"Applied mathematics is mathematics for which I happen to know an application. This, I think, includes almost everything in mathematics." (Henry O. Pollack )
Probably there is no unique definition of applied maths. In this article we report some references that analyze the problem and try to answer this question.
One of the most generic definition is the following:
"Applied (or perhaps Applicable) Mathematics consists of mathematical techniques and results, including those from "pure" math areas such as (abstract) algebra or algebraic topology, which are used to assist in the investigation of problems or questions originating outside of mathematics. " (click here to read more)
In the article " Mathematics Is Biology's Next Microscope", Cohen J. uses a very interesting metaphor:
The landscape of applied mathematics is better visualized as a tetrahedron (a pyramid with a triangular base) than as a matrix with temporal and spatial dimensions. (Mathematical imagery, such as a tetrahedron for applied mathematics and a matrix for biology, is useful even in trying to visualize the landscapes of biology and mathematics.) The four main points of the applied mathematical landscape are data structures, algorithms, theories and models (including all pure mathematics), and computers and software. Data structures are ways to organize data, such as the matrix used above to describe the biological landscape. Algorithms are procedures for manipulating symbols. Some algorithms are used to analyze data, others to analyze models. Theories and models, including the theories of pure mathematics, are used to analyze both data and ideas. Mathematics and mathematical theories provide a testing ground for ideas in which the strength of competing theories can be measured. Computers and software are an important, and frequently the most visible, vertex of the applied mathematical landscape. However, cheap, easy computing increases the importance of theoretical understanding of the results of computation. Theoretical understanding is required as a check on the great risk of error in software, and to bridge the enormous gap between computational results and insight or understanding.
A good presentation of Applied Mathematics is made by the Division of Applied Mathematics at Brown University here.
Further reflections can be found here
Anyway, through this blog, we'll try to tell the various characteristics of the applied mathematics and in particular we'll analyze the vertices of the applied-maths-tetrahedron:
- data structures,
- theories and models (including all pure mathematics),
- computers and software
- Cohen JE (2004) Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better. PLoS Biol 2(12): e439. doi:10.1371/journal.pbio.0020439
- "What is Applied Mathematics?" http://www.dam.brown.edu/documents/WhatisAppliedMathematicsPresentation_000.pdf
Thoughts on Applied Mathematics, https://www.math.ust.hk/~mahsieh/APMATH.htm