mathematical terms with definition

3 min read 16-03-2025

Mathematics, the language of the universe, relies on a precise vocabulary. This article provides definitions for essential mathematical terms, categorized for easier understanding. Whether you're a student brushing up on your knowledge or a curious individual, this resource will expand your mathematical lexicon.

I. Fundamental Concepts

1. Number Systems

Natural Numbers (ℕ): The counting numbers: 1, 2, 3, 4,...
Whole Numbers (𝕎): Natural numbers including zero: 0, 1, 2, 3, 4,...
Integers (ℤ): Whole numbers and their negatives: ..., -3, -2, -1, 0, 1, 2, 3,...
Rational Numbers (ℚ): Numbers expressible as a fraction p/q, where p and q are integers and q ≠ 0. Examples include 1/2, -3/4, 0.75 (which is 3/4).
Irrational Numbers: Numbers that cannot be expressed as a fraction of two integers. Famous examples include π (pi) and √2 (the square root of 2).
Real Numbers (ℝ): The union of rational and irrational numbers. All numbers that can be plotted on a number line.
Complex Numbers (ℂ): Numbers of the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit (√-1).

2. Basic Operations

Addition (+): Combining two or more numbers to find their total.
Subtraction (-): Finding the difference between two numbers.
Multiplication (× or ·): Repeated addition; finding the product of two or more numbers.
Division (÷ or /): Splitting a number into equal parts; finding the quotient of two numbers.
Exponentiation: Raising a number to a power (e.g., 2³ = 2 × 2 × 2 = 8). The base is the number being raised to a power, and the exponent is the power.

3. Algebraic Concepts

Variable: A symbol (usually a letter) representing an unknown quantity.
Constant: A fixed value that does not change.
Expression: A combination of variables, constants, and operations. Example: 3x + 5.
Equation: A statement that two expressions are equal. Example: 3x + 5 = 14.
Inequality: A statement that compares two expressions using inequality symbols (<, >, ≤, ≥). Example: 2x + 1 > 7.
Function: A rule that assigns each input value to exactly one output value. Often represented as f(x) = ...

II. Geometry and Trigonometry

1. Geometric Shapes

Point: A location in space.
Line: A straight path extending infinitely in both directions.
Line Segment: A part of a line with two endpoints.
Ray: A part of a line with one endpoint extending infinitely in one direction.
Angle: Formed by two rays sharing a common endpoint (vertex).
Triangle: A polygon with three sides and three angles.
Quadrilateral: A polygon with four sides and four angles. Examples include squares, rectangles, parallelograms, trapezoids.
Circle: A set of points equidistant from a central point.
Polygon: A closed two-dimensional figure with straight sides.

2. Trigonometric Functions

Sine (sin): In a right-angled triangle, the ratio of the length of the side opposite an angle to the length of the hypotenuse.
Cosine (cos): In a right-angled triangle, the ratio of the length of the side adjacent to an angle to the length of the hypotenuse.
Tangent (tan): In a right-angled triangle, the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle.

III. Calculus and Analysis

Limit: The value a function approaches as its input approaches a certain value.
Derivative: The instantaneous rate of change of a function. It measures the slope of the tangent line to a curve at a point.
Integral: The area under a curve. It's the reverse operation of differentiation.

IV. Statistics and Probability

Mean: The average of a set of numbers.
Median: The middle value in a set of numbers when they are arranged in order.
Mode: The value that appears most frequently in a set of numbers.
Probability: The likelihood of an event occurring. Expressed as a number between 0 and 1.

This is not an exhaustive list, but it covers many fundamental mathematical terms. Further exploration into specific branches of mathematics will introduce more specialized vocabulary. Remember, understanding the definitions is crucial for mastering mathematical concepts.