Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term "discrete mathematics".
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries.
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it.
Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals.
Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory.
Peter David Lax is a Hungarian-born American mathematician and Abel Prize laureate working in the areas of pure and applied mathematics.
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side. Theoretical biology focuses more on the development of theoretical principles for biology while mathematical biology focuses on the use of mathematical tools to study biological systems, even though the two terms are sometimes interchanged.
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called discrete dynamical systems. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a Cantor set, one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations.
Computational science, also known as scientific computing, technical computing or scientific computation (SC), is an area of science that uses advanced computing capabilities to understand and solve complex physical problems. This includes
In electrical engineering, a differential-algebraic system of equations (DAEs) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system. In mathematics these are examples of differential algebraic varieties and correspond to ideals in differential polynomial rings (see the article on differential algebra for the algebraic setup.
Hindawi is a publisher of peer-reviewed, open access, scientific journals currently active in scientific, technical, and medical (STM) literature. It was founded in 1997 in Cairo, Egypt, but purchased in 2021 by John Wiley & Sons, a publishing company based in the United States. The company has its headquarters in London, an office in Cairo, and a virtual office address in New York City.
Contrast Media & Molecular Imaging is a monthly peer-reviewed scientific journal published by John Wiley & Sons since 2006 and by Hindawi Publishing Corporation since 2017. It covers the areas of contrast agents and molecular imaging, covering all areas of imaging technologies with a special emphasis on magnetic resonance imaging and positron emission tomography, but also all other in vivo imaging technologies such as x-Ray, CT, ultrasound etc. The current editor-in-chief is Luc Zimmer, professor of pharmacology at the . On 1 January 2017, the journal became fully open access due to a publishing partnership between John Wiley & Sons and the Hindawi Publishing Corporation, where the journal "remain[s] a Wiley title but will be published and hosted by Hindawi". Molecular imaging articles concentrate on the potential role played by MRI and PET contrast agents at visualizing, at the molecular or cellular level, the physiology and physio-pathological processes from animal models to humans.
Abstract and Applied Analysis is a peer-reviewed mathematics journal covering the fields of abstract and applied analysis and traditional forms of analysis such as linear and nonlinear ordinary and partial differential equations, optimization theory, and control theory.
Complexity is a peer-reviewed open-access scientific journal covering the field of complex adaptive systems. The journal's scope includes Chaos theory, genetic algorithms, cellular automata, neural networks, evolutionary game theory, and econophysics. It was established in 1995 and is published by John Wiley & Sons, since 2017 in collaboration with Hindawi Publishing Corporation.
Ravi P. Agarwal is an Indian mathematician, Ph.D. sciences, professor, professor & chairman, Department of Mathematics Texas A&M University-Kingsville, Kingsville, U.S. Agarwal is the author of over 1000 scientific papers as well as 30 monographs. He was previously a professor in the Department of Mathematical Sciences at Florida Institute of Technology.
Numerical Methods for Partial Differential Equations is a bimonthly peer-reviewed scientific journal covering the development and analysis of new methods for the numerical solution of partial differential equations. It was established in 1985 and is published by John Wiley & Sons. The editors-in-chief are George F. Pinder and John R. Whiteman.
Elena Yanovna Braverman is a Russian, Israeli, and Canadian mathematician known for her research in delay differential equations, difference equations, and population dynamics. She is a professor of mathematics and applied mathematics at the University of Calgary, and one of the editors-in-chief of the journal Advances in Difference Equations.
Jacek BanasiakFAAS is a Polish mathematician who is a Professor and DST/NRF SARChI Chair in Mathematical Models and Methods in Biosciences and Bioengineering at the University of Pretoria, South Africa.
