Niels Henrik Abel, the Glossary

Table of Contents

1. 104 relations: Abel (crater), Abel equation, Abel equation of the first kind, Abel Prize, Abel transform, Abel's binomial theorem, Abel's identity, Abel's inequality, Abel's irreducibility theorem, Abel's summation formula, Abel's test, Abel's theorem, Abel–Jacobi map, Abel–Plana formula, Abel–Ruffini theorem, Abelian and Tauberian theorems, Abelian category, Abelian extension, Abelian group, Abelian variety, Adrien-Marie Legendre, Algebraic equation, Algebraic function, Astronomische Nachrichten, August Leopold Crelle, Augustin-Louis Cauchy, Évariste Galois, Bailiff, Banknote, Bernt Michael Holmboe, Binomial theorem, Carl Ferdinand Degen, Carl Friedrich Gauss, Carl Gustav Jacob Jacobi, Carsten Anker, Catechism, Charles Hermite, Charles XIV John, Christianshavn, Christopher Hansteen, Complex multiplication of abelian varieties, Copenhagen, Crelle's Journal, Denmark–Norway, Divergent series, Dual abelian variety, Duchy of Schleswig, Elliptic function, Elliptic integral, Examen artium, ... Expand index (54 more) »

2. 19th-century Norwegian mathematicians
3. People from Froland
4. Tuberculosis deaths in Norway

Abel (crater)

Abel is an ancient lunar impact crater that lies near the southeast limb of the Moon's near side.

See Niels Henrik Abel and Abel (crater)

Abel equation

The Abel equation, named after Niels Henrik Abel, is a type of functional equation of the form or The forms are equivalent when is invertible.

See Niels Henrik Abel and Abel equation

Abel equation of the first kind

In mathematics, an Abel equation of the first kind, named after Niels Henrik Abel, is any ordinary differential equation that is cubic in the unknown function.

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Abel Prize

The Abel Prize (Abelprisen) is awarded annually by the King of Norway to one or more outstanding mathematicians.

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Abel transform

In mathematics, the Abel transform, named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially symmetric functions.

See Niels Henrik Abel and Abel transform

Abel's binomial theorem

Abel's binomial theorem, named after Niels Henrik Abel, is a mathematical identity involving sums of binomial coefficients.

See Niels Henrik Abel and Abel's binomial theorem

Abel's identity

In mathematics, Abel's identity (also called Abel's formula or Abel's differential equation identity) is an equation that expresses the Wronskian of two solutions of a homogeneous second-order linear ordinary differential equation in terms of a coefficient of the original differential equation.

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Abel's inequality

In mathematics, Abel's inequality, named after Niels Henrik Abel, supplies a simple bound on the absolute value of the inner product of two vectors in an important special case.

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Abel's irreducibility theorem

In mathematics, Abel's irreducibility theorem, a field theory result described in 1829 by Niels Henrik Abel, asserts that if ƒ(x) is a polynomial over a field F that shares a root with a polynomial g(x) that is irreducible over F, then every root of g(x) is a root of ƒ(x).

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Abel's summation formula

In mathematics, Abel's summation formula, introduced by Niels Henrik Abel, is intensively used in analytic number theory and the study of special functions to compute series.

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Abel's test

In mathematics, Abel's test (also known as Abel's criterion) is a method of testing for the convergence of an infinite series.

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Abel's theorem

In mathematics, Abel's theorem for power series relates a limit of a power series to the sum of its coefficients.

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Abel–Jacobi map

In mathematics, the Abel–Jacobi map is a construction of algebraic geometry which relates an algebraic curve to its Jacobian variety.

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Abel–Plana formula

In mathematics, the Abel–Plana formula is a summation formula discovered independently by and.

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Abel–Ruffini theorem

In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients.

See Niels Henrik Abel and Abel–Ruffini theorem

Abelian and Tauberian theorems

In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named after Niels Henrik Abel and Alfred Tauber.

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Abelian category

In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties.

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Abelian extension

In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian.

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Abelian group

In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.

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Abelian variety

In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions.

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Adrien-Marie Legendre

Adrien-Marie Legendre (18 September 1752 – 9 January 1833) was a French mathematician who made numerous contributions to mathematics.

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Algebraic equation

In mathematics, an algebraic equation or polynomial equation is an equation of the form P.

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Algebraic function

In mathematics, an algebraic function is a function that can be defined as the root of an irreducible polynomial equation.

See Niels Henrik Abel and Algebraic function

Astronomische Nachrichten

Astronomische Nachrichten (Astronomical Notes), one of the first international journals in the field of astronomy, was established in 1821 by the German astronomer Heinrich Christian Schumacher.

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August Leopold Crelle

August Leopold Crelle (17 March 1780 – 6 October 1855) was a German mathematician.

See Niels Henrik Abel and August Leopold Crelle

Augustin-Louis Cauchy

Baron Augustin-Louis Cauchy (France:, ; 21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist.

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Évariste Galois

Évariste Galois (25 October 1811 – 31 May 1832) was a French mathematician and political activist. Niels Henrik Abel and Évariste Galois are group theorists.

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Bailiff

A bailiff is a manager, overseer or custodian – a legal officer to whom some degree of authority or jurisdiction is given.

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Banknote

A banknotealso called a bill (North American English), paper money, or simply a noteis a type of negotiable promissory note, made by a bank or other licensed authority, payable to the bearer on demand.

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Bernt Michael Holmboe

Bernt Michael Holmboe (23 March 1795 – 28 March 1850) was a Norwegian mathematician. Niels Henrik Abel and Bernt Michael Holmboe are Norwegian mathematicians and People educated at Oslo Cathedral School.

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Binomial theorem

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.

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Carl Ferdinand Degen

Carl Ferdinand Degen (1 November 1766 – 8 April 1825) was a Danish mathematician.

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Carl Friedrich Gauss

Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist who contributed to many fields in mathematics and science.

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Carl Gustav Jacob Jacobi

Carl Gustav Jacob Jacobi (10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions to elliptic functions, dynamics, differential equations, determinants, and number theory.

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Carsten Anker

Carsten Tank Anker (17 November 1747 – 13 March 1824) was a Norwegian businessman, civil servant, politician and one of the Fathers of the Constitution of Norway.

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Catechism

A catechism (from κατηχέω, "to teach orally") is a summary or exposition of doctrine and serves as a learning introduction to the Sacraments traditionally used in catechesis, or Christian religious teaching of children and adult converts.

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Charles Hermite

Charles Hermite FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.

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Charles XIV John

Charles XIV John (Karl XIV Johan; 26 January 1763 – 8 March 1844) was King of Sweden and Norway from 1818 until his death in 1844 and the first monarch of the Bernadotte dynasty.

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Christianshavn

Christianshavn is a neighbourhood in Copenhagen, Denmark.

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Christopher Hansteen

Christopher Hansteen (26 September 1784 – 11 April 1873) was a Norwegian geophysicist, astronomer and physicist, best known for his mapping of Earth's magnetic field. Niels Henrik Abel and Christopher Hansteen are People educated at Oslo Cathedral School.

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Complex multiplication of abelian varieties

In mathematics, an abelian variety A defined over a field K is said to have CM-type if it has a large enough commutative subring in its endomorphism ring End(A).

See Niels Henrik Abel and Complex multiplication of abelian varieties

Copenhagen

Copenhagen (København) is the capital and most populous city of Denmark, with a population of 1.4 million in the urban area.

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Crelle's Journal

Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).

See Niels Henrik Abel and Crelle's Journal

Denmark–Norway

Denmark–Norway (Danish and Norwegian: Danmark–Norge) is a term for the 16th-to-19th-century multi-national and multi-lingual real unionFeldbæk 1998:11 consisting of the Kingdom of Denmark, the Kingdom of Norway (including the then Norwegian overseas possessions: the Faroe Islands, Iceland, Greenland, and other possessions), the Duchy of Schleswig, and the Duchy of Holstein.

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Divergent series

In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.

See Niels Henrik Abel and Divergent series

Dual abelian variety

In mathematics, a dual abelian variety can be defined from an abelian variety A, defined over a field k. A 1-dimensional abelian variety is an elliptic curve, and every elliptic curve is isomorphic to its dual, but this fails for higher-dimensional abelian varieties, so the concept of dual becomes more interesting in higher dimensions.

See Niels Henrik Abel and Dual abelian variety

Duchy of Schleswig

The Duchy of Schleswig (Hertugdømmet Slesvig; Herzogtum Schleswig; Hartogdom Sleswig; Härtochduum Slaswik) was a duchy in Southern Jutland (Sønderjylland) covering the area between about 60 km (35 miles) north and 70 km (45 mi) south of the current border between Germany and Denmark.

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Elliptic function

In the mathematical field of complex analysis, elliptic functions are special kinds of meromorphic functions, that satisfy two periodicity conditions.

See Niels Henrik Abel and Elliptic function

Elliptic integral

In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied by Giulio Fagnano and Leonhard Euler.

See Niels Henrik Abel and Elliptic integral

Examen artium

Examen artium was the name of the academic certification conferred in Denmark and Norway, qualifying the student for admission to university studies.

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Felix Klein

Felix Christian Klein (25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and the associations between geometry and group theory. Niels Henrik Abel and Felix Klein are group theorists.

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Fermat's Last Theorem

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers,, and satisfy the equation for any integer value of greater than.

See Niels Henrik Abel and Fermat's Last Theorem

Finnøy

Finnøy is a former municipality in Rogaland county, Norway.

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Freiberg

Freiberg is a university and former mining town in Saxony, Germany.

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French Academy of Sciences

The French Academy of Sciences (French: Académie des sciences) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research.

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Froland

Froland is a municipality in Agder county, Norway.

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Frolands verk

Frolands verk is a small village area in Froland municipality in Agder county, Norway.

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Göttingen

Göttingen (Chöttingen) is a university city in Lower Saxony, central Germany, the capital of the eponymous district.

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Georg Amadeus Carl Friedrich Naumann

Georg Amadeus Carl Friedrich Naumann (30 May 1797 – 26 November 1873), also known as Karl Friedrich Naumann, was a German mineralogist and geologist.

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Gjerstad

Gjerstad is a municipality in Agder county, Norway.

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Gjerstad Church

Gjerstad Church (Gjerstad kirke, locally: Gjerstad kjørke) is a parish church of the Church of Norway in Gjerstad Municipality in Agder county, Norway.

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Gustav Lærum

Gustav Lærum (2 June 1870, in Fet – 21 May 1938) was a Norwegian satirical illustrator, caricaturist and sculptor.

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Gustav Vigeland

Gustav Vigeland (11 April 1869 – 12 March 1943), born as Adolf Gustav Thorsen, was a Norwegian sculptor.

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Heinrich Christian Schumacher

Prof Heinrich Christian Schumacher FRS(For) FRSE (3 September 1780 – 28 December 1850) was a German-Danish astronomer and mathematician.

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History of group theory

The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads.

See Niels Henrik Abel and History of group theory

Horace

Quintus Horatius Flaccus (8 December 65 BC – 27 November 8 BC),Suetonius,. commonly known in the English-speaking world as Horace, was the leading Roman lyric poet during the time of Augustus (also known as Octavian). The rhetorician Quintilian regarded his Odes as the only Latin lyrics worth reading: "He can be lofty sometimes, yet he is also full of charm and grace, versatile in his figures, and felicitously daring in his choice of words."Quintilian 10.1.96.

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Humboldt University of Berlin

The Humboldt University of Berlin (Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany.

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Hyperelliptic curve

In algebraic geometry, a hyperelliptic curve is an algebraic curve of genus g > 1, given by an equation of the form y^2 + h(x)y.

See Niels Henrik Abel and Hyperelliptic curve

Johan Gørbitz

Johan Görbitz (8 September 1782 – 3 July 1853) was a Norwegian painter.

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Leipzig

Leipzig (Upper Saxon: Leibz'sch) is the most populous city in the German state of Saxony.

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Leonhard Euler

Leonhard Euler (15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus.

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List of things named after Niels Henrik Abel

This is the list of things named after Niels Henrik Abel (1802–1829), a Norwegian mathematician.

See Niels Henrik Abel and List of things named after Niels Henrik Abel

Ludvig Sylow

Peter Ludvig Meidell Sylow (12 December 1832 – 7 September 1918) was a Norwegian mathematician who proved foundational results in group theory. Niels Henrik Abel and Ludvig Sylow are 19th-century Norwegian mathematicians, group theorists, Norwegian mathematicians and People educated at Oslo Cathedral School.

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Mathematical analysis

Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions.

See Niels Henrik Abel and Mathematical analysis

Mathematical proof

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion.

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Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Moon

The Moon is Earth's only natural satellite.

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Nedstrand

Nedstrand (locally, Stranda) is a village in Tysvær municipality in Rogaland county, Norway.

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Nobel Prize

The Nobel Prizes (Nobelpriset; Nobelprisen) are five separate prizes awarded to those who, during the preceding year, have conferred the greatest benefit to humankind, as established by the 1895 will of Swedish chemist, engineer, and industrialist Alfred Nobel, in the year before he died.

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Norges Bank

Norges Bank is the central bank of Norway.

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Norwegian Constituent Assembly

The Norwegian Constituent Assembly (Grunnlovsforsamlingen or Riksforsamlingen) is the name given to the 1814 constitutional assembly that adopted the Norwegian Constitution and formalised the dissolution of the union with Denmark.

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Norwegian krone

The krone (abbreviation: kr (also NKr for distinction); code: NOK), plural kroner, is the currency of the Kingdom of Norway (including overseas territories and dependencies).

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Norwegian rigsdaler

The rigsdaler specie was a unit of silver currency used in Norway from 1544, renamed as the speciedaler in 1816 and used until 1873.

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Oslo

Oslo (or; Oslove) is the capital and most populous city of Norway.

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Oslo Cathedral School

Schola Osloensis, known in Norwegian as Oslo Katedralskole (Oslo Cathedral School) and more commonly as "Katta", is a selective upper secondary school located in Oslo, Norway.

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Philosophy

Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, value, mind, and language.

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Physics

Physics is the natural science of matter, involving the study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.

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Quintic function

In mathematics, a quintic function is a function of the form where,,,, and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero.

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Rational number

In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Risør (town)

Risør is a Seaside resort, a town and the administrative centre of Risør municipality in Agder county, Norway.

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Royal Palace, Oslo

The Royal Palace (Slottet or Det kongelige slott) in Oslo was built in the first half of the 19th century as the Norwegian residence of the French-born King Charles XIV John, who reigned as king of Norway and Sweden.

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Søren Georg Abel

Søren Georg Abel (3 January 1772 – 5 May 1820) was a Norwegian priest and politician, also known as the father of mathematician Niels Henrik Abel.

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Son, Norway

Son is an old town, and a former municipality.

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Sophus Lie

Marius Sophus Lie (17 December 1842 – 18 February 1899) was a Norwegian mathematician. Niels Henrik Abel and Sophus Lie are 19th-century Norwegian mathematicians and group theorists.

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Stepfamily

A stepfamily is a family where at least one parent has children who are not biologically related to their spouse.

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Storting

The Storting (Stortinget) is the supreme legislature of Norway, established in 1814 by the Constitution of Norway.

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Summation by parts

In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums.

See Niels Henrik Abel and Summation by parts

Theology

Theology is the study of religious belief from a religious perspective, with a focus on the nature of divinity.

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Transcendental number theory

Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation with rational coefficients), in both qualitative and quantitative ways.

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Tuberculosis

Tuberculosis (TB), also known colloquially as the "white death", or historically as consumption, is an infectious disease usually caused by Mycobacterium tuberculosis (MTB) bacteria.

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Union between Sweden and Norway

Sweden and Norway or Sweden–Norway (Svensk-norska unionen; Den svensk-norske union(en)), officially the United Kingdoms of Sweden and Norway, and known as the United Kingdoms, was a personal union of the separate kingdoms of Sweden and Norway under a common monarch and common foreign policy that lasted from 1814 until its peaceful dissolution in 1905.

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University of Oslo

The University of Oslo (Universitetet i Oslo; Universitas Osloensis) is a public research university located in Oslo, Norway.

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Wolfgang Amadeus Mozart

Wolfgang Amadeus Mozart (27 January 17565 December 1791) was a prolific and influential composer of the Classical period.

See Niels Henrik Abel and Wolfgang Amadeus Mozart

See also

19th-century Norwegian mathematicians

• Alf Victor Guldberg
• Carl Anton Bjerknes
• Caspar Wessel
• Cato Maximilian Guldberg
• Ludvig Sylow
• Niels Henrik Abel
• Sophus Lie

People from Froland

• Gotfred Kvifte
• Helge Løvland
• Iver Steen Thomle
• Jan Sagedal
• Marte Olsbu Røiseland
• Niels Henrik Abel

Tuberculosis deaths in Norway

• Elsa Laula Renberg
• Gerda Grepp
• Harald Lie
• Johan Fredrik Eckersberg
• John Savio
• Niels Henrik Abel
• Sigurd Lie

References

[1] https://en.wikipedia.org/wiki/Niels_Henrik_Abel

Also known as ABEL N.H., Abel niels henrik, Abel, N.H., Abel, Niels Henrik, Henrik Abel, Henry Abel, N. H. Abel, Neils Abel, Niels Abel, Niels Henrick Abel, Nils Henrik Abel.

, Felix Klein, Fermat's Last Theorem, Finnøy, Freiberg, French Academy of Sciences, Froland, Frolands verk, Göttingen, Georg Amadeus Carl Friedrich Naumann, Gjerstad, Gjerstad Church, Gustav Lærum, Gustav Vigeland, Heinrich Christian Schumacher, History of group theory, Horace, Humboldt University of Berlin, Hyperelliptic curve, Johan Gørbitz, Leipzig, Leonhard Euler, List of things named after Niels Henrik Abel, Ludvig Sylow, Mathematical analysis, Mathematical proof, Mathematician, Mathematics, Moon, Nedstrand, Nobel Prize, Norges Bank, Norwegian Constituent Assembly, Norwegian krone, Norwegian rigsdaler, Oslo, Oslo Cathedral School, Philosophy, Physics, Quintic function, Rational number, Risør (town), Royal Palace, Oslo, Søren Georg Abel, Son, Norway, Sophus Lie, Stepfamily, Storting, Summation by parts, Theology, Transcendental number theory, Tuberculosis, Union between Sweden and Norway, University of Oslo, Wolfgang Amadeus Mozart.