Mathematical Analysis Subject Area

A Mathematical Analysis Subject Area is a subject area that focuses on the mathematical analysis tasks.

• Context:
  • It can range from being Symbolic Mathematical Analysis to being a Numerical Approximation Domain.
  • It can support Mathematical Algorithm Design.
  • It can use a Mathematical Analysis Concept.
  • …
• Counter-Example(s):
  • Statistical Analysis Subject Area.
  • Machine Learning Subject Area.
• See: Numerical Algorithm, Derivative, Integral, Measure (Mathematics), Limit (Mathematics), Series (Mathematics), Analytic Function, Real Number, Complex Number, Function (Mathematics), Calculus, Geometry, Space (Mathematics).

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/mathematical_analysis Retrieved:2015-2-1.
  • Mathematical analysis is a branch of mathematics that includes the theories of differentiation, integration, measure, limits, infinite series, and analytic functions.

    These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis.

    Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).

1991

• (Efron & Tibshirani, 1991) ⇒ Bradley Efron, and Robert Tibshirani. (1991). “Statistical Data Analysis in the Computer Age.” In: Science, 253(5018). 10.1126/science.253.5018.390
  • … This is possible because traditional methods of mathematical analysis are replaced by specially constructed computer algorithms. Mathematics has not disappeared from statistical theory. It is the main method for deciding which algorithms are correct and efficient tools for automating statistical inference.

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