CALC
Math
What's is Mathematics?
"Mathematics is the abstract study of quantity, structure, space, and change. It acts as a universal language and tool, using logical reasoning, patterns, and symbols to model and solve problems in science, technology, and everyday life." (MAA)
The Four Pillars of Mathematics
Mathematics is broadly divided into several core branches:
Arithmetic & Number Theory: The foundational study of numbers (like addition and multiplication) and their properties.
Algebra: The study of structure and variables, allowing us to generalize relationships and solve unknown quantities through equations.
Geometry & Topology: The study of space, shapes, sizes, and relative positions of objects.
Calculus & Analysis: The study of change and motion, encompassing rates, limits, and how things accumulate over time.
Arithmetic
Arithmetic is the oldest and most fundamental branch of mathematics, focusing on the study of numbers and the basic operations performed with them. It serves as the foundation for almost all other areas of math and is used daily around the world.
Arithmetic is structured around four primary operations:
Addition (+): Combines quantities to find a total.
Subtraction (−): Finds the difference between quantities or removes a part from a whole.
Multiplication (×): Functions as repeated addition of the same number a specific number of times.
Division (÷): Splits a quantity into equal parts or finds how many times one number fits into another.
To perform these operations, arithmetic utilizes different categories of numbers:
Natural Numbers: Whole, positive counting numbers (0, 1, 2, 3...).
Integers: Include natural numbers, their negative opposites, and zero (..., -2, -1, 0, 1, 2...).
Rational Numbers: Fractions and decimals that represent parts of a whole (such as 1/2 or 0.5).