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Laugwitz
Detlef Laugwitz (1932–2000) was a German mathematician and historian, who worked in differential geometry, history of mathematics, functional analysis, and non-standard analysis. Biography He was born on 11 May 1932 in Breslau, Germany. Starting in 1949, he studied mathematics, physics, and philosophy at the Georg-August-University at Göttingen, where he received his doctorate in 1954.''Differential geometry without the axiom of dimension'', Mathematische Zeitschrift Bd.61, 1954, p. 100 Until 1956 he worked in the Mathematical Research Institute of Oberwolfach. In 1958 he became a lecturer at the Technical University of Munich, where he obtained his Habilitation. In 1958 he moved to the Technical University of Darmstadt, where in 1962 he became a professor, and remained until his retirement. From 1976 to 1984 he was a visiting professor at Caltech. Work Laugwitz worked in differential geometry of infinite dimensional vector spaces (his dissertation) and in Finsler geometry. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Detlef Laugwitz
Detlef Laugwitz (1932–2000) was a German mathematician and historian, who worked in differential geometry, history of mathematics, functional analysis, and non-standard analysis. Biography He was born on 11 May 1932 in Breslau, Germany. Starting in 1949, he studied mathematics, physics, and philosophy at the Georg-August-University at Göttingen, where he received his doctorate in 1954.''Differential geometry without the axiom of dimension'', Mathematische Zeitschrift Bd.61, 1954, p. 100 Until 1956 he worked in the Mathematical Research Institute of Oberwolfach. In 1958 he became a lecturer at the Technical University of Munich, where he obtained his Habilitation. In 1958 he moved to the Technical University of Darmstadt, where in 1962 he became a professor, and remained until his retirement. From 1976 to 1984 he was a visiting professor at Caltech. Work Laugwitz worked in differential geometry of infinite dimensional vector spaces (his dissertation) and in Finsler geometry. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinitesimal
In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referred to the "infinity- th" item in a sequence. Infinitesimals do not exist in the standard real number system, but they do exist in other number systems, such as the surreal number system and the hyperreal number system, which can be thought of as the real numbers augmented with both infinitesimal and infinite quantities; the augmentations are the reciprocals of one another. Infinitesimal numbers were introduced in the development of calculus, in which the derivative was first conceived as a ratio of two infinitesimal quantities. This definition was not rigorously formalized. As calculus developed further, infinitesimals were replaced by limits, which can be calculated using the standard real numbers. Infinitesimals regained popu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-standard Analysis
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using epsilon–delta procedures rather than infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers. Nonstandard analysis originated in the early 1960s by the mathematician Abraham Robinson. He wrote: ... the idea of infinitely small or ''infinitesimal'' quantities seems to appeal naturally to our intuition. At any rate, the use of infinitesimals was widespread during the formative stages of the Differential and Integral Calculus. As for the objection ... that the distance between two distinct real numbers cannot be infinitely small, Gottfried Wilhelm Leibniz argued that the theory of infinitesimals implies the introduction of ideal numbers which might be infinitely small or infinit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernhard Riemann
Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician who made 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. Biography Early years Riemann was born on 17 September 1826 in Breselenz, a village near D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finsler Geometry
In mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold where a (possibly asymmetric) Minkowski functional is provided on each tangent space , that enables one to define the length of any smooth curve as :L(\gamma) = \int_a^b F\left(\gamma(t), \dot(t)\right)\,\mathrmt. Finsler manifolds are more general than Riemannian manifolds since the tangent norms need not be induced by inner products. Every Finsler manifold becomes an intrinsic quasimetric space when the distance between two points is defined as the infimum length of the curves that join them. named Finsler manifolds after Paul Finsler, who studied this geometry in his dissertation . Definition A Finsler manifold is a differentiable manifold together with a Finsler metric, which is a continuous nonnegative function defined on the tangent bundle so that for each point of , * for every two vectors tangent to at (subadditivity). * for all (but not necessarily fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1932 Births
Year 193 ( CXCIII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Sosius and Ericius (or, less frequently, year 946 ''Ab urbe condita''). The denomination 193 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * January 1 – Year of the Five Emperors: The Roman Senate chooses Publius Helvius Pertinax, against his will, to succeed the late Commodus as Emperor. Pertinax is forced to reorganize the handling of finances, which were wrecked under Commodus, to reestablish discipline in the Roman army, and to suspend the food programs established by Trajan, provoking the ire of the Praetorian Guard. * March 28 – Pertinax is assassinated by members of the Praetorian Guard, who storm the imperial palace. The Empire is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Staff Of The Technical University Of Munich
An academy ( Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary or tertiary higher learning (and generally also research or honorary membership). The name traces back to Plato's school of philosophy, founded approximately 385 BC at Akademia, a sanctuary of Athena, the goddess of wisdom and skill, north of Athens, Greece. Etymology The word comes from the ''Academy'' in ancient Greece, which derives from the Athenian hero, ''Akademos''. Outside the city walls of Athens, the gymnasium was made famous by Plato as a center of learning. The sacred space, dedicated to the goddess of wisdom, Athena, had formerly been an olive grove, hence the expression "the groves of Academe". In these gardens, the philosopher Plato conversed with followers. Plato developed his sessions into a method of teaching philosophy and in 387 BC, established what is known today as the Old Academy. By extension, ''academia'' has come to mean the accumulation, d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Technical University Of Munich Alumni
Technical may refer to: * Technical (vehicle), an improvised fighting vehicle * Technical analysis, a discipline for forecasting the future direction of prices through the study of past market data * Technical drawing, showing how something is constructed or functions (also known as drafting) * Technical file, set of technical drawings * Technical death metal, a subgenre of death metal that focuses on complex rhythms, riffs, and song structures * Technical foul, an infraction of the rules in basketball usually concerning unsportsmanlike non-contact behavior * Technical rehearsal for a performance, often simply referred to as a technical * Technical support, a range of services providing assistance with technology products * Vocational education Vocational education is education that prepares people to work as a technician or to take up employment in a skilled craft or trade as a tradesperson or artisan. Vocational Education can also be seen as that type of education gi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometers
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying structure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German Historians Of Mathematics
German(s) may refer to: * Germany (of or related to) **Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Germanic peoples (Roman times) * German language **any of the Germanic languages * German cuisine, traditional foods of Germany People * German (given name) * German (surname) * Germán, a Spanish name Places * German (parish), Isle of Man * German, Albania, or Gërmej * German, Bulgaria * German, Iran * German, North Macedonia * German, New York, U.S. * Agios Germanos, Greece Other uses * German (mythology), a South Slavic mythological being * Germans (band), a Canadian rock band * "German" (song), a 2019 song by No Money Enterprise * ''The German'', a 2008 short film * "The Germans", an episode of ''Fawlty Towers'' * ''The German'', a nickname for Congolese rebel André Kisase Ngandu See also * Germanic (other) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
