# Pure Math

## Pre-Algebra & Algebra

**Pre-algebra**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,
- q-analogs,
- 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,
- first-order 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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