Mathematics

The study of numbers, quantities, shapes, structures, patterns, and their relationships, using abstract reasoning and logical thinking.

Arithmetic

The branch of mathematics that deals with numbers and basic operations such as addition, subtraction, multiplication, and division. It forms the foundational building blocks for more advanced mathematical concepts.

Example: 2 + 2 = 4 is arithmetic.

Algebra

A branch of mathematics dealing with symbols and letters and the rules for manipulating those symbols. It involves solving equations and understanding abstract concepts like variables, functions, and algebraic structures.

Example: a + a = 2a is algebra.

Linear Algebra

A branch of mathematics that deals with linear equations, linear functions, and their representations using vectors and matrices.

Abstract Algebra

A branch of mathematics that studies algebraic structures, which are sets equipped with operations that follow certain rules.

Geometry

The study of shapes, sizes, and the properties of space. It involves points, lines, planes, angles, surfaces, and solids, and explores concepts like congruence, similarity, and symmetry.

Calculus

A branch of mathematics that studies change and motion. It helps us understand how things grow, shrink, speed up, or slow down. It has two main parts:

• Differential Calculus: focuses on how things change at a specific moment. It helps answer questions like “How fast is a car moving right now?” (using derivatives).
• Integral Calculus: deals with adding up tiny pieces to find a total. It helps answer questions like “How far did the car travel over time?” (using integrals).

Topology

A branch of mathematics that studies the properties of spaces that are preserved under continuous deformations, such as stretching, bending, and twisting, but not tearing or cutting. It is often referred to as “rubber sheet geometry.”

Number Theory

Deals with properties of integers and their relationships, such as primes and Diophantine equations.

Algebraic Geometry

A branch of mathematics that uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.

Algebraic Number Theory

A branch of number theory that uses the techniques of abstract algebra to study algebraic number fields (extensions of the rational numbers) and their rings of integers.

Algebraic Topology

Uses algebraic methods to study topological spaces and their properties, such as holes, connectivity, and shape.