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* [[Analysis]]. Analysis is concerned with limits and other infinite processes. This subject includes the theory of limits of sequences and series and all forms of [[calculus]], including the calculus of several variables, [[vector calculus]] and [[tensor calculus]]. Also included is [[numerical analysis]], the study of error propagation in algorithms carried out to finite precision.  Additional topics in analysis include [[real analysis]] and [[complex analysis]].

* [[Analysis]]. Analysis is concerned with limits and other infinite processes. This subject includes the theory of limits of sequences and series and all forms of [[calculus]], including the calculus of several variables, [[vector calculus]] and [[tensor calculus]]. Also included is [[numerical analysis]], the study of error propagation in algorithms carried out to finite precision.  Additional topics in analysis include [[real analysis]] and [[complex analysis]].

* [[Geometry]] and [[Topology]]. Geometry was defined by [[Felix Klein]] as the study of [[invariants]] under [[group]]s of [[transformation]]s. For example, the [[Euclidean transformation]]s are [[translation]], [[rotation]] and [[reflection]]. The quantities that are not altered by these transformations are things like angles and distances, so these are the subjects of interest in [[Euclidean geometry]]. Other types of transformations, such as the [[affine transformation]]s, define other types of geometry. Topology is concerned with the connectedness of objects, rather than the distance between them. It is sometimes called 'rubber sheet geometry', as it concerns properties (that is, [[arc]]s between [[node]]s in [[network]]s) of objects that would be preserved even if a diagram of them were to be stretched or shrunk. Topology began with [[Leonard Euler]]'s consideration of the [[Königsberg Bridges Problem]], which also introduced [[Graph Theory]]. [[Beck's map of the London Underground]] in 1933 used a topological distortion of the locations of the subway stations in order to produce a more useful and artistic map.

* [[Geometry]] and [[Topology]]. Geometry was defined by [[Felix Klein]] as the study of [[invariants]] under [[group]]s of [[transformation]]s. For example, the [[Euclidean transformation]]s are [[translation]], [[rotation]] and [[reflection]]. The quantities that are not altered by these transformations are things like angles and distances, so these are the subjects of interest in [[Euclidean geometry]]. Other types of transformations, such as the [[affine transformation]]s, define other types of geometry. Topology is concerned with the connectedness of objects, rather than the distance between them. It is sometimes called 'rubber sheet geometry', as it concerns properties (that is, [[arc]]s between [[node]]s in [[network]]s) of objects that would be preserved even if a diagram of them were to be stretched or shrunk. Topology began with [[Leonard Euler]]'s consideration of the [[Königsberg Bridges Problem]], which also introduced [[Graph Theory]]. [[Beck's map of the London Underground]] in 1933 used a topological distortion of the locations of the subway stations in order to produce a more useful and artistic map.  [[Differential geometry]] is a specialized field of its own.

* [[Logic]] and [[set theory]]. All of mathematics can be expressed in terms of [[set]]s. Sets are defined by a collection of [[axiom]]s called the [[Zermelo-Fraenkel axioms]]. One of the axioms, the [[Axiom of Choice]], has been the subject of much discussion.

* [[Logic]] and [[set theory]]. All of mathematics can be expressed in terms of [[set]]s. Sets are defined by a collection of [[axiom]]s called the [[Zermelo-Fraenkel axioms]]. One of the axioms, the [[Axiom of Choice]], has been the subject of much discussion.

[[Category:Mathematics]]

[[Category:Mathematics]]