Fellowship of the Royal Society is an award granted to individuals that the Royal Society of London judges to have made a 'substantial contribution to the improvement of natural knowledge, including mathematics, engineering science, and medical science'.
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. Numerical analysis naturally finds application in all fields of engineering and the physical sciences, but in the 21st century also the life sciences, social sciences, medicine, business and even the arts have adopted elements of scientific computations. The growth in computing power has revolutionized the use of realistic mathematical models in science and engineering, and subtle numerical analysis is required to implement these detailed models of the world. For example, ordinary differential equations appear in celestial mechanics ; numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology.
The Mathematical Institute is the mathematics department at the University of Oxford, England. It forms one of the twelve departments of the Mathematical, Physical and Life Sciences Division in the University. The department is located between Somerville College and Green Templeton College on Woodstock Road, next to the Faculty of Philosophy.
Lloyd MacGregor Trefethen was an American expert in fluid dynamics known for his invention of the heat pipe and his research on the Coriolis effect and card shuffling. He worked for many years as a professor of mechanical engineering at Tufts University.
Florence Marion Newman Trefethen (1921–2012) was an American codebreaker, historian of operations research, poet, and English professor.
Harvard University is a private Ivy League research university in Cambridge, Massachusetts, with about 6,700 undergraduate students and about 15,250 postgraduate students. Established in 1636 and named for its first benefactor, clergyman John Harvard, Harvard is the United States' oldest institution of higher learning. Its history, influence, and wealth have made it one of the world's most prestigious universities.
Leland Stanford Junior University is a private research university in Stanford, California. Stanford is known for its academic strength, wealth, proximity to Silicon Valley, and ranking as one of the world's top universities.
The Courant Institute of Mathematical Sciences (CIMS) is an independent division of New York University (NYU) under the Faculty of Arts & Science that serves as a center for research and advanced training in computer science and mathematics. It is considered one of the leading and most prestigious mathematics schools and mathematical sciences research centers in the world. It is named after Richard Courant, one of the founders of the Courant Institute and also a mathematics professor at New York University from 1936 to 1972.
The Massachusetts Institute of Technology (MIT) is a private research university in Cambridge, Massachusetts. Founded in 1861 in response to the increasing industrialization of the United States, MIT adopted a European polytechnic university model and stressed laboratory instruction in applied science and engineering. It has since played a key role in the development of many aspects of modern science, engineering, and mathematics, and is widely known for its innovation and academic strength, making it one of the most prestigeous institutions of higher learning in the world. The Institute is a land-grant, sea-grant, and space-grant university, with an urban campus that extends more than a mile alongside the Charles River.
Cornell University is a private and statutory Ivy League research university in Ithaca, New York. Founded in 1865 by Ezra Cornell and Andrew Dickson White, the university was intended to teach and make contributions in all fields of knowledge—from the classics to the sciences, and from the theoretical to the applied. These ideals, unconventional for the time, are captured in Cornell's founding principle, a popular 1868 Ezra Cornell quotation: "I would found an institution where any person can find instruction in any study."
As of 2018[update], he has published around 140 journal papers spanning a wide range of areas within numerical analysis and applied mathematics, including non-normal eigenvalue problems and applications, spectral methods for differential equations, numerical linear algebra, fluid mechanics, computational complex analysis, and approximation theory.[17] He is perhaps best known for his work on pseudospectra of non-normal matrices and operators. This work covers theoretical aspects as well as numerical algorithms, and applications including fluid mechanics, numerical solution of partial differential equations, numerical linear algebra, shuffling of cards, random matrices, differential equations and lasers. Trefethen is currently an ISI highly cited researcher.[18]
Numerical linear algebra is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to mathematical questions. It is a subfield of numerical analysis, and a type of linear algebra. Because computers use floating-point arithmetic, they cannot exactly represent irrational data, and many algorithms increase that imprecision when implemented by a computer. Numerical linear algebra uses properties of vectors and matrices to develop computer algorithms that minimize computer error while retaining efficiency and precision.
Fluid mechanics is the branch of physics concerned with the mechanics of fluids and the forces on them. It has applications in a wide range of disciplines, including mechanical, civil, chemical and biomedical engineering, geophysics, astrophysics, and biology.
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful 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, aerospace, mechanical and electrical engineering.
Trefethen has written a number of books on numerical analysis including Numerical Linear Algebra[19] with David Bau, Spectral Methods in MATLAB, Schwarz–Christoffel Mapping with Tobin Driscoll, and Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators[20] with Mark Embree.[3] He has recently been heavily involved in the creation and development of the MATLAB-based Chebfun software project.
Mark Embree is professor of computational and applied mathematics at Virginia Tech in Blacksburg, Virginia. Until 2013, he was a professor of computational and applied mathematics at Rice University in Houston, Texas.
MATLAB is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, C#, Java, Fortran and Python.
Chebfun is a free/open-source software system written in MATLAB for numerical computation with functions of a real variable. It is based on the idea of overloading MATLAB's commands for vectors and matrices to analogous commands for functions and operators. Thus, for example, whereas the SUM command in MATLAB adds up the elements of a vector, the SUM command in Chebfun evaluates a definite integral. Similarly the backslash command in MATLAB becomes a Chebfun command for solving differential equations.
In 2013 he proposed a new formula to calculate the BMI of a person:[21][22]
Nick Trefethen is distinguished for his many seminal contributions to Numerical Analysis and its applications in Applied Mathematics and in Engineering Science. His research spans theory, algorithms, software and physical applications, particularly involving eigenvalues, pseudospectra – a concept which he introduced – and dynamics. He has an international reputation for his work on nonnormal matrices and operators. He has also made major contributions to finite difference and spectral methods for partial differential equations, numerical linear algebra, and complex analysis. His monograph Numerical Linear Algebra (SIAM, 1997) is one of the SIAM's best selling books and has already been through five printings.[4]
Linear algebra is the branch of mathematics concerning linear equations such as
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero. The term usually refers to square matrices. An example of a 2-by-2 diagonal matrix is ; the following matrix is a 3-by-3 diagonal matrix: . An identity matrix of any size, or any multiple of it, will be a diagonal matrix.
In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems.
In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result of studies of linear algebra and the solutions of systems of linear equations and their generalizations. The theory is connected to that of analytic functions because the spectral properties of an operator are related to analytic functions of the spectral parameter.
In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators or closed operators, and consideration may be given to nonlinear operators. The study, which depends heavily on the topology of function spaces, is a branch of functional analysis.
Numerical partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs).
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it. More formally, if T is a linear transformation from a vector space V over a field F into itself and v is a vector in V that is not the zero vector, then v is an eigenvector of T if T(v) is a scalar multiple of v. This condition can be written as the equation
In mathematics, the pseudospectrum of an operator is a set containing the spectrum of the operator and the numbers that are "almost" eigenvalues. Knowledge of the pseudospectrum can be particularly useful for understanding non-normal operators and their eigenfunctions.
Nicholas John Higham FRS is a British numerical analyst. He is Royal Society Research Professor and Richardson Professor of Applied Mathematics in the School of Mathematics at the University of Manchester.
Leslie Fox was a British mathematician noted for his contribution to numerical analysis.
In the mathematical field of linear algebra and convex analysis, the numerical range or field of values of a complex n × n matrix A is the set
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. For example, the dimensions of the matrix below are 2 × 3, because there are two rows and three columns:
The following is a timeline of numerical analysis after 1945, and deals with developments after the invention of the modern electronic computer, which began during Second World War. For a fuller history of the subject before this period, see timeline and history of mathematics.
Alan Stuart Edelman is an American mathematician and computer scientist. He is a Professor of Applied Mathematics at the Massachusetts Institute of Technology and a Principal Investigator at the MIT Computer Science and AI Laboratory (CSAIL) where he leads a group in Applied Computing. In 2004 Professor Edelman founded Interactive Supercomputing, acquired by Microsoft.
↑ Nachtigal, N. L. M.; Reddy, S. C.; Trefethen, L. N. (1992). "How Fast are Nonsymmetric Matrix Iterations?". SIAM Journal on Matrix Analysis and Applications. 13 (3): 778. CiteSeerX10.1.1.210.62. doi:10.1137/0613049.
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