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Areas of Mathematics

Basics of Counting

  • Numbers, Number Line
  • Addition and Division
  • Operations
  • Fractions and Ratios
  • Integers and Decimals
  • Rational and Irrational Numbers
  • Prime Numbers and Factorization
  • Zero and Infinity
  • Sequences and Series
  • Permutations and Combinations
  • Real and Imaginary Numbers
  • Complex Numbers
  • Bases and Logarithms

Basics of Geomtery

  • Shapes
  • Lines and Angles
  • Parallel and Perpendicular Lines
  • Angle Bisectors
  • Polygons
  • Circles
  • Perimeter and Area
  • Construction of Lines and Shapes
  • Properties of Shapes
  • Sections of Circles
  • Solids
  • Surface Areas and Volumes
  • Polyhedra

Statistics

  • Mean, Median and Mode
  • Charts and Representations
  • Probability

Algebra

  • Variables
  • Graphs
  • Polynomials
  • Inequalities
  • Linear Programming
  • Vectors, Matrices and Tensors
  • Vector Spaces
  • Flow, Divergence and Curl

Sets and Relations

  • Sets
  • Set Operations
  • Relations
  • Properties of Relations
  • Functions
  • Properties of Binary Operations
  • Rings, Groups and Fields

Mathematical Logic

  • Logic and Reasoning
  • Proofs and Derivations

Calculus

  • Limits and Derivatives
  • Differentiation and Integration
  • Differential Equations

Coordinate Geomtery

  • Lines and Distances
  • Conic Sections
  • Trigonometry
  • Three Dimensional Coordinate Geometry
  • Quaternions

Analytical Algebra

  • Approximations
  • Complex Analysis
  • Real Analysis
  • Physics
  • Fractals

Topology

  • Euclidiean Spaces
  • Dimensions
  • Manifolds
  • Orientable and Non-orientable Manifolds

Big Numbers

  • Googology
  • Types of Infinities
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