The fields of applied mathematics

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Discussion Overview

The discussion revolves around the various fields and disciplines that constitute "applied mathematics." Participants explore the scope of applied mathematics, including its relationship to real-world problems and its intersection with theoretical mathematics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants identify Differential Equations, Calculus, Statistics, and Linear Algebra as core components of applied mathematics.
  • Others propose additional fields such as graph theory, combinatorics, number theory, and optimization, suggesting these areas have practical applications.
  • A participant mentions Operations Research as an umbrella term that includes various mathematical disciplines applied to non-physical problems.
  • There is a distinction made between "applied mathematics" and "applicable mathematics," with some arguing that applied mathematics refers specifically to the application of mathematics in real-world contexts.
  • Geometry is noted as a historically significant area of applied mathematics, with references to its modern applications in technology.
  • Participants question the clarity of the original post and seek further elaboration on the intended meaning of "applied mathematics."

Areas of Agreement / Disagreement

Participants generally agree that applied mathematics encompasses a variety of fields, but there is no consensus on the exact definition or scope of what constitutes applied mathematics. Multiple competing views on its components and applications remain present.

Contextual Notes

Some discussions highlight the ambiguity in definitions, such as the difference between applied and applicable mathematics, and the varying interpretations of what constitutes real-world applications.

Cinitiator
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What kind of mathematical disciplines/fields take part in what's called "applied mathematics"?

As far as I know, it's Differential Equations, Calculus, Statistics and Linear Algebra. What other fields are there? I'm sure there are some others.
 
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There are many others: graph theory and combinatorics--the traveling salesman problem, the postage-stamp problem, analysis and design of algorithms; number theory in cryptography, etc.

I'm not an applied mathematician, but AFAIK, many areas once thought to have a purely theoretical scope have found real-world applications.
 
Bacle2 said:
There are many others: graph theory and combinatorics--the traveling salesman problem, the postage-stamp problem, analysis and design of algorithms; number theory in cryptography, etc.
Where I studied, the above (and others, like Optimisation) took the umbrella title of Operations Research, and were described generically as non-physical applied.
 
haruspex said:
Where I studied, the above (and others, like Optimisation) took the umbrella title of Operations Research, and were described generically as non-physical applied.

I'm assuming that applied mathematics refers to the use of mathematics to (help) solve

general real-world problems; I think the cases I stated fall under this category, despite ,

maybe not having what one would call physical (maybe engineering, mostly) applications.
 
Haruspex, maybe the OP can explain better what s/he meant. Otherwise,

only option seems to be to make assumptions about what the actual question was.

Would you ex[and, OP?
 
Bacle2 said:
Haruspex, maybe the OP can explain better what s/he meant. Otherwise,

only option seems to be to make assumptions about what the actual question was.

Would you ex[and, OP?

By applied mathematics I mean mathematics which is very frequently used for the real world applications and sciences. Ex: Calculus, linear algebra, statistics, etc.
 
That would normally be called "applicable mathematics". "Applied mathematics" refers to the actual application of mathematics. But there are very few forms of mathematics that don't get some application. "Number theory" is used in breaking codes and "group theory" is used in quantum mechanics, "differential goemetry" in relativity.
 
Halls of Ivy has, of course, brought up the oldest and longest application of mathematics - geometry.

These days there are many aspects of mathematics with geometry in the title, you are looking at one now that is used to show the pictures on your screen.

And where would you place trigonometry, complex analysis, orthogonal transformations, variational methods,
 

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