Mathematics (or Maths) is the study of numbers, shapes, patterns, and logical relationships between them.
It helps develop logical thinking and problem-solving skills and is widely used in subjects such as science, engineering, economics, and computer science.
Mathematics is made up of different branches that focus on various aspects of numbers and shapes. These include algebra, geometry, calculus, statistics, and many others, each with its own purpose and uses.
Foundations
Arithmetic deals with basic numbers and operations like addition, subtraction, multiplication, and division. It’s the foundation of all math and is used in everyday tasks like shopping or budgeting.
- Numbers
- Arithmetic
- Fractions
- Decimals
- Percentages
- Exponents
- Factors
- Divisibility Rules
- Prime Factorization
- Greatest Common Divisor
- Least Common Multiple
Algebra
Algebra helps us solve problems by setting up equations and representing numbers with letters or symbols, making it easier to work with unknown values.
- Basics of Algebra
- Variables and Constants
- Algebraic Expressions
- Algebraic Equations
- Coefficients
- Properties of Algebraic Equation
Matrices
A matrix is a rectangular arrangement of numbers or functions in rows and columns, used to represent and solve systems of equations and transformations concisely.
Complex Numbers
Complex numbers extend the real number system to include solutions of equations like x² + 1 = 0, using the imaginary unit i, and are written in the form a + ib.
- Introduction
- Algebra of Complex Numbers
- Modulus and Conjugate of a Complex Number
- Argand Plane and Polar Representation
- Complex Roots of Quadratic Equations
- De Moivre's Theorem
Geometry & Measurement
Geometry studies shapes, sizes, and the properties of space. It helps us understand things like angles, lines, circles, and areas.
- Lines and Angles
- Geometric Shapes
- Area and Perimeter
- Surface Area and Volume
- 2D Shapes
- Triangles
- Squares & Rectangles
- Circles
- 3D Shapes
Coordinate Geometry
Coordinate Geometry connects algebra and geometry using a coordinate system. It allows us to represent geometric shapes like points, lines, and curves on a graph using numbers and equations.
- Introduction to Coordinate Geometry
- Points, Lines, and Planes
- Coordinate Axes and Plane
- Cartesian Coordinate System
- X and Y Intercept
- Distance Formula
- Section Formula
- Midpoint Formula
- Conic Section
Trigonometry
Trigonometry studies the relationships between the angles and sides of triangles, especially right-angled triangles.
- Trigonometric Ratios
- Trigonometric Identities
- Trigonometric Functions
- Trigonometric Equations
- Inverse Trigonometric Functions
- Inverse Trigonometric Identities
- Applications of Trigonometry
- Height and Distance
Calculus
Calculus studies continuous change, using concepts such as derivatives, integrals, limits, and infinite series. It is foundational for various fields, including physics, engineering, economics, computer science, and more.
- Differential Calculus
- Differentiation
- Integral Calculus
- Integration
- Limits in Calculus
- Continuity
- Differentiability
- Applications of Derivatives
- Applications of Integrals
Vector Algebra
Vector Algebra deals with vectors, which are quantities that have both magnitude and direction. It helps in solving problems related to movement, force, and geometry in 2D or 3D space using simple mathematical operations.
- Vectors in Maths
- Types of Vectors
- Vector Operations
- Vector Addition
- Dot and Cross Product of Vectors
- Vector Space
Discrete Mathematics
Set Theory
Set Theory is a branch of mathematics that studies collections of objects, called sets. It focuses on understanding relationships between sets, such as union, intersection, and difference.
Number Theory
Number Theory studies the properties and patterns of integers (whole numbers), including how numbers relate through divisibility, remainders, and special number types.
- Integer Properties
- Euclid Division Algorithm
- Fundamental Theorem of Arithmetic
- Modular Arithmetic
- Fermat’s Little Theorem
Combinatorics
Combinatorics helps solve problems related to combinations, permutations, and probabilities simply and logically.
- Fundamental Principle of Counting
- Permutations
- Combinations
- Pigeonhole Principle
- Inclusion-Exclusion Principle
Probability & Statistics
Probability deals with events and quantifies their likelihood of occurring with numerical values ranging from 0 to 1.
- Basic Concepts of Probability
- Probability Theory
- Conditional Probability
- Bayes Theorem
- Random Variable
- Probability Distribution
- Joint, Marginal, and Conditional Distributions
- Descriptive Statistics
- Data Handling
- Measures of Central Tendency
- Inferential Statistics
- Sampling Methods
- Descriptive vs Inferential Statistics
- Measures of Dispersion
Learn by Grade Wise
Explore mathematics resources organized by grade, covering fundamental concepts and topics from primary to senior secondary levels.
- Grade 1 to 5 Maths
- Grade 6 Maths
- Grade 7 Maths
- Grade 8 Maths
- Grade 9 Maths
- Grade 10 Maths
- Grade 11 (Junior High) Maths
- Grade 12 (Senior High) Maths
Maths for Different Domains
Learn how mathematical concepts are applied across various academic and technical domains.
Some Theorems & Formulas
In addition to these branches, some common mathematical theorems and formulas are: