Branch
Primary Focus
Key Concepts & Areas
Arithmetic
The study of numbers and basic operations.
Addition, Subtraction, Multiplication, Division, Fractions, Percentages.
Algebra
The study of structure, represented by variables and symbols in formulas and equations.
Solving equations, Polynomials, Abstract Algebra (groups, rings, fields), Linear Algebra (vectors, matrices).
Geometry
The study of shapes, sizes, positions, and properties of space.
Triangles, Circles, Angles, Area, Volume, Euclidean and Non-Euclidean Geometry.
Trigonometry
The study of the relationships between the sides and angles of triangles.
Sine (sin), Cosine (cos), Tangent (tan), Identities, and applications in surveying and navigation.
Calculus
The study of continuous change, including limits, rates of change, and accumulation.
Differential Calculus (derivatives, slopes) and Integral Calculus (integrals, area under curves).
Number Theory
The study of the properties and relationships of integers (whole numbers).
Prime numbers, Divisibility, Modular Arithmetic, applications in Cryptography.
Analysis
The rigorous study of limits, continuity, and the mathematical foundations of calculus.
Real Analysis, Complex Analysis, Functional Analysis, Differential Equations.
Statistics & Probability
The study of data (collection, analysis, interpretation) and the mathematics of chance and uncertainty.
Mean, Median, Mode, Regression, Normal Distribution, Statistical Inference.
Discrete Mathematics
The study of countable or separate structures, often used in computer science.
Combinatorics (counting), Graph Theory, Logic, Algorithms, Set Theory.
Topology
The study of properties of spaces that are preserved under continuous deformations (stretching, bending, but not tearing).
Homeomorphism, Manifolds, Algebraic Topology, Knot Theory.