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A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials.
Maple is a symbolic and numeric computing environment as well as a multi-paradigm programming language. It covers several areas of technical computing, such as symbolic mathematics, numerical analysis, data processing, visualization, and others. A toolbox, MapleSim, adds functionality for multidomain physical modeling and code generation.
Maxima is a computer algebra system (CAS) based on a 1982 version of Macsyma. It is written in Common Lisp and runs on all POSIX platforms such as macOS, Unix, BSD, and Linux, as well as under Microsoft Windows and Android. It is free software released under the terms of the GNU General Public License (GPL).
A graphing calculator is a handheld computer that is capable of plotting graphs, solving simultaneous equations, and performing other tasks with variables. Most popular graphing calculators are also programmable and therefore considered to be programmable calculators, allowing the user to create customized programs, typically for scientific, engineering and education applications. Because they have large displays in comparison to standard four-operation handheld calculators, graphing calculators also typically display several lines of text and calculations at the same time.
In mathematics, a closed-form expression is a mathematical expression expressed using a finite number of standard operations. It may contain constants, variables, certain "well-known" operations, and functions, but usually no limit, differentiation, or integration. The set of operations and functions admitted in a closed-form expression may vary with author and context.
Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data.
A computer-assisted proof is a mathematical proof that has been at least partially generated by computer.
Mathomatic is a free, portable, general-purpose computer algebra system (CAS) that can symbolically solve, simplify, combine, and compare algebraic equations, and can perform complex number, modular, and polynomial arithmetic, along with standard arithmetic. It does some symbolic calculus, numerical integration, and handles all elementary algebra except logarithms. Trigonometric functions can be entered and manipulated using complex exponentials, with the GNU m4 preprocessor. Not currently implemented are general functions like f(x), arbitrary-precision and interval arithmetic, and matrices.
SageMath is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, numerical analysis, number theory, calculus and statistics.
Euler is a free and open-source numerical software package. It contains a matrix language, a graphical notebook style interface, and a plot window. Euler is designed for higher level math such as calculus, optimization, and statistics.
Computational mathematics involves mathematical research in mathematics as well as in areas of science where computation plays a central and essential role, and emphasizes algorithms, numerical methods, and symbolic computations.
Xcas is a user interface to Giac, which is a free, open source Computer Algebra System (CAS) for Microsoft Windows, Apple macOS, Linux, and FreeBSD; Xcas is written in C++. Giac can be used directly inside software written in C++.
Microsoft Math Solver, is an entry-level educational app that solves math and science problems. Developed and maintained by Microsoft, it is primarily targeted at students as a learning tool. Until 2015, it ran on Microsoft Windows. Since then, it has been developed for the web platform and mobile devices.
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.
MuPAD is a computer algebra system (CAS). Originally developed by the MuPAD research group at the University of Paderborn, Germany, development was taken over by the company SciFace Software GmbH & Co. KG in cooperation with the MuPAD research group and partners from some other universities starting in 1997. MuPAD's graphics package was particularly successful, especially considering the era when it was developed.
Bootstrap is based at Brown University (USA), and builds on the research and development done there. Bootstrap curriculum consists of 4 research-based curricular computer science modules for grades 6-12. The 4 modules are Bootstrap:Algebra, Bootstrap:Reactive, Bootstrap:Data Science, and Bootstrap:Physics. Bootstrap materials reinforce core concepts from mainstream subjects like Math, Physics and more, enabling non-CS teachers to adopt the introductory materials while delivering rigorous and engaging computing content drawn from Computer Science classes at universities like Brown, WPI, and Northeastern.
Validated numerics, or rigorous computation, verified computation, reliable computation, numerical verification is numerics including mathematically strict error evaluation, and it is one field of numerical analysis. For computation, interval arithmetic is used, and all results are represented by intervals. Validated numerics were used by Warwick Tucker in order to solve the 14th of Smale's problems, and today it is recognized as a powerful tool for the study of dynamical systems.
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