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Otto Hölder
Ludwig Otto Hölder (December 22, 1859 – August 29, 1937) was a German mathematician born in Stuttgart. Early life and education Hölder was the youngest of three sons of professor Otto Hölder (1811–1890), and a grandson of professor Christian Gottlieb Hölder (1776–1847); his two brothers also became professors. He first studied at the ''Polytechnikum'' (which today is the University of Stuttgart) and then in 1877 went to Berlin where he was a student of Leopold Kronecker, Karl Weierstrass, and Ernst Kummer. In 1877, he entered the University of Berlin and took his doctorate from the University of Tübingen in 1882. The title of his doctoral thesis was "Beiträge zur Potentialtheorie" ("Contributions to potential theory"). Following this, he went to the University of Leipzig but was unable to habilitate there, instead earning a second doctorate and habilitation at the University of Göttingen, both in 1884. Academic career and later life He was unable to get government ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stuttgart
Stuttgart (; ; Swabian German, Swabian: ; Alemannic German, Alemannic: ; Italian language, Italian: ; ) is the capital city, capital and List of cities in Baden-Württemberg by population, largest city of the States of Germany, German state of Baden-Württemberg. It is located on the Neckar river in a fertile valley known as the ''Stuttgarter Kessel'' (Stuttgart Cauldron) and lies an hour from the Swabian Jura and the Black Forest. Stuttgart has a population of 632,865 as of 2022, making it the list of cities in Germany by population, sixth largest city in Germany, while over 2.8 million people live in the city's administrative region and nearly 5.5 million people in Stuttgart Metropolitan Region, its metropolitan area, making it the metropolitan regions in Germany, fourth largest metropolitan area in Germany. The city and metropolitan area are consistently ranked among the List of EU metropolitan regions by GDP#2021 ranking of top four German metropolitan regions, top 5 Europea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hölder Summation
In mathematics, Hölder summation is a method for summing divergent series introduced by . Definition Given a series : a_1+a_2+\cdots, define :H^0_n=a_1+a_2+\cdots+a_n :H^_n=\frac If the limit :\lim_H^k_n exists for some ''k'', this is called the Hölder sum, or the (''H'',''k'') sum, of the series. Particularly, since the Cesàro sum of a convergent series always exists, the Hölder sum of a series (that is Hölder summable) can be written in the following form: :\lim_H^k_n See also *Cesàro summation In mathematical analysis, Cesàro summation (also known as the Cesàro mean or Cesàro limit) assigns values to some Series (mathematics), infinite sums that are Divergent series, not necessarily convergent in the usual sense. The Cesàro sum ... References * * Summability methods {{analysis-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aurel Wintner
Aurel Friedrich Wintner (8 April 1903 – 15 January 1958) was a mathematician noted for his research in mathematical analysis, number theory, differential equations and probability theory. He was one of the founders of probabilistic number theory. He received his Ph.D. from the University of Leipzig in 1928 under the guidance of Leon Lichtenstein. He taught at Johns Hopkins University. He was a nephew of the astronomer Samuel Oppenheim, and the son-in-law of mathematician Otto Hölder. Works * Spektraltheorie der unendlichen Matrizen', 1929 * ''The Analytical Foundations of Celestial Mechanics'', 1941 (reprinted in 2014 by Dover) * Eratosthenian Averages', 1943 * The Theory of Measure in Arithmetical Semi-Groups', 1944 * An Arithmetical Approach to Ordinary Fourier Series', 1945 * The Fourier Transforms of Probability Distributions', 1947 References External links * * Spektraltheorie Der Unendlichen Matrizenat the Internet Archive The Internet Archive is an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sophus Lie
Marius Sophus Lie ( ; ; 17 December 1842 – 18 February 1899) was a Norwegian mathematician. He largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations. He also made substantial contributions to the development of algebra. Life and career Marius Sophus Lie was born on 17 December 1842 in the small town of Nordfjordeid. He was the youngest of six children born to Lutheran pastor Johann Herman Lie and his wife, who came from a well-known Trondheim family. He had his primary education in the south-eastern coast of Moss, before attending high school in Oslo (known then as Christiania). After graduating from high school, his ambition towards a military career was dashed when the army rejected him due to poor eyesight. He then enrolled at the University of Christiania. Sophus Lie's first mathematical work, ''Repräsentation der Imaginären der Plangeometrie'', was published in 1869 by the Academy of Sciences in Chris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Habilitation
Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excellence in research, teaching, and further education, which usually includes a dissertation. The degree, sometimes abbreviated ''Dr. habil''. (), ''dr hab.'' (), or ''D.Sc.'' ('' Doctor of Sciences'' in Russia and some CIS countries), is often a qualification for full professorship in those countries. In German-speaking countries it allows the degree holder to bear the title ''PD'' (for ). In a number of countries there exists an academic post of docent, appointment to which often requires such a qualification. The degree conferral is usually accompanied by a public oral defence event (a lecture or a colloquium) with one or more opponents. Habilitation is usually awarded 5–15 years after a PhD degree or its equivalent. Achieving this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potential Theory
In mathematics and mathematical physics, potential theory is the study of harmonic functions. The term "potential theory" was coined in 19th-century physics when it was realized that the two fundamental forces of nature known at the time, namely gravity and the electrostatic force, could be modeled using functions called the gravitational potential and electrostatic potential, both of which satisfy Poisson's equation—or in the vacuum, Laplace's equation. There is considerable overlap between potential theory and the theory of Poisson's equation to the extent that it is impossible to draw a distinction between these two fields. The difference is more one of emphasis than subject matter and rests on the following distinction: potential theory focuses on the properties of the functions as opposed to the properties of the equation. For example, a result about the Mathematical singularity, singularities of harmonic functions would be said to belong to potential theory whilst a result ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ernst Kummer
Ernst Eduard Kummer (29 January 1810 – 14 May 1893) was a German mathematician. Skilled in applied mathematics, Kummer trained German army officers in ballistics; afterwards, he taught for 10 years in a '' gymnasium'', the German equivalent of high school, where he inspired the mathematical career of Leopold Kronecker. Life Kummer was born in Sorau, Brandenburg (then part of Prussia). He was awarded a PhD from the University of Halle in 1831 for writing a prize-winning mathematical essay (''De cosinuum et sinuum potestatibus secundum cosinus et sinus arcuum multiplicium evolvendis''), which was published a year later. In 1840, Kummer married Ottilie Mendelssohn, daughter of Nathan Mendelssohn and Henriette Itzig. Ottilie was a cousin of Felix Mendelssohn and his sister Rebecca Mendelssohn Bartholdy, the wife of the mathematician Peter Gustav Lejeune Dirichlet. His second wife (whom he married soon after the death of Ottilie in 1848), Bertha Cauer, was a maternal cousin of Ottil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Weierstrass
Karl Theodor Wilhelm Weierstrass (; ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the " father of modern analysis". Despite leaving university without a degree, he studied mathematics and trained as a school teacher, eventually teaching mathematics, physics, botany and gymnastics. He later received an honorary doctorate and became professor of mathematics in Berlin. Among many other contributions, Weierstrass formalized the definition of the continuity of a function and complex analysis, proved the intermediate value theorem and the Bolzano–Weierstrass theorem, and used the latter to study the properties of continuous functions on closed bounded intervals. Biography Weierstrass was born into a Roman Catholic family in Ostenfelde, a village near Ennigerloh, in the Province of Westphalia. Karl Weierstrass was the son of Wilhelm Weierstrass and Theodora Vonderforst, the former of whom was a government official and both of whom were Cat ... [...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] |
Berlin
Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population within city limits, highest population within its city limits of any city in the European Union. The city is also one of the states of Germany, being the List of German states by area, third smallest state in the country by area. Berlin is surrounded by the state of Brandenburg, and Brandenburg's capital Potsdam is nearby. The urban area of Berlin has a population of over 4.6 million and is therefore the most populous urban area in Germany. The Berlin/Brandenburg Metropolitan Region, Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's second-largest metropolitan region after the Rhine-Ruhr region, as well as the List of EU metropolitan areas by GDP, fifth-biggest metropolitan region by GDP in the European Union. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ernst Hölder
Ernst Otto Hölder (2 April 1901 in Leipzig – 30 June 1990 in Mainz) was a German mathematician who made contributions to partial differential equations and continuum mechanics. Education and career Hölder was born in Leipzig and studied at the University of Leipzig, where he earned his PhD in 1926 with a dissertation on fluid dynamics. Afterwards, he worked as an assistant at the University of Leipzig and passed the First State Examination in 1926. In 1929 he earned his habilitation, also at the University of Leipzig, with a topic on celestial mechanics. From 1929 to 1939, he worked as a privatdozent at the University of Leipzig, and from 1939 to 1945, he was a scientific member at the German Aeronautical Research Institute in Braunschweig. After World War II, Hölder held various academic positions at the University of Leipzig, including as an extraordinary professor, head of the Mathematical Institute, and dean of the Philosophical Faculty II. In 1958, he left Leipzig and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
