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Heidelberg University Faculty Of Mathematics And Computer Science
The Faculty of Mathematics and Computer Science is one of twelve faculties at the University of Heidelberg. It comprises the Institute of Mathematics, the Institute of Applied Mathematics, the School of Applied Sciences, and the Institute of Computer Science. The faculty maintains close relationships to the Interdisciplinary Center for Scientific Computing (IWR) and thMathematics Center Heidelberg (MATCH) The first chair of mathematics was entrusted to the physiciain the year 1547. Institute of Mathematics In 1547, the first chair of mathematics was entrusted to the physician Jacob Curio. Today, areas of research include: * Complex analysis: automorphic functions and modular forms * Arithmetic: algebraic number theory, algorithmic algebra, and arithmetical geometry * Topology and geometry: geometric partial differential equations, algebraic topology, differential topology, and differential geometry Institute of Applied Mathematics In 1957, Gottfried Köthe became ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Heidelberg
} Heidelberg University, officially the Ruprecht Karl University of Heidelberg, (german: Ruprecht-Karls-Universität Heidelberg; la, Universitas Ruperto Carola Heidelbergensis) is a public research university in Heidelberg, Baden-Württemberg, Germany. Founded in 1386 on instruction of Pope Urban VI, Heidelberg is Germany's oldest university and one of the world's oldest surviving universities; it was the third university established in the Holy Roman Empire. Heidelberg is one of the most prestigious and highly ranked universities in Europe and the world. Heidelberg has been a coeducational institution since 1899. The university consists of twelve faculties and offers degree programmes at undergraduate, graduate and postdoctoral levels in some 100 disciplines. The language of instruction is usually German, while a considerable number of graduate degrees are offered in English as well as some in French. As of 2021, 57 Nobel Prize winners have been affiliated with the city o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gottfried Köthe
Gottfried Maria Hugo Köthe (born 25 December 1905 in Graz – died 30 April 1989 in Frankfurt) was an Austrian mathematician working in abstract algebra and functional analysis. Scientific career In 1923 Köthe enrolled in the University of Graz. He started studying chemistry, but switched to mathematics a year later after meeting the philosopher Alfred Kastil. In 1927 he submitted his thesis ''Beiträge zu Finslers Grundlegung der Mengenlehre'' ("Contributions to Finsler's foundations of set theory") and was awarded a doctorate. After spending a year in Zürich working with Paul Finsler, Köthe received a fellowship to visit the University of Göttingen, where he attended the lectures of Emmy Noether and Bartel van der Waerden on the emerging subject of abstract algebra. He began working in ring theory and in 1930 published the Köthe conjecture stating that a sum of two left nil ideals in an arbitrary ring is a nil ideal. By a recommendation of Emmy Noether, he was appointe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knowledge Management
Knowledge management (KM) is the collection of methods relating to creating, sharing, using and managing the knowledge and information of an organization. It refers to a multidisciplinary approach to achieve organisational objectives by making the best use of knowledge. An established List of academic disciplines, discipline since 1991, KM includes courses taught in the fields of business administration, information systems, management, Library science, library, and information science. Other fields may contribute to KM research, including information and media, computer science, public health and policy, public policy. Several universities offer dedicated master's degrees in knowledge management. Many large companies, public institutions, and non-profit organisations have resources dedicated to internal KM efforts, often as a part of their strategic management, business strategy, information technology, IT, or human resource management departments. Several consulting companies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Systems
An information system (IS) is a formal, sociotechnical, organizational system designed to collect, process, information storage, store, and information distribution, distribute information. From a sociotechnical perspective, information systems are composed by four components: task, people, structure (or roles), and technology. Information systems can be defined as an integration of components for collection, storage and data processing, processing of data of which the data is used to provide information, contribute to knowledge as well as digital products that facilitate decision making. A computer information system is a system that is composed of people and computers that processes or interprets information. The term is also sometimes used to simply refer to a computer, computer system with software installed. "Information systems" is also an academic field study about systems with a specific reference to information and the complementary networks of computer hardware and soft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
High-performance Computing
High-performance computing (HPC) uses supercomputers and computer clusters to solve advanced computation problems. Overview HPC integrates systems administration (including network and security knowledge) and parallel programming into a multidisciplinary field that combines digital electronics, computer architecture, system software, programming languages, algorithms and computational techniques. HPC technologies are the tools and systems used to implement and create high performance computing systems. Recently, HPC systems have shifted from supercomputing to computing clusters and grids. Because of the need of networking in clusters and grids, High Performance Computing Technologies are being promoted by the use of a collapsed network backbone, because the collapsed backbone architecture is simple to troubleshoot and upgrades can be applied to a single router as opposed to multiple ones. The term is most commonly associated with computing used for scientific research or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computability
Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem. The most widely studied models of computability are the Turing-computable and μ-recursive functions, and the lambda calculus, all of which have computationally equivalent power. Other forms of computability are studied as well: computability notions weaker than Turing machines are studied in automata theory, while computability notions stronger than Turing machines are studied in the field of hypercomputation. Problems A central idea in computability is that of a (computational) problem, which is a task whose computability can be explored. There are two key types of problems: * A decision problem fixes a set ''S'', which may be a set of strings, natural numbers, or oth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Computing
Computational science, also known as scientific computing or scientific computation (SC), is a field in mathematics that uses advanced computing capabilities to understand and solve complex problems. It is an area of science that spans many disciplines, but at its core, it involves the development of models and simulations to understand natural systems. * Algorithms ( numerical and non-numerical): mathematical models, computational models, and computer simulations developed to solve science (e.g., biological, physical, and social), engineering, and humanities problems * Computer hardware that develops and optimizes the advanced system hardware, firmware, networking, and data management components needed to solve computationally demanding problems * The computing infrastructure that supports both the science and engineering problem solving and the developmental computer and information science In practical use, it is typically the application of computer simulation and other fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization (mathematics)
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymptotic Theory
In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function as becomes very large. If , then as becomes very large, the term becomes insignificant compared to . The function is said to be "''asymptotically equivalent'' to , as ". This is often written symbolically as , which is read as " is asymptotic to ". An example of an important asymptotic result is the prime number theorem. Let denote the prime-counting function (which is not directly related to the constant pi), i.e. is the number of prime numbers that are less than or equal to . Then the theorem states that \pi(x)\sim\frac. Asymptotic analysis is commonly used in computer science as part of the analysis of algorithms and is often expressed there in terms of big O notation. Definition Formally, given functions and , we define a binary relation f(x) \sim g(x) \quad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonparametrics
Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance). Nonparametric statistics is based on either being distribution-free or having a specified distribution but with the distribution's parameters unspecified. Nonparametric statistics includes both descriptive statistics and statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are violated. Definitions The term "nonparametric statistics" has been imprecisely defined in the following two ways, among others: Applications and purpose Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars). The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences. In terms of levels of mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
