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Algebraic Geometry treats solution sets of polynomial equations as geometric objects. A basic example is provided by the equation x²+y²=1 whose real solutions form a circle in 2-space. Algebraic geometry combines the intuition from geometry with concepts from advanced algebra, such as rings and modules, to study geometric properties of these solution sets.
Since polynomial equations are ubiquitous in mathematics and science, there are many connections to other fields, such as Kähler geometry, complex analysis, number theory and mathematical physics. Furthermore algebraic geometry has applications in seemingly distant fields, such as cryptography and coding theory.
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