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A mathematics dictionary you can calculate with.
Look up a term, see what its symbols mean, follow a compact example, then open a calculator that puts the concept to work.
Browse A–Z Browse symbols Mathematics calculatorsSearch by term, symbol or meaning
71 mathematical terms
71 terms
A
Absolute value
The non-negative distance of a real number from zero on the number line.
|x| Read and calculate Geometry and trigonometry Angle
The amount of rotation between two rays that share an endpoint.
θ Read and calculate Symbols and notation Approximately equal symbol
The symbol ≈ states that two quantities are close enough for the stated purpose but are not necessarily exactly equal.
a ≈ b Read and calculate Geometry and trigonometry Area
The two-dimensional measure of the region enclosed by a shape.
square units Read and calculate Numbers and algebra Arithmetic sequence
A sequence in which consecutive terms differ by the same constant amount.
aₙ = a₁ + (n−1)d Read and calculate C
Circle
The set of all points in a plane that are the same distance from one centre point.
(x−h)²+(y−k)²=r² Read and calculate Statistics and probability Combination
A selection in which order does not matter.
C(n,r)=n!/[r!(n−r)!] Read and calculate Waves and mathematical physics Complex number
A number with real and imaginary components, where the imaginary unit satisfies i²=−1.
z=a+bi Read and calculate Vectors and matrices Cross product
A three-dimensional vector perpendicular to two input vectors, with magnitude equal to the parallelogram area they span.
a×b Read and calculate D
Delta symbol
Uppercase delta usually represents a finite change or difference, while lowercase delta often represents a small change, variation or parameter whose precise meaning depends on context.
Δx=x₂−x₁; δ Read and calculate Calculus and change Derivative
The instantaneous rate of change of a function, defined as a limit of average rates where that limit exists.
f′(x) = lim[h→0] (f(x+h)−f(x))/h Read and calculate Vectors and matrices Determinant
A scalar associated with a square matrix that describes signed scale change and indicates invertibility when non-zero.
det(A) or |A| Read and calculate Calculus and change Differential equation
An equation that relates an unknown function to one or more of its derivatives.
F(x,y,y′,…)=0 Read and calculate Geometry and trigonometry Distance formula
The Pythagorean relationship used to find straight-line distance between two coordinate points.
d=√((x₂−x₁)²+(y₂−y₁)²) Read and calculate Vectors and matrices Dot product
A scalar product that combines corresponding vector components and also equals the product of magnitudes times the cosine of their angle.
a·b=Σaᵢbᵢ Read and calculate E
Eigenvalue
A scalar by which a linear transformation stretches an associated non-zero eigenvector without changing its direction line.
Av=λv Read and calculate Symbols and notation Epsilon symbol
Epsilon commonly denotes a small positive quantity, an error tolerance or an arbitrarily small bound, although individual formulas may define it differently.
ε>0 Read and calculate Symbols and notation Equals and not-equal symbols
The equals sign asserts that two expressions have the same value, while the not-equal sign asserts that their values differ.
a=b; a≠b Read and calculate Numbers and algebra Equation
A statement that two mathematical expressions have equal value.
left side = right side Read and calculate Calculus and change Euler's method
A first-order numerical method that advances an approximate differential-equation solution using the current slope.
yₙ₊₁=yₙ+h f(tₙ,yₙ) Read and calculate Numbers and algebra Exponent
A number that states how many times a base is multiplied by itself, with broader definitions extending to zero, negative and non-integer powers.
bⁿ Read and calculate Numbers and algebra Exponential function
A function in which the variable appears in the exponent and changes by a constant multiplicative factor over equal intervals.
f(x) = abˣ Read and calculate F
Factorial
The product of every positive integer from 1 through a non-negative integer n, with 0! defined as 1.
n! Read and calculate Waves and mathematical physics Fourier transform
A transformation that represents a signal or function through frequency components.
Xₖ=Σxₙe⁻ⁱ²πkn/N Read and calculate Numbers and algebra Fraction
A quotient that represents one number divided by another non-zero number.
a/b, b ≠ 0 Read and calculate Waves and mathematical physics Frequency
The number of cycles or repeated events per unit time.
f=1/T Read and calculate Numbers and algebra Function
A rule that assigns exactly one output to every permitted input.
y = f(x) Read and calculate G
Geometric sequence
A sequence in which each non-zero term is obtained by multiplying the previous term by a constant ratio.
aₙ = a₁rⁿ⁻¹ Read and calculate Numbers and algebra Greatest common factor
The largest positive integer that divides each supplied integer without a remainder.
gcf(a,b) Read and calculate I
Infinity symbol
The infinity symbol describes unbounded growth, extent or continuation; it is not an ordinary real number on which standard arithmetic rules always apply.
∞ Read and calculate Calculus and change Integral
A mathematical construction representing accumulation; a definite integral is the signed limit of sums over an interval.
∫ₐᵇf(x)dx Read and calculate Symbols and notation Integral sign
The elongated integral sign indicates continuous accumulation, with limits marking the interval for a definite integral and a differential identifying the variable.
∫f(x)dx; ∫ₐᵇf(x)dx Read and calculate Vectors and matrices Inverse matrix
A matrix that reverses an invertible square matrix under multiplication.
AA⁻¹=I Read and calculate L
Lambda symbol
Lambda is a Greek letter commonly used for wavelength, an eigenvalue, a rate parameter or another quantity explicitly defined by its formula.
λ Read and calculate Numbers and algebra Logarithm
The exponent to which a positive base must be raised to produce a positive value.
log_b(x) = y ⇔ bʸ = x Read and calculate M
Matrix
A rectangular arrangement of values used to represent linear maps, systems, data and other structured relationships.
A=[aᵢⱼ] Read and calculate Statistics and probability Mean
The arithmetic average found by adding values and dividing by the number of values.
x̄=Σxᵢ/n Read and calculate Statistics and probability Median
The central value in an ordered dataset, or the mean of the two central values when the count is even.
middle ordered value Read and calculate Waves and mathematical physics Momentum
A vector quantity equal to mass times velocity in classical mechanics.
p=mv Read and calculate Symbols and notation Mu symbol
Mu is a Greek letter commonly used for a population mean, a coefficient or a physical parameter whose meaning must be read from context.
μ Read and calculate N
Nabla symbol
Nabla is the vector differential operator used to write gradients, divergence and curl in multivariable calculus and mathematical physics.
∇f; ∇·F; ∇×F Read and calculate Waves and mathematical physics Normalisation
Scaling a mathematical state so that its total norm or probability satisfies a required convention, commonly one.
Σ|aᵢ|²=1 Read and calculate P
Partial derivative symbol
The rounded symbol ∂ marks differentiation with respect to one variable while other independent variables are held constant.
∂f/∂x Read and calculate Numbers and algebra Percentage
A dimensionless ratio expressed as a number of parts per hundred, allowing proportions with different totals to be compared.
percentage = part/whole × 100% Read and calculate Statistics and probability Permutation
An ordered arrangement of selected objects, so changing the order creates a different outcome.
P(n,r)=n!/(n−r)! Read and calculate Symbols and notation Pi symbol
Lowercase pi usually denotes the circle constant, while uppercase pi can denote multiplication across an indexed collection of factors.
π≈3.14159; ∏ᵢaᵢ Read and calculate Symbols and notation Plus-minus symbol
The plus-minus sign compactly represents two values or cases, one formed with addition and the other with subtraction.
a±b Read and calculate Statistics and probability Probability
A number from zero to one that measures how likely an event is under a stated model.
P(A) Read and calculate Numbers and algebra Proportion
An equation stating that two ratios are equal.
a/b = c/d Read and calculate Geometry and trigonometry Pythagorean theorem
In a right triangle, the square of the hypotenuse equals the sum of the squares of the two shorter sides.
a²+b²=c² Read and calculate R
Radian
An angle unit defined by the ratio of arc length to circle radius.
θ=s/r Read and calculate Numbers and algebra Ratio
A comparison of two quantities by division.
a:b or a/b Read and calculate Numbers and algebra Root
A value that reverses a power, or a value that makes an equation or function equal zero, depending on context.
ⁿ√x or f(x)=0 Read and calculate S
Scalar
A single quantity that can scale another mathematical object and has magnitude but no vector direction.
k Read and calculate Symbols and notation Sigma symbols
Uppercase sigma commonly denotes a sum, while lowercase sigma commonly denotes standard deviation; context determines the intended quantity.
Σᵢxᵢ; σ Read and calculate Geometry and trigonometry Slope
The rate at which a line's vertical coordinate changes relative to its horizontal coordinate.
m=(y₂−y₁)/(x₂−x₁) Read and calculate Symbols and notation Square-root symbol
The radical sign requests a root; without a written index it means the principal square root, and with an index it specifies another root degree.
√x; ⁿ√x Read and calculate Statistics and probability Standard deviation
The square root of variance, measuring the typical spread of observations around their mean in the original units.
σ=√(Σ(xᵢ−μ)²/N) Read and calculate T
Tangent
In right-triangle trigonometry, tangent is opposite side divided by adjacent side; in geometry it can also mean a line touching a curve locally.
tan(θ)=opposite/adjacent Read and calculate Symbols and notation Theta symbol
Theta is a Greek letter frequently used for an unknown angle, phase or parameter whose role is defined by the surrounding formula.
θ Read and calculate Geometry and trigonometry Trigonometry
The study of relationships among angles, side lengths and periodic functions.
sin, cos, tan Read and calculate U
Uncertainty principle
A quantum-mechanical bound on the product of standard deviations of conjugate observables such as position and momentum.
ΔxΔp≥ℏ/2 Read and calculate Symbols and notation Union and intersection symbols
Union combines everything belonging to either set, while intersection keeps only elements belonging to both sets.
A∪B; A∩B Read and calculate V
Variance
The average squared deviation from the mean under the selected population or sample convention.
σ²=Σ(xᵢ−μ)²/N Read and calculate Vectors and matrices Vector
An ordered mathematical object with components, commonly used to represent magnitude and direction.
v=(v₁,v₂,…) Read and calculate Symbols and notation Vertical bars
Vertical bars can denote absolute value, a determinant, a vector magnitude, divisibility or set size, so their meaning is determined by the enclosed object and context.
|x|; |A|; ‖v‖ Read and calculate W
Clear answers
About the mathematics dictionary
What is the MW SysArc Mathematics Dictionary?
It is a concise A–Z reference for mathematical terms, notation and examples, with each concept linked to calculators that let you use it.
Can I search by a symbol or another name?
Yes. Search includes terms, definitions, notation, examples and aliases such as gradient for slope or GCD for greatest common factor.
How does the dictionary connect to the calculators?
Every term page links to one or more relevant calculators, so you can move directly from a definition to a worked numerical model.