Applied mathematics
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Applied mathematics is the application of mathematical methods in various fields such as science, engineering, business, computer science, and industry. Thus, applied mathematics combines mathematical science and specialized knowledge. The term also refers to the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. Historically, practical applications have motivated the development of mathematical theories, which then became subjects of study in pure mathematics. Therefore, applied mathematics is closely connected to research in pure mathematics.
History[edit]
Historically, applied mathematics mainly consisted of applied analysis, particularly differential equations, approximation theory, and applied probability. These areas directly related to the development of Newtonian physics. The distinction between mathematicians and physicists was not sharply drawn before the mid-19th century, leaving a pedagogical legacy in the United States. Subjects like classical mechanics were often taught in applied mathematics departments rather than physics departments. Nowadays, quantitative finance and mathematical finance are considered branches of applied mathematics.
Divisions[edit]
Today, "applied mathematics" includes classical areas like differential equations and numerical analysis, as well as newer areas that are increasingly important in applications. Fields like number theory, traditionally part of pure mathematics, are now important in applications such as cryptography. The term "applicable mathematics" is sometimes used to distinguish traditional applied mathematics from newer areas applicable to real-world problems today.
There is no consensus on the various branches of applied mathematics. The categorizations are made difficult by how mathematics and science change over time and how universities organize departments, courses, and degrees. Many mathematicians distinguish between "applied mathematics" and the "applications of mathematics" within science and engineering. The use and development of mathematics to solve industrial problems is also called "industrial mathematics".
Utility[edit]
Historically, mathematics was most important in the natural sciences and engineering. Since World War II, fields outside the physical sciences have spawned new areas of mathematics, such as game theory and social choice theory. The advent of the computer has enabled new applications, including studying and using computer technology itself (computer science) and the mathematics of computation. Statistics is widespread in the social sciences, but other areas of mathematics, especially economics, are increasingly useful in these disciplines.
Status in academic departments[edit]
Academic institutions vary in how they group and label courses, programs, and degrees in applied mathematics. Some have a single mathematics department, while others have separate departments for Applied Mathematics and (Pure) Mathematics. Many applied mathematics programs consist of cross-listed courses and jointly appointed faculty in departments representing applications. Some Ph.D. programs in applied mathematics require little or no coursework outside mathematics, while others require substantial coursework in a specific area of application.
Associated mathematical sciences[edit]
Applied mathematics is closely related to other mathematical sciences.
Scientific computing[edit]
Scientific computing includes applied mathematics (especially numerical analysis), computing science (especially high-performance computing), and mathematical modeling in scientific disciplines.
Computer science[edit]
Computer science relies on logic, algebra, graph theory, and combinatorics.
Operations research and management science[edit]
Operations research and management science are often taught in faculties of engineering, business, and public policy.
Statistics[edit]
Applied mathematics has substantial overlap with statistics. Statistical theorists study and improve statistical procedures with mathematics, and statistical research often raises mathematical questions.
Actuarial science[edit]
Actuarial science applies probability, statistics, and economic theory to assess risk in insurance, finance, and other industries.
Mathematical economics[edit]
Mathematical economics applies mathematical methods to represent theories and analyze problems in economics. It relies on statistics, probability, mathematical programming, operations research, game theory, and methods from mathematical analysis.
Applicable mathematics[edit]
Applicable mathematics is a subdiscipline of applied mathematics, though there is no consensus on a precise definition. Some mathematicians use "applicable mathematics" to distinguish traditional applied mathematics from newer applications arising from fields previously seen as pure mathematics.
See also[edit]
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References[edit]
Further reading[edit]
Applicable Mathematics[edit]
- The Morehead Journal of Applicable Mathematics hosted by Morehead State University
- Handbook of Applicable Mathematics Series by Walter Ledermann
External links[edit]
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Wikiversity has learning resources about School:Mathematics |
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Wikibooks has a book on the topic of: Applicable Mathematics |
- The Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to promoting the interaction between mathematics and other scientific and technical communities.
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