|
Dirichlet
Johann Peter Gustav Lejeune Dirichlet (; ; 13 February 1805 – 5 May 1859) was a German mathematician. In number theory, he proved special cases of Fermat's last theorem and created analytic number theory. In Mathematical analysis, analysis, he advanced the theory of Fourier series and was one of the first to give the modern formal definition of a function (mathematics), function. In mathematical physics, he studied potential theory, boundary-value problem, boundary-value problems, and heat diffusion, and hydrodynamics. Although his surname is Lejeune Dirichlet, he is commonly referred to by his mononym Dirichlet, in particular for results named after him. Biography Early life (1805–1822) Gustav Lejeune Dirichlet was born on 13 February 1805 in Düren, a town on the left bank of the Rhine which at the time was part of the First French Empire, reverting to Prussia after the Congress of Vienna in 1815. His father Johann Arnold Lejeune Dirichlet was the postmaster, merchant, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Things Named After Peter Gustav Lejeune Dirichlet
The Germany, German mathematician Peter Gustav Lejeune Dirichlet (1805–1859) is the eponym of many things. Mathematics * Theorems named ''Dirichlet's theorem'': **Dirichlet's approximation theorem (diophantine approximation) **Dirichlet's theorem on arithmetic progressions (number theory, specifically prime numbers) **Dirichlet's unit theorem (algebraic number theory and Ring (mathematics), rings) * Dirichlet algebra * Dirichlet beta function * Dirichlet boundary condition (differential equations) **Neumann–Dirichlet method * Dirichlet characters (number theory, specifically Dirichlet series, zeta and Dirichlet L-function, L-functions. 1831) * Dirichlet conditions (Fourier series) * Dirichlet convolution (number theory and arithmetic functions) * Dirichlet density (number theory) **Dirichlet average * Dirichlet distribution (probability theory) **Dirichlet-multinomial distribution ** Dirichlet negative multinomial distribution **Generalized Dirichlet distribution (probabil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Dedekind
Julius Wilhelm Richard Dedekind (; ; 6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to number theory, abstract algebra (particularly ring theory), and the axiomatic foundations of arithmetic. His best known contribution is the definition of real numbers through the notion of Dedekind cut. He is also considered a pioneer in the development of modern set theory and of the philosophy of mathematics known as ''logicism''. Life Dedekind's father was Julius Levin Ulrich Dedekind, an administrator of Collegium Carolinum in Braunschweig. His mother was Caroline Henriette Dedekind (née Emperius), the daughter of a professor at the Collegium. Richard Dedekind had three older siblings. As an adult, he never used the names Julius Wilhelm. He was born in Braunschweig (often called "Brunswick" in English), which is where he lived most of his life and died. His body rests at Braunschweig Main Cemetery. He first attended the Collegium Carol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernhard Riemann
Georg Friedrich Bernhard Riemann (; ; 17September 182620July 1866) was a German mathematician who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis. His 1859 paper on the prime-counting function, containing the original statement of the Riemann hypothesis, is regarded as a foundational paper of analytic number theory. Through his pioneering contributions to differential geometry, Riemann laid the foundations of the mathematics of general relativity. He is considered by many to be one of the greatest mathematicians of all time. Early years Riemann was born on 17 September 1826 in Breselenz, a village near Danne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leopold Kronecker
Leopold Kronecker (; 7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, abstract algebra and logic, and criticized Georg Cantor's work on set theory. Heinrich Weber quoted Kronecker as having said, "'" ("God made the integers, all else is the work of man").The English translation is from Gray. In a footnote, Gray attributes the German quote to "Weber 1891/92, 19, quoting from a lecture of Kronecker's of 1886". Weber, Heinrich L. 1891–1892Kronecker 2:5-23. (The quote is on p. 19.) Kronecker was a student and life-long friend of Ernst Kummer. Biography Leopold Kronecker was born ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory can often be understood through the study of Complex analysis, analytical objects, such as the Riemann zeta function, that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for instance how irrational numbers can be approximated by fractions (Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rudolf Lipschitz
Rudolf Otto Sigismund Lipschitz (14 May 1832 – 7 October 1903) was a German mathematician who made contributions to mathematical analysis (where he gave his name to the Lipschitz continuity condition) and differential geometry, as well as number theory, algebras with involution and classical mechanics. Biography Rudolf Lipschitz was born on 14 May 1832 in Königsberg. He was the son of a landowner and was raised at his father's estate at Bönkein which was near Königsberg. He entered the University of Königsberg when he was 15, but later moved to the University of Berlin where he studied with Gustav Dirichlet. Despite having his studies delayed by illness, in 1853 Lipschitz graduated with a PhD in Berlin. After receiving his PhD, Lipschitz started teaching at local Gymnasiums. In 1857 he married Ida Pascha, the daughter of one of the landowners with an estate near to his father's, and earned his habilitation at the University of Bonn, where he remained as a privatdozent. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elwin Bruno Christoffel
Elwin Bruno Christoffel (; 10 November 1829 – 15 March 1900) was a German mathematician and physicist. He introduced fundamental concepts of differential geometry, opening the way for the development of tensor calculus, which would later provide the mathematical basis for general relativity. Life Christoffel was born on 10 November 1829 in Montjoie (now Monschau) in Prussia in a family of cloth merchants. He was initially educated at home in languages and mathematics, then attended the Jesuit Gymnasium and the Friedrich-Wilhelms Gymnasium in Cologne. In 1850 he went to the University of Berlin, where he studied mathematics with Gustav Dirichlet (which had a strong influence over him) among others, as well as attending courses in physics and chemistry. He received his doctorate in Berlin in 1856 for a thesis on the motion of electricity in homogeneous bodies written under the supervision of Martin Ohm, Ernst Kummer and Heinrich Gustav Magnus. After receiving his doctorate, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Fourier
Jean-Baptiste Joseph Fourier (; ; 21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre, Burgundy and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and vibrations. The Fourier transform and Thermal conduction#Fourier's law, Fourier's law of conduction are also named in his honour. Fourier is also generally credited with the discovery of the greenhouse effect. Biography Fourier was born in Auxerre (now in the Yonne département of France), the son of a tailor. He was orphaned at the age of nine. Fourier was recommended to the Bishop of Auxerre and, through this introduction, he was educated by the Benedictine Order of the Convent of St. Mark. The commissions in the scientific corps of the army were reserved for those of good birth, and being thus ineligible, he accepted a military lectureship on mathematics. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Wilhelm Borchardt
Carl Wilhelm Borchardt (22 February 1817 – 27 June 1880) was a German mathematician. Borchardt was born to a Jewish family in Berlin. His father, Moritz, was a respected merchant, and his mother was Emma Heilborn. Borchardt studied under a number of tutors, including Julius Plücker and Jakob Steiner. He studied at the University of Berlin under Lejeune Dirichlet in 1836 and at the University of Königsberg in 1839. In 1848 he began teaching at the University of Berlin. He did research in the area of the arithmetic-geometric mean, continuing work by Gauss and Lagrange. He generalised the results of Kummer on diagonalising symmetric matrices, using determinants and Sturm functions. He was also an editor of ''Crelle's Journal'' from 1856 to 1880, during which time it was known as ''Borchardt's Journal''. He died in Rüdersdorf, Germany. His grave is preserved in the Protestant ''Friedhof III der Jerusalems- und Neuen Kirchengemeinde'' (Cemetery No. III of the congregatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eduard Heine
Heinrich Eduard Heine (16 March 1821 – 21 October 1881) was a German mathematician. Heine became known for results on special functions and in real analysis. In particular, he authored an important treatise on spherical harmonics and Legendre functions (''Handbuch der Kugelfunctionen''). He also investigated basic hypergeometric series. He introduced the Mehler–Heine formula. Biography Heinrich Eduard Heine was born on 16 March 1821 in Berlin, as the eighth child of banker Karl Heine and his wife Henriette Märtens. Eduard was initially home schooled, then studied at the Friedrichswerdersche Gymnasium and Köllnische Gymnasium in Berlin. In 1838, after graduating from gymnasium, he enrolled at the University of Berlin, but transferred to the University of Göttingen to attend the mathematics lectures of Carl Friedrich Gauss and Moritz Stern. In 1840 Heine returned to Berlin, where he studied mathematics under Peter Gustav Lejeune Dirichlet, while also attending cla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rheinische Friedrich-Wilhelms-Universität Bonn
The University of Bonn, officially the Rhenish Friedrich Wilhelm University of Bonn (), is a public research university in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the () on 18 October 1818 by Frederick William III, as the linear successor of the () which was founded in 1777. The University of Bonn offers many undergraduate and graduate programs in a range of subjects and has 544 professors. The University of Bonn is a member of the U15 (German universities), German U15 association of major research-intensive universities in Germany and has the title of "University of Excellence" under the German Universities Excellence Initiative. Bonn has 6 Clusters of Excellence, the most of any German university; the Hausdorff Center for Mathematics, the Matter and Light for Quantum Computing cluster, Bonn Center for Dependency and Slavery Studies, PhenoRob: Research for the Future of Crop Production, the Immune Sensory System cluster, and ECONtribute: M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ludwig Schläfli
Ludwig Schläfli (; 15 January 1814 – 20 March 1895) was a Swiss mathematician, specialising in geometry and complex analysis (at the time called function theory) who was one of the key figures in developing the notion of higher-dimensional spaces. Early life and education Schläfli spent most of his life in Switzerland. He was born in Grasswil (now part of Seeberg), his mother's hometown, and moved to nearby Burgdorf as a child. His clumsiness soon showed that he would not follow his father into tradework. Instead, he entered the gymnasium in Bern in 1829, at age 15, already deep into study of mathematics by way of a calculus text, Abraham Gotthelf Kästner's ''Mathematische Anfangsgründe der Analysis des Unendlichen''. In 1831 he entered the Akademie in Bern to study theology. By 1834 the Akademie had become the new Universität Bern, and he continued there as a student. He graduated in 1836. Career and later life Schläfli became a schoolteacher in Thun, where he worke ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
