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Mathematics

 
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Basic Math

Adding, substracting, multiplying and division, whole numbers, consumer math, and more!
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Pure Math

 
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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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Applied Math

 
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Dynamical Systems & Differential Equations

Differential equations are "equations having an unknown functions and its derivative." Dynamical systems are when "a fixed rule describes the time dependence of a point in a geometrical space." [src]
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Mathematical Physics

Mathematical physics is "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories." [src] Covers the topics:
  • classical mechanics,
  • quantum theory,
  • relativity,
  • string theory, and
  • wave.

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Computation

Computation is "the study of algorithms and data structures, and in scientific computing, the study of algorithmic methods for solving problems in math, science and engineering." [src] Topics include:
  • computability and complexity,
  • computer vision,
  • formal language and literal string, and
  • numerical analysis.

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Information Theory & Signal Processing

Essentially, information theory "involves the quantification of information." Signal processing is "the analysis, interpretation, and manipulation of signals." [src] Topics include cryptography and algebraic coding.
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Probability & Statistics

This is used to calculate uncertain events "or knowledge." Statistics, of course, is "the science with collecting and analyzing data." [src] Topics of study include:
  • stochastic processes,
  • probability distributions and theory, and
  • regression analysis.

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Game Theory

Game theory "uses model to study interactions with formalized incentive structures." [src]
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Operations Research

"The study and use of mathematical models, statistics, and algorithms to aid in decision-making, typically with the goal of improving or optimizing performance of real-world systems." [src]
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