Analytic areas of mathematics
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Analysis looks carefully at the results obtained in calculus and
related areas. One might characterize algebra and geometry as the
search for elegant conclusions from small sets of axioms; in analysis
on the other hand the measure of success is more frequently the
ability to hone a tool which could be applied throughout science. Thus
in particular, most of the calculations are done with the real numbers
or complex numbers being implicitly understood.
Mathematical Analysis includes many of the MSC primary headings, a large portion of the
mathematics literature, and much of the most directly applicable mathematics.
Perhaps, then, it is appropriate to subdivide this topic; although schemes for
this subdivision are not very standard, we may identify five neighborhoods
in the "MathMap", shown here in varying shades of green.
We will treat each of these areas in a separate page. (The division of
Analysis into parts is not particularly sharp, but we will be able to make
comments drawing together neighboring fields on the MathMap, so we accept
this division for the purposes of a tour!).
- Calculus and real analysis: differentiation, integration, series, and so on.
- Complex variables: considers those aspects of analytic behaviour unique to complex functions. (Complex variables are also often accepted in other parts of analysis when this causes no essential change in the theory).
- Differential and integral equations: seeks to describe functions f using relationships between f and its derivatives or integrals; study of differential operators and their applications in mathematics
- Theory of functions: study of vector spaces of functions, bases (e.g. Fourier analysis), and linear maps (e.g. integral transforms)
- Numerical analysis and optimization
Click on any of these major headings to take a short tour. You might
want to begin with classical analysis.
When you're done with analysis,
you might want to continue the tour with a trip through probability and statistics.
You can reach this page through http://www.math-atlas.org/welcome.html
Last modified 2000/01/25 by Dave Rusin. Mail: