Mathematics vocabulary list with definitions

Mathematics vocabulary list with definitions

Mathematics: A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entierely constitued with symbols of various types, many symbols are needed for expressing all mathematics.

List of Mathematics vocabulary

Mathematics Vocabulary with Definitions and Examples

Addition

• Definition: The process of finding the total or sum by combining two or more numbers.
• Example: 5+3=85 + 3 = 85+3=8

Subtraction

• Definition: The process of finding the difference between two numbers by removing the value of one from the other.
• Example: 10−4=610 – 4 = 610−4=6

Multiplication

• Definition: The process of finding the product by combining multiples of one number with another.
• Example: 6×7=426 \times 7 = 426×7=42

Division

• Definition: The process of finding how many times one number is contained within another.
• Example: 20÷4=520 \div 4 = 520÷4=5

Equation

• Definition: A mathematical statement that asserts the equality of two expressions.
• Example: x+2=5x + 2 = 5x+2=5

Fraction

• Definition: A numerical quantity that is not a whole number, representing a part of a whole.
• Example: 34\frac{3}{4}43​

Decimal

• Definition: A number that uses a decimal point to show a part of a whole.
• Example: 0.750.750.75

Percentage

• Definition: A fraction or ratio expressed as a part of 100.
• Example: 50%50\%50% means 50 out of 100.

Ratio

• Definition: A relationship between two numbers indicating how many times the first number contains the second.
• Example: The ratio of 2 to 5 is 2:52:52:5.

Proportion

• Definition: An equation that states two ratios are equivalent.
• Example: 12=24\frac{1}{2} = \frac{2}{4}21​=42​

Variable

• Definition: A symbol used to represent a number in mathematical expressions or equations.
• Example: In x+3=7x + 3 = 7x+3=7, xxx is the variable.

Constant

• Definition: A fixed value that does not change.
• Example: In the equation y=2x+5y = 2x + 5y=2x+5, 5 is a constant.

Algebra

• Definition: A branch of mathematics dealing with symbols and the rules for manipulating those symbols.
• Example: Solving for xxx in 2x+3=72x + 3 = 72x+3=7 is an algebra problem.

Geometry

• Definition: The branch of mathematics concerning the properties and relations of points, lines, surfaces, and solids.
• Example: Calculating the area of a triangle is a geometry problem.

Trigonometry

• Definition: The branch of mathematics dealing with the relationships between the angles and sides of triangles.
• Example: Using sine, cosine, and tangent functions to find missing sides or angles in a right triangle.

Calculus

• Definition: The branch of mathematics that deals with the finding and properties of derivatives and integrals of functions.
• Example: Calculating the rate of change of a function is a calculus problem.

Theorem

• Definition: A statement that has been proven on the basis of previously established statements.
• Example: The Pythagorean theorem states that a2+b2=c2a^2 + b^2 = c^2a2+b2=c2 for a right triangle.

Proof

• Definition: A logical argument that shows a statement is true.
• Example: Proving that the sum of the angles in a triangle is 180 degrees.

Function

• Definition: A relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
• Example: f(x)=x2f(x) = x^2f(x)=x2 is a function.

Graph

• Definition: A diagram representing a mathematical function or relationship between variables.
• Example: The graph of y=x2y = x^2y=x2 is a parabola.

Matrix

• Definition: A rectangular array of numbers or other mathematical objects, for which operations such as addition and multiplication are defined.
• Example: (1234)\begin{pmatrix}1 & 2 \\ 3 & 4\end{pmatrix}(13​24​) is a matrix.

Determinant

• Definition: A scalar value that can be computed from the elements of a square matrix and encodes certain properties of the matrix.
• Example: The determinant of the matrix (1234)\begin{pmatrix}1 & 2 \\ 3 & 4\end{pmatrix}(13​24​) is 1⋅4−2⋅3=−21 \cdot 4 – 2 \cdot 3 = -21⋅4−2⋅3=−2.

Vector

• Definition: A quantity having direction as well as magnitude.
• Example: v=(34)\mathbf{v} = \begin{pmatrix}3 \\ 4\end{pmatrix}v=(34​) is a vector.

Scalar

• Definition: A quantity with only magnitude.
• Example: Speed is a scalar quantity, whereas velocity is a vector.

Integral

• Definition: A fundamental concept of calculus that represents the area under a curve.
• Example: The integral of f(x)=xf(x) = xf(x)=x from 0 to 1 is 12\frac{1}{2}21​.

Derivative

• Definition: A measure of how a function changes as its input changes.
• Example: The derivative of f(x)=x2f(x) = x^2f(x)=x2 is f′(x)=2xf'(x) = 2xf′(x)=2x.

Limit

• Definition: The value that a function or sequence approaches as the input or index approaches some value.
• Example: The limit of f(x)=1xf(x) = \frac{1}{x}f(x)=x1​ as xxx approaches infinity is 0.

Sequence

• Definition: An ordered list of numbers.
• Example: The sequence 2, 4, 6, 8, … is an arithmetic sequence.

Series

• Definition: The sum of the terms of a sequence.
• Example: The series 1 + 2 + 3 + … + n.

Polynomial

• Definition: An expression consisting of variables and coefficients, involving only addition, subtraction, multiplication, and non-negative integer exponents of variables.
• Example: x2+2x+1x^2 + 2x + 1×2+2x+1 is a polynomial.

Quadratic

• Definition: A polynomial of degree two.
• Example: ax2+bx+cax^2 + bx + cax2+bx+c is a quadratic equation.

Linear

• Definition: An expression or equation of degree one.
• Example: y=2x+3y = 2x + 3y=2x+3 is a linear equation.

Exponential

• Definition: A function in which an independent variable appears in the exponent.
• Example: f(x)=exf(x) = e^xf(x)=ex is an exponential function.

Logarithm

• Definition: The inverse operation to exponentiation.
• Example: log⁡10(100)=2\log_{10}(100) = 2log10​(100)=2 because 102=10010^2 = 100102=100.

Probability

• Definition: A measure of the likelihood that an event will occur.
• Example: The probability of flipping a coin and getting heads is 12\frac{1}{2}21​.

Statistics

• Definition: The practice or science of collecting and analyzing numerical data.
• Example: Statistics is used to analyze survey results.

Mean

• Definition: The average of a set of numbers.
• Example: The mean of 2, 4, 6 is 2+4+63=4\frac{2 + 4 + 6}{3} = 432+4+6​=4.

Median

• Definition: The middle value in a list of numbers.
• Example: The median of 1, 3, 3, 6, 7, 8, 9 is 6.

Mode

• Definition: The value that appears most frequently in a data set.
• Example: The mode of 1, 2, 2, 3, 4 is 2.

Range

• Definition: The difference between the highest and lowest values in a data set.
• Example: The range of 4, 6, 9, 3 is 9−3=69 – 3 = 69−3=6.

Standard deviation

• Definition: A measure of the amount of variation or dispersion in a set of values.
• Example: A small standard deviation indicates that the values are close to the mean.

Variance

• Definition: The expectation of the squared deviation of a random variable from its mean.
• Example: Variance measures how far a set of numbers are spread out from their average value.

Histogram

• Definition: A graphical representation of the distribution of numerical data.
• Example: A histogram can show the frequency of data within certain intervals.

Probability distribution

• Definition:A mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.
• The normal distribution is a type of probability distribution.

Sample

• Definition: A subset of a population that is selected for study to gather information about the whole.
• Example: A survey might collect a sample of 1000 people to estimate public opinion.

Population

• Definition: The entire pool from which a statistical sample is drawn.
• Example: The population of a country consists of all its residents.

Hypothesis

• Definition: A proposed explanation for a phenomenon based on limited evidence as a starting point for further investigation.
• Example: A scientist might propose a hypothesis to explain the results of an experiment.

Regression

• Definition: A statistical method used to determine the strength and direction of the relationship between two or more variables.
• Example: Linear regression can be used to predict the value of one variable based on another.

Correlation

• Definition: A statistical measure indicating how closely two variables are related.
• Example: There is a positive correlation between study hours and exam scores.

Permutation

• Definition: An arrangement of objects in a specific order.
• Example: The number of permutations of the letters in the word “math” is 24.

Combination

• Definition: A selection of items from a larger pool where the order of selection does not matter.
• Example: The number of combinations of 3 items from a set of 5 is 10.

Factorial

• Definition: The product of all positive integers up to a given number.
• Example: 5!=5×4×3×2×1=1205! = 5 \times 4 \times 3 \times 2 \times 1 = 1205!=5×4×3×2×1=120.

Prime number

• Definition: A natural number greater than 1 that has no positive divisors other than 1 and itself.
• Example: 7 is a prime number because its only divisors are 1 and 7.

Composite number

• Definition: A natural number greater than 1 that is not prime, meaning it has divisors other than 1 and itself.
• Example: 9 is a composite number because it can be divided evenly by 3 and 9.

Rational number

• Definition: A number that can be expressed as a fraction where the numerator and denominator are integers.
• Example: 34\frac{3}{4}43​ is a rational number.

Irrational number

• Definition: A number that cannot be expressed as a fraction of two integers and has an infinite decimal representation that does not repeat.
• Example: 2\sqrt{2}2​ is an irrational number.

Real number

• Definition: A number that can be found on the number line, including both rational and irrational numbers.
• Example: 3, π\piπ, and 5\sqrt{5}5​ are all real numbers.

Complex number

• Definition: A number that can be expressed in the form a+bia + bia+bi, where aaa and bbb are real numbers and iii is the imaginary unit.
• Example: 3+2i3 + 2i3+2i is a complex number.

Imaginary number

• Definition: A number that can be expressed as a real number multiplied by the imaginary unit iii, where i2=−1i^2 = -1i2=−1.
• Example: 2i2i2i is an imaginary number.

Angle

• Definition: The figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
• Example: In a right triangle, one of the angles is 90 degrees.

Triangle

• Definition: A polygon with three edges and three vertices.
• Example: An equilateral triangle has all sides and angles equal.

Circle

• Definition: The set of all points in a plane that are at a given distance from a given point, the center.
• Example: The Earth’s equator is an example of a circle.

Radius

• Definition: A line segment joining the center of a circle or sphere to any point on the circumference or surface.
• Example: The radius of a circle is half of its diameter.

Diameter

• Definition: A straight line passing from side to side through the center of a body or figure, especially a circle or sphere.
• Example: The diameter of a circle is twice its radius.

Circumference

• Definition: The distance around the edge of a circle.
• Example: The circumference of a circle can be found using the formula 2πr2 \pi r2πr, where rrr is the radius.

Area

• Definition: The amount of space inside the boundary of a flat (two-dimensional) object.
• Example: The area of a rectangle is calculated by multiplying its length by its width.

Perimeter

• Definition: The distance around the edge of a closed two-dimensional shape.
• Example: The perimeter of a square with side length 5 units is 4×5=204 \times 5 = 204×5=20 units.

Volume

• Definition: The amount of space occupied by a three-dimensional object or region of space, expressed in cubic units.
• Example: The volume of a cube with side length 3 units is 33=273^3 = 2733=27 cubic units.

Surface area

• Definition: The total area of the surface of a three-dimensional object.
• Example: The surface area of a cylinder can be found using the formula 2πrh+2πr22\pi rh + 2\pi r^22πrh+2πr2, where rrr is the radius and hhh is the height.

Cube

• Definition: A three-dimensional geometric shape with six square faces, twelve edges, and eight vertices.
• Example: A Rubik’s cube is an example of a cube.

Sphere

• Definition: A perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball.
• Example: The Earth is approximately a sphere.

Cylinder

• Definition: A three-dimensional geometric shape with two parallel bases that are congruent circles.
• Example: A can of soda is in the shape of a cylinder.

Pyramid

• Definition: A polyhedron formed by connecting a polygonal base and a point, called the apex, by triangular faces.
• Example: The Great Pyramid of Giza is an example of a pyramid.

Cone

• Definition: A three-dimensional geometric shape that tapers smoothly from a flat, round base to a point called the apex or vertex.
• Example: An ice cream cone is a cone-shaped object.

Parallelogram

• Definition: A quadrilateral with opposite sides parallel and equal in length.
• Example: A rectangle and a rhombus are examples of parallelograms.

Rectangle

• Definition: A quadrilateral with four right angles.
• Example: The screen of a television is shaped like a rectangle.

Square

• Definition: A regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or right angles).
• Example: A chessboard is made up of 64 squares.

Trapezoid

• Definition: A quadrilateral with at least one pair of parallel sides.
• Example: The shape of a baseball field, a kite, and a basketball court are all trapezoids.

Polygon

• Definition: A flat shape with straight sides.
• Example: A triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, and decagon are all types of polygons.

Vertex

• Definition: A point where two or more straight lines meet.
• Example: In geometry, a vertex is a point where two or more edges meet.

Edge

• Definition: The line segment where two faces of a solid figure meet.
• Example: The edges of a cube are the 12 line segments where the faces meet.

Face

• Definition: A flat surface of a three-dimensional object.
• Example: A cube has six faces, each of which is a square.

Coordinate system

• Definition: A system that uses one or more numbers, or coordinates, to determine the position of a point or other geometric element on a plane or in space.
• Example: The Cartesian coordinate system is used to plot points in a plane.

Cartesian plane

• Definition: A two-dimensional coordinate system in which a point is determined by its distance from two perpendicular lines.
• Example: The x-axis and y-axis intersect at right angles to form the Cartesian plane.

Origin

• Definition: The point where the x-axis and y-axis intersect in a Cartesian coordinate system, usually represented by (0,0).
• Example: In the Cartesian plane, the origin is the point (0, 0).

Slope

• Definition: A measure of the steepness or incline of a line, usually represented as the ratio of the rise to the run.
• Example: The slope of the line y = 2x + 3 is 2.

Intercept

• Definition: The point at which a line crosses the x-axis or y-axis.
• Example: The y-intercept of the line y = 2x + 3 is 3.

Asymptote

• Definition: A line that a curve approaches as it heads towards infinity.
• Example: The line y = 0 is a horizontal asymptote of the function f(x)=1xf(x) = \frac{1}{x}f(x)=x1​.

Parabola

• Definition: A symmetric, U-shaped curve that represents the graph of a quadratic function.
• Example: The graph of y = x^2 is a parabola.

Hyperbola

• Definition: A type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.
• Example: The graph of the equation x2a2−y2b2=1\frac{x^2}{a^2} – \frac{y^2}{b^2} = 1a2x2​−b2y2​=1 is a hyperbola.

Ellipse

• Definition: A plane curve that surrounds two focal points, such that the sum of the distances to the two focal points is constant for every point on the curve.
• Example: The orbit of planets around the sun is elliptical.

Vector space

• Definition: A collection of vectors that can be added together and multiplied by numbers, called scalars in this context.
• Example: The set of all 3-dimensional vectors forms a vector space.

Eigenvalue

• Definition: A scalar value associated with a linear system of equations that, when multiplied by a given eigenvector, does not change its direction in the vector space.
• Example: If Av=λvA \mathbf{v} = \lambda \mathbf{v}Av=λv, then λ\lambdaλ is the eigenvalue.

Eigenvector

• Definition: A vector that does not change direction during a linear transformation, only its magnitude is scaled by a factor called the eigenvalue.
• Example: In the equation Av=λvA \mathbf{v} = \lambda \mathbf{v}Av=λv, v\mathbf{v}v is the eigenvector.

Diagonalization

• Definition: The process of finding a corresponding diagonal matrix for a given square matrix.
• Example: Matrix AAA can be diagonalized if there exists a matrix PPP such that P−1APP^{-1}APP−1AP is a diagonal matrix.

Orthogonality

• Definition: The property of being perpendicular to each other.
• Example: In vector spaces, two vectors are orthogonal if their dot product is zero.

Symmetry

• Definition: A characteristic where one part of an object is a mirror image or exact replica of another part.
• Example: A circle has rotational symmetry.

Transformation

• Definition: An operation that moves or changes a shape in some way, while still preserving its general properties.
• Example: Translation, rotation, reflection, and scaling are types of transformations.

Rotation

• Definition: A circular movement of an object around a center or point of rotation.
• Example: Rotating a square 90 degrees around its center.

Reflection

• – Definition: A transformation representing a flip of a figure over a line, where the figure is the mirror image of the other side of the line.
• – Example: Reflecting a triangle over the y-axis.

Divider

• – Definition: A tool used in geometry for measuring and marking off distances.
• – Example: A pair of dividers is used to measure the distance between two points on a map.

Integer

• – Definition: A whole number that can be positive, negative, or zero, but not a fraction.
• – Example: -3, 0, and 7 are integers.

Problem

• – Definition: A question or exercise in mathematics that requires a solution.
• – Example: Solving for xxx in the equation 2x+5=132x + 5 = 132x+5=13 is a problem.

Quotient

• – Definition: The result obtained by dividing one quantity by another.
• – Example: The quotient of 10 divided by 2 is 5.

Remainder

• – Definition: The amount left over after division when one number does not exactly divide another.
• – Example: The remainder of 10 divided by 3 is 1.

Simplex

• – Definition: A generalization of the concept of a triangle or tetrahedron to arbitrary dimensions.
• – Example: A 2-simplex is a triangle, and a 3-simplex is a tetrahedron.

Mathematics Dictionary

Letter A

Letter B

Letter C

Letter D

Letter E

Letter F

Letter G

Letter H

Letter I

Letter J

Letter K

Letter L

Letter M

Letter N

Letter O

Letter P

Letter Q

Letter R

Letter S

Letter T

Letter U

Letter V

Letter W

Letter X

Letter Y

Letter Z

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