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