Math Basics

Number Systems

• Natural Numbers: 1, 2, 3,... (positive integers)
• Whole Numbers: 0, 1, 2, 3,... (non-negative integers)
• Integers:..., -3, -2, -1, 0, 1, 2, 3,... (positive and negative whole numbers, including zero)
• Rational Numbers: a/b, where a and b are integers, and b ≠ 0 (fractions)
• Irrational Numbers: cannot be expressed as a/b, where a and b are integers (e.g. π, e)
• Real Numbers: includes rational and irrational numbers
• Complex Numbers: a + bi, where a and b are real numbers, and i is the imaginary unit (i² = -1)

Algebra

• Variables: letters or symbols that represent unknown values
• Constants: numbers
• Expressions: combinations of variables, constants, and mathematical operations
• Equations: statements that two expressions are equal
• Inequalities: statements that one expression is greater than, less than, or equal to another

Geometry

• Points: locations in space, represented by coordinates (x, y) in 2D, or (x, y, z) in 3D
• Lines: sets of points extending infinitely in two directions
• Rays: lines extending from a single point
• Angles: formed by two rays sharing a common endpoint
• Triangles: polygons with three sides and three angles

Calculus

• Limits: the behavior of a function as the input approaches a certain value
• Derivatives: rates of change of functions with respect to the input
• Integrals: accumulation of rates of change over a defined interval
• Differentiation: finding the derivative of a function
• Integration: finding the integral of a function

This is a brief overview of some key concepts in mathematics. There is much more to explore in each of these areas!