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Édouard Goursat
Édouard Jean-Baptiste Goursat (21 May 1858 – 25 November 1936) was a French mathematician, now remembered principally as an expositor for his ''Cours d'analyse mathématique'', which appeared in the first decade of the twentieth century. It set a standard for the high-level teaching of mathematical analysis, especially complex analysis. This text was reviewed by William Fogg Osgood for the Bulletin of the American Mathematical Society. This led to its translation into English by Earle Raymond Hedrick published by Ginn and Company. Goursat also published texts on partial differential equations and hypergeometric series. Life Edouard Goursat was born in Lanzac, Lot. He was a graduate of the École Normale Supérieure, where he later taught and developed his ''Cours''. At that time the topological foundations of complex analysis were still not clarified, with the Jordan curve theorem considered a challenge to mathematical rigour (as it would remain until L. E. J. Brouwer took in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lanzac
Lanzac () is a commune in the Lot department in south-western France. See also *Communes of the Lot department The following is a list of the 313 communes of the Lot department of France France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and ... References Communes of Lot (department) {{Lot-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...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 Dannenb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arthur Cayley
Arthur Cayley (; 16 August 1821 – 26 January 1895) was a prolific United Kingdom of Great Britain and Ireland, British mathematician who worked mostly on algebra. He helped found the modern British school of pure mathematics. As a child, Cayley enjoyed solving complex maths problems for amusement. He entered Trinity College, Cambridge, where he excelled in Greek language, Greek, French language, French, German language, German, and Italian language, Italian, as well as mathematics. He worked as a lawyer for 14 years. He postulated the Cayley–Hamilton theorem—that every square matrix is a root of its own characteristic polynomial, and verified it for matrices of order 2 and 3. He was the first to define the concept of a group (mathematics), group in the modern way—as a set with a Binary function, binary operation satisfying certain laws. Formerly, when mathematicians spoke of "groups", they had meant permutation groups. Cayley tables and Cayley graphs as well as Cayle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
August Ferdinand Möbius
August Ferdinand M̦bius (, ; ; 17 November 1790 Р26 September 1868) was a German mathematician and theoretical astronomer. Early life and education M̦bius was born in Schulpforta, Electorate of Saxony, and was descended on his mother's side from religious reformer Martin Luther. He was home-schooled until he was 13, when he attended the college in Schulpforta in 1803, and studied there, graduating in 1809. He then enrolled at the University of Leipzig, where he studied astronomy under the mathematician and astronomer Karl Mollweide.August Ferdinand M̦bius, The MacTutor History of Mathematics archive History.mcs.st-andrews.ac.uk. Retrieved on 2017-04-26. In 1813, he began to study astronomy under mathematician |
Cauchy–Goursat Theorem
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat), is an important statement about line integrals for holomorphic functions in the complex plane. Essentially, it says that if f(z) is holomorphic in a simply connected domain Ω, then for any simply closed contour C in Ω, that contour integral is zero. \int_C f(z)\,dz = 0. Statement Fundamental theorem for complex line integrals If is a holomorphic function on an open region , and \gamma is a curve in from z_0 to z_1 then, \int_f'(z) \, dz = f(z_1)-f(z_0). Also, when has a single-valued antiderivative in an open region , then the path integral \int_f'(z) \, dz is path independent for all paths in . Formulation on simply connected regions Let U \subseteq \Complex be a simply connected open set, and let f: U \to \Complex be a holomorphic function. Let \gamma: ,b\to U be a smooth closed curve. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy Integral Theorem
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat), is an important statement about line integrals for holomorphic functions in the complex plane. Essentially, it says that if f(z) is holomorphic in a simply connected domain Ω, then for any simply closed contour C in Ω, that contour integral is zero. \int_C f(z)\,dz = 0. Statement Fundamental theorem for complex line integrals If is a holomorphic function on an open region , and \gamma is a curve in from z_0 to z_1 then, \int_f'(z) \, dz = f(z_1)-f(z_0). Also, when has a single-valued antiderivative in an open region , then the path integral \int_f'(z) \, dz is path independent for all paths in . Formulation on simply connected regions Let U \subseteq \Complex be a simply connected open set, and let f: U \to \Complex be a holomorphic function. Let \gamma: ,b\to U be a smooth closed curve. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Topology
In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes. After the proof of the simplicial approximation theorem this approach provided rigour. The change of name reflected the move to organise topological classes such as cycles-modulo-boundaries explicitly into abelian groups. This point of view is often attributed to Emmy Noether, and so the change of title may reflect her influence. The transition is also attributed to the work of Heinz Hopf, who was influenced by Noether, and to Leopold Vietoris and Walther Mayer, who independently defined homology. A fairly precise date can be supplied in the internal notes of the Bourbaki group. While topology was still ''combinatorial'' in 1942, it had become ''algebraic'' by 1944. This corresponds also to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Rigour
Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness. These constraints may be environmentally imposed, such as "the rigours of famine"; logically imposed, such as mathematical proofs which must maintain consistent answers; or socially imposed, such as the process of defining ethics and law. Etymology "Rigour" comes to English through old French (13th c., Modern French '' rigueur'') meaning "stiffness", which itself is based on the Latin ''rigorem'' (nominative ''rigor'') "numbness, stiffness, hardness, firmness; roughness, rudeness", from the verb ''rigere'' "to be stiff". The noun was frequently used to describe a condition of strictness or stiffness, which arises from a situation or constraint either chosen or experienced passively. For example, the title of the book ''Theologia Moralis Inter Rigorem et Laxitatem Medi'' roughly translates as "mediating theological morality between rigour and lax ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jordan Curve Theorem
In topology, the Jordan curve theorem asserts that every ''Jordan curve'' (a plane simple closed curve) divides the plane into an " interior" region bounded by the curve and an "exterior" region containing all of the nearby and far away exterior points. Every continuous path connecting a point of one region to a point of the other intersects with the curve somewhere. While the theorem seems intuitively obvious, it takes some ingenuity to prove it by elementary means. ''"Although the JCT is one of the best known topological theorems, there are many, even among professional mathematicians, who have never read a proof of it."'' (). More transparent proofs rely on the mathematical machinery of algebraic topology, and these lead to generalizations to higher-dimensional spaces. The Jordan curve theorem is named after the mathematician Camille Jordan (1838–1922), who found its first proof. For decades, mathematicians generally thought that this proof was flawed and that the first rigo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a ''topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. Basic examples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; connecte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
