Mathematical software is

The progress of mathematical information presentation such as

Internet Accessible Mathematical Computation

Institute for Computational Mathematics,

swMATH

Database on mathematical software :

software
Software is a collection of instructions
Instruction or instructions may refer to:
Computing
* Instruction, one operation of a processor within a computer architecture instruction set
* Computer program, a collection of instructions
Music
* I ...

used to model
In general, a model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. ...

, analyze or calculate numeric, symbolic or geometric data.
Evolution of mathematical software

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). Numerical analysis ...

and symbolic computation
In mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...

had been in most important place of the subject, but other kind of them is also growing now. A useful mathematical knowledge of such as algorism
Algorism is the technique of performing basic arithmetic
Arithmetic (from the Ancient Greek, Greek wikt:en:ἀριθμός#Ancient Greek, ἀριθμός ''arithmos'', 'number' and wikt:en:τική#Ancient Greek, τική wikt:en:τέχνη#Anci ...

which exist before the invention
An invention is a unique or novelty (patent), novel machine, device, method, composition or process. The invention process is a process within an overall engineering and product development process. It may be an improvement upon a machine or p ...

of electronic computer
Electronic may refer to:
*Electronics, the science of how to control electric energy in semiconductor
*Electronics (magazine), ''Electronics'' (magazine), a defunct American trade journal
*Electronic storage, the storage of data using an electronic ...

, helped to mathematical software developing. On the other hand, by the growth of computing power
In computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes and development of both computer hardware , hardware and softwar ...

(such as seeing on Moore's law
Moore's law is the observation that Transistor count, the number of transistors in a dense integrated circuit (IC) doubles about every two years. Moore's law is an observation and Forecasting, projection of a historical trend. Rather than a ph ...

), the new treatment (for example, a new kind of technique such as data assimilation
Data assimilation is a mathematical discipline that seeks to optimally combine theory (usually in the form of a numerical model) with observations. There may be a number of different goals sought, for example—to determine the optimal state estim ...

which combined numerical analysis and statistics
Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data
Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...

) needing conversely the progress of the mathematical science
The mathematical sciences are a group of areas of study that includes, in addition to mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algeb ...

or applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and be ...

.The progress of mathematical information presentation such as

TeX
TeX (, see below), stylized within the system as TeX, is a typesetting system which was designed and mostly written by Donald Knuth and released in 1978. TeX is a popular means of typesetting complex mathematical formulae; it has been noted ...

or MathML
Mathematical Markup Language (MathML) is a mathematical markup language, an application of XML for describing mathematics, mathematical notations and capturing both its structure and content. It aims at integrating mathematical formulae into Wo ...

will demand to evolution form ''formula manipulation language'' to true ''mathematics manipulation language'' (notwithstanding the problem that whether mathematical theory is inconsistent or not). And popularization of general purpose mathematical software, special purpose mathematical software so called ''one purpose software'' which used special subject will alive with adapting for environment progress at normalization of platform. So the diversity of mathematical software will be kept.
Software calculator

A software calculator allows the user to perform simple mathematical operations, like addition, multiplication, exponentiation and trigonometry. Data input is typically manual, and the output is a text label.Computer algebra systems

Many mathematical suites arecomputer algebra system
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software
Mathematical software is software used to mathematical model, model, analyze or calculate numeric, symbolic or geometric data.
It is a type of applica ...

s that use symbolic mathematics. They are designed to solve classical algebra equations and problems in human readable notation.
Statistics

Many tools are available for statistical analysis of data. See alsoComparison of statistical packages The following tables compare general and technical information for a number of statistical analysis packages.
General information
Operating system support
ANOVA
Support for various ANOVA methods
Regression
Support for various Regression anal ...

.
Theorem provers and proof assistants

Optimization software

Geometry

Numerical analysis

TK Solver
TK Solver (originally TK!Solver) is a mathematical modeling and problem solving software system based on a declarative, rule-based language, commercialized by Universal Technical Systems, Inc.
History
Invented by Milos Konopasek in the late 1970s ...

is a mathematical modeling and problem solving software system based on a declarative, rule-based language, commercialized by Universal Technical Systems, Inc..
The Netlib Netlib is a repository of software for scientific computing
Computational science, also known as scientific computing or scientific computation (SC), is a field that uses advanced computing
Computing is any goal-oriented activity requiring, bene ...

repository contains various collections of software routines for numerical problems, mostly in Fortran
Fortran (; formerly FORTRAN) is a general-purpose, compiled language, compiled imperative programming, imperative programming language that is especially suited to numerical analysis, numeric computation and computational science, scientific com ...

and C. Commercial products implementing many different numerical algorithms include the IMSL, NMath and NAG libraries; a free alternative is the GNU Scientific Library
The GNU Scientific Library (or GSL) is a software library for numerical computations in applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics
Physics (from grc, φυσ ...

. A different approach is taken by the Numerical Recipes
''Numerical Recipes'' is the generic title of a series of books on algorithm
In and , an algorithm () is a finite sequence of , computer-implementable instructions, typically to solve a class of problems or to perform a computation. Algori ...

library, where emphasis is placed on clear understanding of algorithms.
Many computer algebra system
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software
Mathematical software is software used to mathematical model, model, analyze or calculate numeric, symbolic or geometric data.
It is a type of applica ...

s (listed above) can also be used for numerical computations.
Music mathematics software

''Music mathematics software utilizes mathematics to analyze or synthesize musical symbols and patterns.'' * Musimat (by Gareth Loy)Websites

A growing number of mathematical software is available in web browsers, without the need to download or install any code.Institute for Computational Mathematics,

Kent State University
Kent State University (KSU) is a public
In public relations
Public relations (PR) is the practice of managing and disseminating information from an individual or an organization
An organization, or organisation (English in t ...

, retrieved 2015-02-15.
Programming libraries

Low-level mathematical libraries intended for use within other programming languages: * GMP, theGNU Multi-Precision Library
GNU Multiple Precision Arithmetic Library (GMP) is a free library for arbitrary-precision arithmetic, operating on signed integer
An integer (from the Latin wikt:integer#Latin, ''integer'' meaning "whole") is colloquially defined as a numb ...

for extremely fast arbitrary precision arithmetic.
* Class Library for Numbers, a high-level C++
C++ () is a general-purpose programming language
In computer software, a general-purpose programming language is a programming language dedicated to a general-purpose, designed to be used for writing software in a wide variety of application ...

library for arbitrary precision arithmetic.
* AMD Core Math Library, a software development library released by AMD
* Boost.Math
References

{{reflistExternal links

swMATH

Database on mathematical software :