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Development of Mathematics

Basics of Counting

  • Numbers
  • Number Line
  • Addition and Division
  • Subtraction, Multiplication, Exponentiation
  • Fractions
  • Ratios
  • Decimals
  • Zero and Infinity
  • Prime Numbers
  • Factorization
  • Natural Numbers
  • Whole Numbers
  • Integers
  • Negative Numbers
  • Rational and Irrational Numbers
  • Sequences and Series
  • Arithmetic, Geometric and Harmonic Progressions
  • Permutations and Combinations
  • Real Numbers
  • Imaginary Numbers
  • Complex Numbers
  • Bases and Logarithms

Basics of Geomtery

  • Shapes
  • Lines and Rays
  • Angles
  • Parallel and Perpendicular Lines
  • Angle Bisectors
  • Triangles
  • Circles
  • Squares and Rectangles
  • Parallelograms, Trapeziums and Rhombuses
  • Quadrilaterals
  • Polygons
  • Perimeters and Areas of Shapes
  • Construction of Shapes
  • Theory of Shapes
  • Properties of Triangles
  • Sections of Circles
  • Cubes and Spheres
  • Cones and Frustums
  • Surface Areas and Volumes of Solids
  • Polyhedra

Statistics

  • Mean
  • Charts and Graphs
  • Probability
  • Median and Mode

Algebra

  • Variables and Constants
  • Linear Algebra in one variable
  • Linear Algebra in two variables
  • Graphs
  • Polynomials
  • Linear Inequalities
  • Linear Programming
  • Matrices
  • Determinants
  • Dimensions
  • Vectors
  • Flow
  • Divergence and Curl
  • Tensors

Sets and Relations

  • Sets
  • Set Operations
  • Relations
  • Properties of Relations
  • Functions
  • Properties of Binary Operations
  • Category Theory
  • Rings
  • Groups
  • Fields

Mathematical Logic

  • Logic and Reasoning
  • Proofs and Derivations

Calculus

  • Limits
  • Derivatives and Differentiation
  • Integration
  • Calculus in one variable
  • Differential Equations
  • Functions of multiple variables
  • Calculus in multiple variables

Coordinate Geomtery

  • Lines and Distances
  • Sections of Cones
  • Circles
  • Ellipses
  • Parabolas
  • Hyperbolas
  • Trigonometry
  • Trigonometric Functions
  • Three Dimensional Coordinate Geometry
  • Quaternions

Analytical Algebra

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

Topology

  • Euclidiean Spaces
  • Orientable Surfaces
  • Non-orientable Surfaces
  • Mobius Strips
  • Klein Bottles
  • Toruses

Big Numbers

  • Googology
  • Tetration
  • TREE()
  • SSCG()
  • Rayo's Number
  • Types of Infinities
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