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Max Noether
Max Noether (24 September 1844 – 13 December 1921) was a German mathematician who worked on algebraic geometry and the theory of algebraic functions. He has been called "one of the finest mathematicians of the nineteenth century". He was the father of Emmy Noether. Biography Max Noether was born in Mannheim in 1844, to a Jewish family of wealthy wholesale hardware dealers. His grandfather, Elias Samuel, had started the business in Bruchsal in 1797. In 1809 the Grand Duchy of Baden established a "Tolerance Edict", which assigned a hereditary surname to the male head of every Jewish family which did not already possess one. Thus the Samuels became the Noether family, and as part of this Christianization of names, their son Hertz (Max's father) became Hermann. Max was the third of five children Hermann had with his wife Amalia Würzburger. At 14, Max contracted polio and was afflicted by its effects for the rest of his life. Through self-study, he learned advanced mathematics a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mannheim, Baden
Mannheim (; Palatine German: or ), officially the University City of Mannheim (german: Universitätsstadt Mannheim), is the second-largest city in the German state of Baden-Württemberg after the state capital of Stuttgart, and Germany's 21st-largest city, with a 2020 population of 309,119 inhabitants. The city is the cultural and economic centre of the Rhine-Neckar Metropolitan Region, Germany's seventh-largest metropolitan region with nearly 2.4 million inhabitants and over 900,000 employees. Mannheim is located at the confluence of the Rhine and the Neckar in the Kurpfalz ( Electoral Palatinate) region of northwestern Baden-Württemberg. The city lies in the Upper Rhine Plain, Germany's warmest region. Together with Hamburg, Mannheim is the only city bordering two other federal states. It forms a continuous conurbation of around 480,000 inhabitants with Ludwigshafen am Rhein in the neighbouring state of Rhineland-Palatinate, on the other side of the Rhine. Some northern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jewish Family
Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The people of the Kingdom of Israel and the ethnic and religious group known as the Jewish people that descended from them have been subjected to a number of forced migrations in their history" and Hebrews of historical Israel and Judah. Jewish ethnicity, nationhood, and religion are strongly interrelated, "Historically, the religious and ethnic dimensions of Jewish identity have been closely interwoven. In fact, so closely bound are they, that the traditional Jewish lexicon hardly distinguishes between the two concepts. Jewish religious practice, by definition, was observed exclusively by the Jewish people, and notions of Jewish peoplehood, nation, and community were suffused with faith in the Jewish God, the practice of Jewish (religious) la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Space
In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet ''at infinity''. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in such a way that there is one point at infinity of each direction of parallel lines. This definition of a projective space has the disadvantage of not being isotropic, having two different sorts of points, which must be considered separately in proofs. Therefore, other definitions are generally preferred. There are two classes of definitions. In synthetic geometry, ''point'' and ''line'' are primitive entities that are related by the incidence relation "a point is on a line" or "a line passes through a point", which is subject to the axioms of projective geometry. For some such set of axioms, the projective spaces that are defined have been shown to be equivalent to those resulting from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Curve
In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane curve can be completed in a projective algebraic plane curve by homogenizing its defining polynomial. Conversely, a projective algebraic plane curve of homogeneous equation can be restricted to the affine algebraic plane curve of equation . These two operations are each inverse to the other; therefore, the phrase algebraic plane curve is often used without specifying explicitly whether it is the affine or the projective case that is considered. More generally, an algebraic curve is an algebraic variety of dimension one. Equivalently, an algebraic curve is an algebraic variety that is birationally equivalent to an algebraic plane curve. If the curve is contained in an affine space or a projective space, one can take a projection for s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brill–Noether Theory
In algebraic geometry, Brill–Noether theory, introduced by , is the study of special divisors, certain divisors on a curve that determine more compatible functions than would be predicted. In classical language, special divisors move on the curve in a "larger than expected" linear system of divisors. Throughout, we consider a projective smooth curve over the complex numbers (or over some other algebraically closed field). The condition to be a special divisor can be formulated in sheaf cohomology terms, as the non-vanishing of the cohomology of the sheaf of sections of the invertible sheaf or line bundle associated to . This means that, by the Riemann–Roch theorem, the cohomology or space of holomorphic sections is larger than expected. Alternatively, by Serre duality, the condition is that there exist holomorphic differentials with divisor on the curve. Main theorems of Brill–Noether theory For a given genus , the moduli space for curves of genus should conta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann Surface
In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite different. For example, they can look like a sphere or a torus or several sheets glued together. The main interest in Riemann surfaces is that holomorphic functions may be defined between them. Riemann surfaces are nowadays considered the natural setting for studying the global behavior of these functions, especially multi-valued functions such as the square root and other algebraic functions, or the logarithm. Every Riemann surface is a two-dimensional real analytic manifold (i.e., a surface), but it contains more structure (specifically a complex structure) which is needed for the unambiguous def ... [...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] |
Alexander Von Brill
Alexander Wilhelm von Brill (20 September 1842 – 18 June 1935) was a German mathematician. Born in Darmstadt, Hesse, Brill was educated at the University of Giessen, where he earned his doctorate under supervision of Alfred Clebsch. He held a chair at the University of Tübingen, where Max Planck was among his students. In 1933, he joined the National Socialist Teachers League as one of the first members from Tübingen. The London Science Museum contains sliceform objects prepared by Brill and Felix Kleinbr> Selected publications''Vorlesungen über ebene algebraische Kurven und Funktionen.'' 1925.*''Vorlesungen über allgemeine Mechanik.'' 1928. *''Vorlesungen zur Einführung in die Mechanik raumerfüllender Massen.'' 1909. *''Graphische Darstellungen aus der reinen und angewandten Mathematik.'' 1894. *with Max Noether''Über algebraische Funktionen und ihre Anwendung in der Geometrie.'' Mitt. Göttinger Akad.1873 and their article with the same name in the Mathematischen Ann ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fritz Noether
Fritz Alexander Ernst Noether (7 October 1884 – 10 September 1941) was a Jewish German mathematician who emigrated from Nazi Germany to the Soviet Union. He was later executed by the NKVD. Biography Fritz Noether's father Max Noether was a mathematician and professor in Erlangen. The notable mathematician Emmy Noether was his elder sister. He had two sons, Herman D. Noether and Gottfried E. Noether. His eldest son Herman was a chemist. Gottfried was an American statistician and educator, and wrote a brief biography of his father. Fritz Noether was also an able mathematician. Not allowed to work in Nazi Germany for being a Jew, he moved to the Soviet Union, where he was appointed to a professorship at the Tomsk State University. In November 1937, during the Great Purge, he was arrested at his home in Tomsk by the NKVD. On 23 October 1938, Noether was sentenced to 25 years of imprisonment on charges of espionage and sabotage. He served time in different pris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during a reaction with other substances. Chemistry also addresses the nature of chemical bonds in chemical compounds. In the scope of its subject, chemistry occupies an intermediate position between physics and biology. It is sometimes called the central science because it provides a foundation for understanding both basic and applied scientific disciplines at a fundamental level. For example, chemistry explains aspects of plant growth ( botany), the formation of igneous rocks ( geology), how atmospheric ozone is formed and how environmental pollutants are degraded ( ecology), the properties of the soil on the moon ( cosmochemistry), how medications work (pharmacology), and how to collect DNA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''abstract algebra'' was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called the '' variety of groups''. History Before the nineteenth century, alge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Autodidacticism
Autodidacticism (also autodidactism) or self-education (also self-learning and self-teaching) is education without the guidance of masters (such as teachers and professors) or institutions (such as schools). Generally, autodidacts are individuals who choose the subject they will study, their studying material, and the studying rhythm and time. Autodidacts may or may not have formal education, and their study may be either a complement or an alternative to formal education. Many notable contributions have been made by autodidacts. Etymology The term has its roots in the Ancient Greek words (, ) and (, ). The related term '' didacticism'' defines an artistic philosophy of education. Terminology Various terms are used to describe self-education. One such is heutagogy, coined in 2000 by Stewart Hase and Chris Kenyon of Southern Cross University in Australia; others are ''self-directed learning'' and ''self-determined learning''. In the heutagogy paradigm, a learner shou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
