Divisions of applied mathematics

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Discussion Overview

The discussion revolves around the various divisions within applied mathematics, as defined by a Wikipedia entry. Participants explore different fields and applications of applied mathematics, including their own interests and areas of expertise.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant lists numerous areas of applied mathematics, including differential equations, numerical analysis, and mathematical physics.
  • Another participant suggests that meteorology and atmospheric science should be included in the list, proposing that they fall under differential equations.
  • A participant mentions their focus on nonlinear differential equations, including ODEs, PDEs, and DDEs, and notes the relevance of matrix theory and bifurcation theory.
  • Another participant introduces additional fields such as calculus of variations, elastic theory, and various types of analysis, expressing concern that the list mixes mathematical branches with applied fields.
  • This participant emphasizes the practical applications of differential equations in various industries and states their intention to focus on specific areas like calculus of variations and mathematical finance.

Areas of Agreement / Disagreement

Participants express differing opinions on which fields should be included in the divisions of applied mathematics, indicating a lack of consensus on the completeness and categorization of the list.

Contextual Notes

Some participants highlight the ambiguity in categorizing certain fields as either branches of mathematics or applied areas, suggesting that definitions may vary based on context.

J77
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Complementing the fields of physics thread, and as a bit of fun :wink:, I wondered what people make of wikipedia's definition of divisions within applied maths:

Applicable areas of mathematics include most notably

* differential equations (ODEs and PDEs)
* numerical analysis/scientific computing
* approximation theory and representation theory
* matrix theory
* mathematical physics
* mathematical methods of engineering
* nonlinear optimization
* operations research, including linear programming
* continuous modelling
* control theory
* mathematical biology
* bioinformatics
* information theory
* game theory
* probability
* mathematical economics
* financial mathematics
* actuarial science
* cryptography
* graph theory (as applied to network analysis)
* statistics
* parts of theoretical computer science


http://en.wikipedia.org/wiki/Applied_mathematics
 
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what about meteorology/ atmospheric science? Also J77, what type of applied math are you into?
 
courtrigrad said:
what about meteorology/ atmospheric science? Also J77, what type of applied math are you into?
That's a good one.

I think it would come under differential equations in this formulation but then so should, for example, math biology.

The base of my work would be nonlinear differential equations but of many forms... ODEs (including nonsmooth), PDEs, DDEs...

This involves matrix theory too.

And, bifurcation theory which I think should be on the list!

Actually, if you number the lsit from 1 to 22, in my research I've employed...

1, 2, 4, 5, 6, 10, 22

I'm not sure what 3 and 9 would include...
 
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Calculus of Variation?

Elastic theory?

All kind of analysis find applications in Physics, and practical Industry.
like
Differential Geometry
Tensor Analysis
Algebraic Topology
Variation Analysis
Elastic Theory
Mathematical Dynamic of any kind.

The list looks weird to me because some of the items are maths, and some are applicable field. Personally, I would consider Differential Eqn is a branch of Maths which has a lot of applications in practical world.

PS: I am going to be focusing on Calculus of Variation, Differential Geometry, Elastic Theory, and Mathematical Finance.
 
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