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Michio Kuga
was a mathematician who received his Ph.D. from University of Tokyo in 1960. His work helped lead to a proof of the Ramanujan conjecture which partly follows from the proof of the Weil conjectures by . In 1963–1964, he introduced Kuga fiber varieties in a book published by the University of Chicago Press. In the summer of 1965 he gave a talk on Kuga fiber varieties at the American Mathematical Society's Symposium in Pure Mathematics held at the University of Colorado Boulder. In 2019 Beijing's Higher Education Press published a reprint of Kuga's 1964 book. One of his books, ''Galois' Dream: Group Theory and Differential Equations'', is a series of lectures on group theory and differential equations for undergraduate students, considering such topics as covering spaces and Fuchsian differential equation In mathematics, in the theory of ordinary differential equations in the complex plane \Complex, the points of \Complex are classified into ''ordinary points'', at which th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Colorado Boulder
The University of Colorado Boulder (CU Boulder, CU, or Colorado) is a public research university in Boulder, Colorado. Founded in 1876, five months before Colorado became a state, it is the flagship university of the University of Colorado system. CU Boulder is a member of the Association of American Universities, a selective group of major research universities in North America, and is classified among R1: Doctoral Universities – Very high research activity. In 2021, the university attracted support of over $634 million for research and spent $536 million on research and development according to the National Science Foundation, ranking it 50th in the nation. The university consists of nine colleges and schools and offers over 150 academic programs, enrolling more than 35,000 students as of January 2022. To date, 5 Nobel Prize laureates, 10 Pulitzer Prize winners, 11 MacArthur "Genius Grant" recipients, 1 Turing Award laureate, and 20 astronauts have been affiliated with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stony Brook University Faculty
Stony may refer to: Places * Stony Brook (other) * Stony Creek (other) * Stony Lake (other) * Stony River (other) * Stony Island (other) * Stony Point (other) * Stony Mountain (Missouri) * Stony Down, a hill and an area of forested countryside in the county of Dorset, England * Stony Pass, a mountain pass in the San Juan Mountains of southwest Colorado Other uses * Stony (rapper) (born 1995), Icelandic actor and rapper * Stony Awards The Stony Awards (a.k.a. the Stonys) recognize and celebrate notable stoner films and :American television episodes about cannabis, television. The Stonys began as a feature in ''High Times'' magazine in 2000. Six ''High Times'' Stony Awards ceremo ..., also known as "the Stonys", recognizing the "highest and stoniest" movies and TV shows of the year * Stony Stratford, or "Stony", part of Milton Keynes See also * Stoney (other) * Stonys, a Lithuanian family name {{ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Tokyo Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Publications Mathématiques De L'IHÉS
''Publications Mathématiques de l'IHÉS'' is a peer-reviewed mathematical journal. It is published by Springer Science+Business Media on behalf of the Institut des Hautes Études Scientifiques, with the help of the Centre National de la Recherche Scientifique. The journal was established in 1959 and was published at irregular intervals, from one to five volumes a year. It is now biannual. The editor-in-chief is Claire Voisin (Collège de France). See also *''Annals of Mathematics'' *'' Journal of the American Mathematical Society'' *''Inventiones Mathematicae ''Inventiones Mathematicae'' is a mathematical journal published monthly by Springer Science+Business Media. It was established in 1966 and is regarded as one of the most prestigious mathematics journals in the world. The current managing editors ...'' External links * Back issues from 1959 to 2010 Mathematics journals Publications established in 1959 Springer Science+Business Media academic journals Biannual journal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galois Theory
In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to group theory, which makes them simpler and easier to understand. Galois introduced the subject for studying roots of polynomials. This allowed him to characterize the polynomial equations that are solvable by radicals in terms of properties of the permutation group of their roots—an equation is ''solvable by radicals'' if its roots may be expressed by a formula involving only integers, th roots, and the four basic arithmetic operations. This widely generalizes the Abel–Ruffini theorem, which asserts that a general polynomial of degree at least five cannot be solved by radicals. Galois theory has been used to solve classic problems including showing that two problems of antiquity cannot be solved as they were stated (doubling the cub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fuchsian Differential Equation
In mathematics, in the theory of ordinary differential equations in the complex plane \Complex, the points of \Complex are classified into ''ordinary points'', at which the equation's coefficients are analytic functions, and ''singular points'', at which some coefficient has a singularity. Then amongst singular points, an important distinction is made between a regular singular point, where the growth of solutions is bounded (in any small sector) by an algebraic function, and an irregular singular point, where the full solution set requires functions with higher growth rates. This distinction occurs, for example, between the hypergeometric equation, with three regular singular points, and the Bessel equation which is in a sense a limiting case, but where the analytic properties are substantially different. Formal definitions More precisely, consider an ordinary linear differential equation of -th order \sum_^n p_i(z) f^ (z) = 0 with meromorphic functions. One can assume that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covering Space
A covering of a topological space X is a continuous map \pi : E \rightarrow X with special properties. Definition Let X be a topological space. A covering of X is a continuous map : \pi : E \rightarrow X such that there exists a discrete space D and for every x \in X an open neighborhood U \subset X, such that \pi^(U)= \displaystyle \bigsqcup_ V_d and \pi, _:V_d \rightarrow U is a homeomorphism for every d \in D . Often, the notion of a covering is used for the covering space E as well as for the map \pi : E \rightarrow X. The open sets V_ are called sheets, which are uniquely determined up to a homeomorphism if U is connected. For each x \in X the discrete subset \pi^(x) is called the fiber of x. The degree of a covering is the cardinality of the space D. If E is path-connected, then the covering \pi : E \rightarrow X is denoted as a path-connected covering. Examples * For every topological space X there exists the covering \pi:X \rightarrow X with \pi(x)=x, which is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Equations
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field (mathematics), fields, and vector spaces, can all be seen as groups endowed with additional operation (mathematics), operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, and Standard Model, three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Higher Education Press
Higher Education Press (HEP) is a publisher in China of university and college-level textbooks, owned by Ministry of Education of the People's Republic of China. The company's headquarters is in Beijing. HEP was among the world Top 50 publishers. HEP partnered with ScienceOpen in April 2016, indexing one of its flagship Open Access journals Frontiers of Agricultural Science and Engineering (FASE). Journals * ''Engineering'' *''Frontiers of Architectural Research'' *''Frontiers in Biology'' *''Frontiers of Computer Science'' *'' Frontiers in Energy'' *'' Frontiers of Law in China'' *''Frontiers of Medicine'' *''Frontiers of Physics ''Frontiers of Physics'' (formerly ''Frontiers of Physics in China'' from 2006 to 2010) is a bimonthly peer-reviewed academic journal established in 2006 and co-published by Higher Education Press (China) and Springer Verlag (Germany). Topics cov ...'' *'' Protein & Cell'' References {{Authority control Publishing companies of China ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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