Pure Math
PreAlgebra & Algebra
Prealgebra problems and discussion, such as natural numbers, variables, expressions evaluation, integers, fractions, decimals and negative numbers; and algebra topics, discussing such problems as inequalities, polynomials, exponents, monomials, relations and functions.
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Calculus
Calculus involves: complex, functional and real analysis,
 integration and measure theory,
 harmonic analysis,
 multivariable calculus,
 qanalogs,
 variational topics, and
 tensor theory.
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Geometry
Geometry is "the study of spatial figures like circles and cubes." [src] Includes topology. Geometry studies topics such as: curves,
 triangles,
 circles and pi,
 general topology,
 differential and algebraic geometry,
 algebraic and geometric topology,
 knot theory and lie groups,
 properties of points,
 Riemannian and metric geometry, and
 scheme theory.
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Combinatorics
Combinatorics is "the study of discrete (and usually finite) objects," [src] as well as graph theory.
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Logic
Logical mathematics is the foundation of all mathematics, and focuses on: Boolean algebra,
 firstorder theories,
 large cardinal properties, and
 set theory.
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Number Theory
Number Theory "studies natural, or whole, numbers," [src] and also discusses: algebraic and recreational number theory,
 Diophantine theory,
 prime numbers, and
 zeta functions.
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