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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 (now in Poland). His parents were Siegmund Courant and Martha Freund of Oels. Edith Stein was Richard's cousin on the maternal 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's assista ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lubliniec
Lubliniec (, ; Silesian language, Silesian: ''Lublini'c'') is a town in southern Poland with 23,784 inhabitants (2019). It is the capital of Lubliniec County, part of Silesian Voivodeship. 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 industry, 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 Silesian Piasts, Piast duke Władysław Opolski, 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 Kingdom of Poland (1025� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Keller
Joseph Bishop Keller (July 31, 1923 – September 7, 2016) was an American mathematician who specialized in applied mathematics. He was best known for his work on the "geometrical theory of diffraction" (GTD). Early life and education Born in Paterson, New Jersey on July 31, 1923, Keller attended Eastside High School, where he was a member of the math team. After earning his undergraduate degree in 1943 at New York University, Keller obtained his PhD in 1948 from NYU under the supervision of Richard Courant. He was a professor of mathematics in the Courant Institute at New York University until 1979. Then he was Professor of Mathematics and Mechanical Engineering at Stanford University until 1993, when he became professor emeritus. Research Keller worked on the application of mathematics to problems in science and engineering, such as wave propagation. He contributed to the Einstein–Brillouin–Keller method for computing eigenvalues in quantum mechanical systems. Awar ... [...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?''. 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 undergraduate, Robbins attended Harvard University, where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
What Is Mathematics?
''What Is Mathematics?'' is the title of a classic book by Richard Courant and Herbert Robbins, published by Oxford University Press. Written in the belief that "the traditional place of mathematics in education is in grave danger," it is an introduction to mathematics, intended to offer "vantage points from which the substance and driving forces of modern mathematics can be surveyed" both by students and by the general public. First published in 1941, it discusses number theory, geometry, topology, and calculus. A posthumous edition was published in 1996 with an additional chapter on recent progress in mathematics, written by Ian Stewart. Authorship The book was based on Courant's course material. Although Robbins assisted in writing a large part of the book, he had to fight for authorship. Courant alone held the copyright for the book. This resulted in Robbins receiving a smaller share of the royalties.Reid, Constance, Courant in Göttingen and New York. The story of an imp ... [...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] |
Methoden Der Mathematischen Physik
''Methoden der mathematischen Physik'' (translated into English with the title Methods of Mathematical Physics) is a 1924 book, in two volumes totalling around 1000 pages, published under the names of Richard Courant and David Hilbert. It was a comprehensive treatment of the "methods of mathematical physics" of the time. The second volume is devoted to the theory of partial differential equations. It contains presages of the finite element method, on which Courant would work subsequently, and which would eventually become basic to numerical analysis. The material of the book was worked up from the content of Hilbert's lectures. While Courant played the major editorial role, many at the University of Göttingen were involved in the writing-up, and in that sense it was a collective production. On its appearance in 1924 it apparently had little direct connection to the Quantum mechanics, quantum theory questions at the centre of the theoretical physics of the time. That changed withi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Courant–Friedrichs–Lewy Condition
In mathematics, the convergence condition by Courant–Friedrichs–Lewy (CFL) 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 upper bound, given a fixed spatial increment, in many explicit time-marching computer simulations; otherwise, the simulation produces incorrect or unstable 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, ... [...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'', weekly newspaper in Northumberland, England * '' The New-England Courant'', American newspaper, founded in Boston in 1721 * ''Hartford Courant'', newspaper in the United States, founded in 1764 * ''Leeuwarder Courant'', oldest newspaper in the Netherlands, founded in 1752 * Courant (surname) * Courant, Charente-Maritime, commune in France * Courant, in heraldry, signifying a running animal with all four paws raised, see Attitude (heraldry)#Courant * Courant Institute of Mathematical Sciences at New York University * Courant, an alternative spelling for the Baroque dance form courante * Courant–Friedrichs–Lewy condition (CFL condition) in mathematics * 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 ... (1888–1972), G ... [...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 N ... [...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 fe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hans Lewy
Hans Lewy (20 October 1904 – 23 August 1988) was an American mathematician, known for his work on partial differential equations and on the theory of functions of several complex variables. Life Lewy was born to a Jewish family in Breslau, Silesia, on October 20, 1904. He began his studies at the University of Göttingen in 1922, after being advised to avoid the more local University of Breslau because it was too old-fashioned,. supporting himself during the Weimar hyperinflation by a side job doing railroad track maintenance. At Göttingen, he studied both mathematics and physics; his teachers there included Max Born, Richard Courant, James Franck, David Hilbert, Edmund Landau, Emmy Noether, and Alexander Ostrowski. He earned his doctorate in 1926, at which time he and his friend Kurt Otto Friedrichs both became assistants to Courant and privatdozents at Göttingen. The famous Courant-Friedrichs-Lewy condition originated from that time in 1928.. At the recommendatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
