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Richard Courant
Richard Courant (January 8, 1888 – January 27, 1972) was a German American mathematician. He is best known by the general public for the book '' What is Mathematics?'', co-written with Herbert Robbins. His research focused on the areas of real analysis, mathematical physics, the calculus of variations and partial differential equations. He wrote textbooks widely used by generations of students of physics and mathematics. He is also known for founding the institute now bearing his name. Life and career Courant was born in Lublinitz, in the Prussian Province of Silesia. His parents were Siegmund Courant and Martha Courant ''née'' Freund of Oels. Edith Stein was Richard's cousin on the paternal side. During his youth his parents moved often, including to Glatz, then to Breslau and in 1905 to Berlin. He stayed in Breslau and entered the university there, then continued his studies at the University of Zürich and the University of Göttingen. He became David Hilbert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lubliniec
Lubliniec (german: Lublinitz) is a town in southern Poland with 23,784 inhabitants (2019). It is the capital of Lubliniec County, part of Silesian Voivodeship (since 1999); previously it was in Częstochowa Voivodeship (1975–1998). Geography Lubliniec is situated in the north of the historic Upper Silesia region at the rim of the Upper Silesian Industrial Region, about northwest of Katowice. It is an important rail hub, with two major lines crossing there – east-west (from Częstochowa to Opole) and south–north (from Katowice to Poznań) – and a site of light and chemical industry. The surrounding area is characterized by extended forests (''Lasy Lublinieckie''), including the Upper Liswarta Forests Landscape Park north of the town. History Lubliniec was established about 1270 by the Piast duke Władysław of Opole on the road leading from his residence Opole to Kraków. It was part of the Duchy of Opole within fragmented Piast-ruled Poland. According to o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edgar Krahn
Edgar Krahn ( – 6 March 1961) was an Estonian mathematician. Krahn was born in Sootaga (now Laiuse, Jõgeva County), Governorate of Livonia, as a member of the Baltic German minority. He died in Rockville, Maryland, United States. Krahn studied at the University of Tartu and the University of Göttingen. He graduated at Tartu in 1918, received his doctoral degree at Göttingen in 1926, with Richard Courant as his advisor, and his habilitation took place at Tartu in 1928. He is co-author of the Rayleigh–Faber–Krahn inequality. Krahn worked in Estonia, Germany, the United Kingdom, and the United States in the following areas of pure and applied mathematics: * Differential geometry * Differential equations * ''Bausparmathematik'', which is distantly related to insurance mathematics * Probability theory * Gas dynamics Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Analysis
In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include convergence, limits, continuity, smoothness, differentiability and integrability. Real analysis is distinguished from complex analysis, which deals with the study of complex numbers and their functions. Scope Construction of the real numbers The theorems of real analysis rely on the properties of the real number system, which must be established. The real number system consists of an uncountable set (\mathbb), together with two binary operations denoted and , and an order denoted . The operations make the real numbers a field, and, along with the order, an ordered field. The real number system is the unique ''complete ordered field'', in the sense that any other complete ordered field is isomorphic to it. Intuitively, completeness ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herbert Robbins
Herbert Ellis Robbins (January 12, 1915 – February 12, 2001) was an American mathematician and statistician. He did research in topology, measure theory, statistics, and a variety of other fields. He was the co-author, with Richard Courant, of '' What is Mathematics?'', a popularization that is still () in print. The Robbins lemma, used in empirical Bayes methods, is named after him. Robbins algebras are named after him because of a conjecture (since proved) that he posed concerning Boolean algebras. The Robbins theorem, in graph theory, is also named after him, as is the Whitney–Robbins synthesis, a tool he introduced to prove this theorem. The well-known unsolved problem of minimizing in sequential selection the expected rank of the selected item under full information, sometimes referred to as the fourth secretary problem, also bears his name: Robbins' problem (of optimal stopping). Biography Robbins was born in New Castle, Pennsylvania. As an undergrad ... [...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, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); 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' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) 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 mathematician recorded by history was Hyp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German American
German Americans (german: Deutschamerikaner, ) are Americans who have full or partial German ancestry. With an estimated size of approximately 43 million in 2019, German Americans are the largest of the self-reported ancestry groups by the United States Census Bureau in its American Community Survey. German Americans account for about one third of the total population of people of German ancestry in the world. Very few of the German states had colonies in the new world. In the 1670s, the first significant groups of German immigrants arrived in the British colonies, settling primarily in Pennsylvania, New York and Virginia. The Mississippi Company of France moved thousands of Germans from Europe to Louisiana and to the German Coast, Orleans Territory between 1718 and 1750. Immigration ramped up sharply during the 19th century. There is a "German belt" that extends all the way across the United States, from eastern Pennsylvania to the Oregon coast. Pennsylvania, with 3.5 mill ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Courant–Friedrichs–Lewy Condition
In mathematics, the convergence condition by Courant–Friedrichs–Lewy is a necessary condition for convergence while solving certain partial differential equations (usually hyperbolic PDEs) numerically. It arises in the numerical analysis of explicit time integration schemes, when these are used for the numerical solution. As a consequence, the time step must be less than a certain time in many explicit time-marching computer simulations, otherwise the simulation produces incorrect results. The condition is named after Richard Courant, Kurt Friedrichs, and Hans Lewy who described it in their 1928 paper. Heuristic description The principle behind the condition is that, for example, if a wave is moving across a discrete spatial grid and we want to compute its amplitude at discrete time steps of equal duration, then this duration must be less than the time for the wave to travel to adjacent grid points. As a corollary, when the grid point separation is reduced, the upper limit for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Courant Minimax Principle
In mathematics, the Courant minimax principle gives the eigenvalues of a real symmetric matrix. It is named after Richard Courant. Introduction The Courant minimax principle gives a condition for finding the eigenvalues for a real symmetric matrix. The Courant minimax principle is as follows: For any real symmetric matrix ''A'', : \lambda_k=\min\limits_C\max\limits_\langle Ax,x\rangle, where C is any (k-1)\times n matrix. Notice that the vector ''x'' is an eigenvector to the corresponding eigenvalue ''λ''. The Courant minimax principle is a result of the maximum theorem, which says that for q(x)=\langle Ax,x\rangle, ''A'' being a real symmetric matrix, the largest eigenvalue is given by \lambda_1 = \max_ q(x) = q(x_1), where x_1 is the corresponding eigenvector. Also (in the maximum theorem) subsequent eigenvalues \lambda_k and eigenvectors x_k are found by induction and orthogonal to each other; therefore, \lambda_k =\max q(x_k) with \langle x_j, x_k \rangle = 0, \ j [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Courant Number
Courant may refer to: * ''Hexham Courant'', a weekly newspaper in Northumberland, England * '' The New-England Courant'', an American newspaper, founded in Boston in 1721 * ''Hartford Courant'', a newspaper in the United States, founded in 1764 * Courant (surname) * Courant, Charente-Maritime, a commune in France *Courant, in heraldry, signifying a running animal with all four paws raised - see Attitude (heraldry)#Courant * The Courant Institute of Mathematical Sciences at New York University * Courant, an alternative spelling for the Baroque dance form, courante * The Courant–Friedrichs–Lewy condition (CFL condition) in mathematics * Richard Courant, German 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, structure, space, models, and change. History On ... See also * Corante {{disambiguation ru:Курант< ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Franz Rellich
Franz Rellich (September 14, 1906 – September 25, 1955) was an Austrian-German mathematician. He made important contributions in mathematical physics, in particular for the foundations of quantum mechanics and for the theory of partial differential equations. The Rellich–Kondrachov theorem is named after him. Biography Rellich was born in Tramin, then in the County of Tyrol. He studied from 1924 to 1929 at the universities of Graz and Göttingen and received his doctor's degree in 1929 under Richard Courant at Georg August University of Göttingen with the thesis about ''"Verallgemeinerung der Riemannschen Integrationsmethode auf Differentialgleichungen n-ter Ordnung in zwei Veränderlichen" ("Generalization of Riemann's integration method on differential equations of ''n''-th order in two variables"). When in 1933 the great mathematical-physical tradition in Göttingen terminated with the ''Machtergreifung'' of the Nazis, Rellich, having taken an active position against Na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Otto Neugebauer
Otto Eduard Neugebauer (May 26, 1899 – February 19, 1990) was an Austrian-American mathematician and historian of science who became known for his research on the history of astronomy and the other exact sciences as they were practiced in antiquity and the Middle Ages. By studying clay tablets, he discovered that the ancient Babylonians knew much more about mathematics and astronomy than had been previously realized. The National Academy of Sciences has called Neugebauer "the most original and productive scholar of the history of the exact sciences, perhaps of the history of science, of our age." Career Neugebauer was born in Innsbruck, Austria. His father Rudolph Neugebauer was a railroad construction engineer and a collector and scholar of Oriental carpets. His parents died when he was quite young. During World War I, Neugebauer enlisted in the Austrian Army and served as an artillery lieutenant on the Italian front and then in an Italian prisoner-of-war camp alongside fell ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
