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Amplitwist
In mathematics, the amplitwist is a concept created by Tristan Needham in the book ''Visual Complex Analysis'' (1997) to represent the derivative of a complex function visually. Definition The ''amplitwist'' associated with a given function is its derivative in the complex plane. More formally, it is a complex number z such that in an infinitesimally small neighborhood of a point a in the complex plane, f(\xi) = z \xi for an infinitesimally small vector \xi. The complex number z is defined to be the derivative of f at a. Uses The concept of an amplitwist is used primarily in complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ... to offer a way of visualizing the derivative of a complex-valued function as a local amplification and twist of vectors at a point in the comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tristan Needham
Tristan Needham is a British mathematician and professor of mathematics at the University of San Francisco. Education, career and publications Tristan is the son of social anthropologist Rodney Needham of Oxford, England. He attended the Dragon School. Later Needham attended the University of Oxford and studied physics at Merton College, and then transferred to the Mathematical Institute where he studied under Roger Penrose. He obtained his D.Phil. in 1987 and in 1989 took up his post at University of San Francisco. In 1993 he published ''A Visual Explanation of Jensen's inequality''. The following year he published ''The Geometry of Harmonic Functions'', which won the Carl B. Allendoerfer Award for 1995. Needham wrote the book ''Visual Complex Analysis'', which has received positive reviews. Though it is described as a "radical first course in complex analysis aimed at undergraduates", writing in ''Mathematical Reviews'' D.H. Armitage said that "the book will be appreciated mo ... [...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] |
Complex Analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and particularly quantum mechanics. By extension, use of complex analysis also has applications in engineering fields such as nuclear engineering, nuclear, aerospace engineering, aerospace, mechanical engineering, mechanical and electrical engineering. As a differentiable function of a complex variable is equal to its Taylor series (that is, it is Analyticity of holomorphic functions, analytic), complex analysis is particularly concerned with analytic functions of a complex variable (that is, holomorphic functions). History Complex analysis is one of the classical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PRIMUS (journal)
''PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies'' is a peer-reviewed academic journal covering the teaching of undergraduate mathematics, established in 1991. The journal has been published by Taylor & Francis since March 2007. It is abstracted and indexed in Cambridge Scientific Abstracts, MathEduc, PsycINFO, and ''Zentralblatt MATH''. PRIMUS is an affiliated journal of the Mathematical Association of America, so all MAA members have access to PRIMUS. Editorial Team PRIMUS was started by founding editor-in-chief Brian Winkel in 1991 to address the lack of venues for tertiary mathematics educators to share their pedagogical work. In 2011, Jo Ellis-Monaghan Joanna Anthony Ellis-Monaghan is an American mathematician and mathematics educator whose research interests include graph polynomials and topological graph theory. She is a professor of mathematics at the Korteweg-de Vries Institute for Mathema ... became the second editor-in-chief, with Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functions And Mappings
In mathematics, a map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map: ''mapping'' the Earth surface to a sheet of paper. The term ''map'' may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial. In category theory, a map may refer to a morphism. The term ''transformation'' can be used interchangeably, but ''transformation'' often refers to a function from a set to itself. There are also a few less common uses in logic and graph theory. Maps as functions In many branches of mathematics, the term ''map'' is used to mean a function, sometimes with a specific property of particular importance to that branch. For instance, a "map" is a "continuous function" in topology, a "linear transformation" in linear algebra, etc. Some au ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
