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[Geometric areas of MathMap]

Geometric Areas of Mathematics

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Here we consider all the fields which exercise our geometric intuition: from Euclidean and analytic geometry to tilings and tessellations, from the Klein bottle to knots, along with curvature, soap bubbles and the very idea of dimension.

One of the oldest areas of mathematical discovery, geometry has undergone several rebirths over the centuries. At one extreme, geometry includes the very precise study of rigid structures first seen in Euclid's Elements; at the other extreme, general topology focuses on the very fundamental kinships among shapes. (There is also a more subtle notion of "geometry" implied in Algebraic Geometry (14), which is frankly quite algebraic.)

Here the MathMap shows the Geometry areas in a yellow-orange and the Topology areas in a yellow-green. Other fairly geometric areas are K-theory (19), Lie Groups (22), Several Complex Variables (32), and to some extent Global Analysis (58) and the Calculus of Variations (49).

The remaining three areas are collectively known as Topology.

The geometric areas share with the fields of algebra the tendency to distill their inquiry to the study of certain axioms and their consequences; during the last half-century the ties between these broad areas have increased. On the other hand, some of the geometric areas remain close to analysis, particularly General Topology (to measure theory and functional analysis) and Differential Geometry (to differential equations and complex analysis).

You might want to continue the tour with a trip through analysis.

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Last modified 1999/05/12 by Dave Rusin. Mail: feedback@math-atlas.org