Mathematics
What Is Mathematics?
Mathematics is the study of numbers, quantities, shapes, and patterns. It's the language we use to describe the structure of the universe — from the orbits of planets to the algorithms running on your phone.
Arithmetic: The Basics
Arithmetic deals with basic operations on numbers:
- Addition (+) — combining quantities
- Subtraction (−) — finding the difference
- Multiplication (×) — repeated addition
- Division (÷) — splitting into equal parts
Algebra
Algebra uses symbols (usually letters like x, y) to represent unknown values. Instead of solving one specific problem, algebra gives you tools to solve entire families of problems.
Geometry
Geometry studies shapes, sizes, and the properties of space. Key concepts include:
- Points, lines, and planes — the building blocks of space
- Angles — measured in degrees or radians
- Triangles — the sum of interior angles always equals 180°
- Circles — circumference = 2πr, area = πr²
Calculus
Calculus is the mathematics of change. It has two main branches:
- Differentiation — finds the rate at which something changes (the slope of a curve at any point)
- Integration — accumulates quantities over time or space (the area under a curve)
These two operations are inverses of each other, connected by the Fundamental Theorem of Calculus.
Statistics & Probability
Statistics helps us make sense of data. Probability quantifies uncertainty. Together they power everything from medical trials to weather forecasts.
- Mean — the average of a dataset
- Median — the middle value
- Standard deviation — how spread out the data is
- Probability — a value from 0 (impossible) to 1 (certain)