Mathematics

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Mathematics

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Mathematics is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies these concepts. Abbreviated forms of the name include math (in American English) and maths (in British English).

Main conceptual divisions

Quantity

Quantity is a fundamental concept related to counting distinct objects and measuring magnitudes that occur along a continuum (examples of the latter idea include length of time, physical length, mass, area, volume, and so forth). This dual nature of quantity is captured in the everyday concepts of "how many" versus "how much", and by the more technical terms discrete versus continuous.

Areas of mathematics primarily focused on quantity include:

• Arithmetic
• Algebra
• Combinatorics
• Number theory
• Numerical analysis

Structure

Structure refers primarily to logical structure, as opposed to physical structure (see also the section on Space below).

Areas of mathematics primarily focused on notions of structure include:

• Algebra
• Analysis

Space

Space refers to both physical and conceptual notions of space, not simply "outer space" (for which see Astronomy and Cosmology).

Areas of mathematics primarily focused on notions of space include:

• Geometry
• Calculus
• Topology

Change

Change...

Areas of mathematics primarily focused on change include:

• Calculus
• Differential equations
• Dynamical systems