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Abstract algebraic logic
In mathematical logic, abstract algebraic logic is the study of the algebraization of deductive systems arising as an abstraction of the well-known Lindenbaum–Tarski algebra, and how the resulting algebras are related to logical systems.
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Abstract and concrete
Abstract and concrete are classifications that denote whether a term describes an object with a physical referent or one with no physical referents.
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Abstract logic
In mathematical logic, an abstract logic is a formal system consisting of a class of sentences and a satisfaction relation with specific properties related to occurrence, expansion, isomorphism, renaming and quantification.
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Abstract model theory
In mathematical logic, abstract model theory is a generalization of model theory which studies the general properties of extensions of first-order logic and their models.
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Abstract nonsense
In mathematics, abstract nonsense, general abstract nonsense, and general nonsense are terms used by mathematicians to describe abstract methods related to category theory and homological algebra.
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Abstract structure
An abstract structure is a formal object that is defined by a set of laws, properties and relationships in a way that is logically if not always historically independent of the structure of contingent experiences, for example, those involving physical objects.
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Abstraction
Abstraction in its main sense is a conceptual process where general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or "concrete") signifiers, first principles, or other methods.
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Affine geometry
In mathematics, affine geometry is what remains of Euclidean geometry when not using (mathematicians often say "when forgetting") the metric notions of distance and angle.
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Analytic geometry
In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.
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Arithmetic
Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.
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Axiomatic system
In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.
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Bernhard Riemann
Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry.
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Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, historian, writer, social critic, political activist, and Nobel laureate.
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Carl Friedrich Gauss
Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.
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Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
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Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
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Constructivism (philosophy of education)
Constructivism is a philosophical viewpoint about the nature of knowledge.
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Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
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Erlangen program
The Erlangen program is a method of characterizing geometries based on group theory and projective geometry.
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Essence
In philosophy, essence is the property or set of properties that make an entity or substance what it fundamentally is, and which it has by necessity, and without which it loses its identity.
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Euclid's Elements
The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.
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Felix Klein
Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory.
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Finite geometry
A finite geometry is any geometric system that has only a finite number of points.
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Generalization
A generalization (or generalisation) is the formulation of general concepts from specific instances by abstracting common properties.
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Hippocrates of Chios
Hippocrates of Chios (Ἱπποκράτης ὁ Χῖος) was an ancient Greek mathematician, geometer, and astronomer who lived c. 470 – c. 410 BC.
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Invariant (mathematics)
In mathematics, an invariant is a property, held by a class of mathematical objects, which remains unchanged when transformations of a certain type are applied to the objects.
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János Bolyai
János Bolyai (15 December 1802 – 27 January 1860) or Johann Bolyai, was a Hungarian mathematician, one of the founders of non-Euclidean geometry — a geometry that differs from Euclidean geometry in its definition of parallel lines.
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Mathematical maturity
Mathematical maturity is an informal term used by mathematicians to refer to a mixture of mathematical experience and insight that cannot be directly taught.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Model theory
In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic.
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Montessori education
The Montessori Method of education, developed by Maria Montessori, is a child-centered educational approach based on scientific observations of children from birth to adulthood.
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Nikolai Lobachevsky
Nikolai Ivanovich Lobachevsky (a; –) was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry and also his fundamental study on Dirichlet integrals known as Lobachevsky integral formula.
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Non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.
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Phenomenon
A phenomenon (Greek: φαινόμενον, phainómenon, from the verb phainein, to show, shine, appear, to be manifest or manifest itself, plural phenomena) is any thing which manifests itself.
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Principle of abstraction
The principle of abstraction is a grouping principle, whereby a hierarchy is adhered to with higher levels of abstraction placed near the top with more specific concepts underneath.
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Projective geometry
Projective geometry is a topic in mathematics.
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René Descartes
René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.
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Symmetry
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.
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References
[1] https://en.wikipedia.org/wiki/Abstraction_(mathematics)
