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