Math Abbreviations
91 abbreviations · part of Units of Measurement Abbreviations
Abbreviations and function names used in mathematics, from school arithmetic and geometry (GCF, LCM, PEMDAS, SOHCAHTOA, CPCTC) to calculus, linear algebra and proof writing (lim, det, iff, QED, WLOG), plus number shorthand such as K, M, MM and bn, whose meaning depends on the field. In typeset mathematics, function names such as sin, log and max are set in upright roman type to distinguish them from variables.
| Abbreviation | Stands for | Description |
|---|---|---|
| a.e. | Almost everywhere | Measure-theory phrase meaning a property holds except on a set of measure zero, such as a finite or countable set of points. |
| AAS | Angle-Angle-Side (congruence) | Triangle congruence criterion using two angles and a side that is not between them. |
| abs | Absolute value | Function name for absolute value in programming languages and spreadsheets: abs(x) returns the distance of x from zero, so abs(−7) = 7. |
| arccos | Arccosine (inverse cosine) | Returns the angle whose cosine is a given value, with outputs from 0° to 180° (0 to π). |
| arcmin | Arcminute | One sixtieth of a degree of angle, written ′ (prime). |
| arcsec | Arcsecond | One sixtieth of an arcminute, or 1/3,600 of a degree, written ″. |
| arcsin | Arcsine (inverse sine) | The inverse of the sine function, returning the angle whose sine is a given number. |
| arctan | Arctangent (inverse tangent) | Gives the angle whose tangent is a given number, with outputs strictly between −90° and 90°. |
| arg | Argument (of a complex number) | The angle a complex number makes with the positive real axis in the complex plane, measured in radians. |
| ASA | Angle-Side-Angle (congruence) | Two triangles are congruent by ASA when two angles and the side between them match. |
| B | Billion | Shorthand for billion (a thousand million, 10^9) in headlines, market values and statistics: $3B means three billion dollars. |
| BEDMAS | Brackets, Exponents, Division/Multiplication, Addition/Subtraction | The order-of-operations mnemonic used mainly in Canada and New Zealand, combining the British "brackets" with the American "exponents". |
| bn | Billion | Abbreviation for billion favored by British newspapers, The Economist, the Financial Times and many company reports, as in £4bn or $2.5bn. |
| BODMAS | Brackets, Orders, Division/Multiplication, Addition/Subtraction | The order-of-operations mnemonic taught in the UK, India, Pakistan, Australia and other Commonwealth countries. |
| C | Complex numbers | The set of complex numbers a + bi, where i² = −1, written in blackboard bold as ℂ. |
| cis | Cosine plus i sine | Shorthand for cos θ + i sin θ, used to write complex numbers in polar form: z = r cis θ. |
| Cor | Corollary | A result that follows quickly from a theorem just proved, abbreviated Cor in lecture notes and references such as "Cor 2.5". |
| cos | Cosine | The trigonometric function giving the ratio of the side adjacent to an angle to the hypotenuse in a right triangle; on the unit circle it is the x-coordinate. |
| cosec | Cosecant | The form of cosecant used in British, Indian, Australian and many other textbooks, identical in meaning to the American csc: cosec θ = 1/sin θ. |
| cosh | Hyperbolic cosine | Hyperbolic function defined as (e^x + e^−x)/2. |
| cot | Cotangent | Reciprocal of tangent: cot θ = cos θ/sin θ, or adjacent over opposite. |
| CPCTC | Corresponding parts of congruent triangles are congruent | A justification used in US high school geometry proofs: once two triangles are shown congruent (by SSS, SAS, ASA, AAS or HL), every pair of matching sides and angles is… |
| csc | Cosecant | Reciprocal of sine: csc θ = 1/sin θ, or hypotenuse over opposite side. |
| deg | Degree (angle) | Unit of angle equal to 1/360 of a full turn, written deg in plain text, programming and calculator modes; the symbol is °. |
| det | Determinant | A scalar computed from a square matrix that tells whether it is invertible (det ≠ 0) and how the corresponding linear transformation scales area or volume. |
| dim | Dimension | The number of vectors in a basis of a vector space, written dim V. |
| exp | Exponential function | Notation for e raised to a power: exp(x) = e^x. |
| FOIL | First, Outer, Inner, Last | Mnemonic for multiplying two binomials: multiply the first terms, the outer terms, the inner terms and the last terms, then add. (x + 3)(x + 2) = x² + 2x + 3x + 6 = x²… |
| FTC | Fundamental theorem of calculus | The theorem linking differentiation and integration: the derivative of an accumulated integral is the original function, and a definite integral can be evaluated with… |
| GCD | Greatest common divisor | The largest positive integer that divides two or more integers without a remainder; gcd(48, 18) = 6. |
| GCF | Greatest common factor | The name US elementary and middle schools use for the greatest common divisor: the largest number that is a factor of every number in a set. |
| HCF | Highest common factor | British, Indian, Australian and other Commonwealth name for the greatest common divisor: the largest number that divides each of a set of numbers exactly. |
| HL | Hypotenuse-Leg (congruence) | Congruence test for right triangles: if the hypotenuse and one leg of a right triangle equal the hypotenuse and a leg of another, the triangles are congruent. |
| iff | If and only if | Logical connective stating that two statements are equivalent, each implying the other. |
| Im | Imaginary part | The coefficient of i in a complex number: for z = 3 + 4i, Im(z) = 4, itself a real number. |
| inf | Infimum | The greatest lower bound of a set: the largest number less than or equal to every element. |
| IVT | Intermediate value theorem | A calculus theorem stating that a continuous function on a closed interval takes every value between its endpoint values. |
| K | Thousand | Shorthand for thousand in salaries, prices, social media follower counts and mileage, borrowed from the metric prefix kilo-. |
| ker | Kernel | The set of vectors a linear map sends to zero, written ker T; for a matrix it is the null space. |
| lb | Binary logarithm | ISO 80000-2 symbol for the logarithm to base 2, so lb 8 = 3. |
| LCD | Least common denominator | The smallest number that can serve as a common denominator for a set of fractions, equal to the least common multiple of the denominators. |
| LCM | Least common multiple | The smallest positive number that is a multiple of each of two or more integers: lcm(4, 6) = 12. |
| lg | Logarithm (base 10 or base 2) | Compact logarithm notation whose base depends on the field: the ISO 80000-2 standard defines lg as the base-10 (common) logarithm, while many computer science texts use… |
| LHS | Left-hand side | The expression to the left of an equals sign or inequality. |
| lim | Limit | Notation for the value a function or sequence approaches as the input approaches some point or infinity. |
| ln | Natural logarithm | The logarithm to base e, about 2.71828, written ln x from Latin logarithmus naturalis. |
| log | Logarithm | The inverse of exponentiation: log_b(x) is the power to which base b must be raised to give x, so log₁₀ 1000 = 3. |
| M | Million | Modern shorthand for million in headlines, financial reports, startup funding news and statistics: $5M means five million dollars, and 2.3M views means 2.3 million. |
| max | Maximum | The largest value in a set or attained by a function, written max{3, 7, 5} = 7 or max f(x). |
| mil | Million | Informal clipping of million, common in speech, sports contract coverage and casual writing, as in a "$20 mil" deal or "3 mil views". |
| min | Minimum | The smallest value in a set or attained by a function, written min{4, 1, 9} = 1. |
| MM | Million (from Roman numerals MM) | Financial, banking and oil-and-gas shorthand for million, built from two Roman-numeral thousands (a thousand thousands). |
| mod | Modulo | The remainder operation and the notation for congruence: 17 mod 5 = 2, and a ≡ b (mod n) means a and b leave the same remainder when divided by n. |
| MVT | Mean value theorem | States that a function continuous on [a, b] and differentiable on (a, b) has at least one point where the instantaneous rate of change equals the average rate of change… |
| N | Natural numbers | The set of natural numbers, the counting numbers 1, 2, 3 and so on, usually written in blackboard bold as ℕ. |
| nCr | Combinations (n choose r) | Calculator and textbook notation for the number of ways to choose r items from n when order does not matter: nCr = n! / (r!(n − r)!). |
| nPr | Permutations | Calculator notation for the number of ordered arrangements of r items chosen from n: nPr = n! / (n − r)!. |
| ODE | Ordinary differential equation | An equation relating a function of one variable to its derivatives, such as dy/dt = ky for exponential growth. |
| pct | Percent | Abbreviation for percent in newspapers, financial tables, sports statistics and data headers where the % sign is avoided. |
| PDE | Partial differential equation | An equation involving partial derivatives of a function of several variables, such as position and time. |
| PEMDAS | Parentheses, Exponents, Multiplication/Division, Addition/Subtraction | US mnemonic for the order of operations: parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left… |
| Pf | Proof | Shorthand heading for a proof in handwritten notes, problem sets and blackboard lectures, followed by the argument and closed with QED or a box. |
| Q | Rational numbers | Written ℚ in blackboard bold, this is the set of all fractions p/q of integers with q not zero. |
| QED | Quod erat demonstrandum (which was to be demonstrated) | Latin phrase written at the end of a proof to signal that the claimed result has been established. |
| R | Real numbers | All points on the number line, rational and irrational, form the set written R or ℝ, including numbers such as π and the square root of 2. |
| Re | Real part | The real component of a complex number: for z = 3 + 4i, Re(z) = 3. |
| resp. | Respectively | Used in mathematical writing to pair two parallel statements in one sentence, as in "f is increasing (resp. decreasing) if f′ > 0 (resp. f′ < 0)". |
| RHS | Right-hand side | The expression to the right of an equals sign, inequality or other relation. |
| RREF | Reduced row echelon form | The simplified matrix produced by Gauss-Jordan elimination: each leading entry is 1, it is the only nonzero entry in its column, and leading entries move right going… |
| s.t. | Such that | Shorthand in mathematical notes, proofs and problem sets that introduces a condition, as in "there exists x s.t. x² = 2". |
| SA | Surface area | The total area of all the faces or curved surfaces of a three-dimensional object, measured in square units. |
| SAS | Side-Angle-Side (congruence) | Congruence test for triangles that compares two sides and the angle between them; the angle must be the included one. |
| sec | Secant | The reciprocal of cosine: sec θ = 1/cos θ, or hypotenuse over adjacent side in a right triangle. |
| sgn | Sign function | Function returning −1 for negative numbers, 0 for zero and 1 for positive numbers. |
| sin | Sine | The trigonometric function that gives, in a right triangle, the ratio of the side opposite an angle to the hypotenuse. |
| sinh | Hyperbolic sine | Hyperbolic function defined as (e^x − e^−x)/2, an analog of sine for the hyperbola x² − y² = 1 rather than the circle. |
| SOHCAHTOA | Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent | Mnemonic for the three basic trigonometric ratios in a right triangle: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse and tangent is opposite over… |
| sqrt | Square root | Function name for the square root in programming languages, spreadsheets and plain-text math, returning the nonnegative number whose square equals the input: sqrt(49) =… |
| SSS | Side-Side-Side (congruence) | Triangle congruence criterion: if all three sides of one triangle equal the corresponding sides of another, the triangles are congruent. |
| sup | Supremum | The least upper bound of a set of real numbers: the smallest number greater than or equal to every element. |
| SVD | Singular value decomposition | Factorization of any matrix A into UΣVᵀ, where U and V are orthogonal matrices and Σ is diagonal with nonnegative singular values. |
| tan | Tangent | Sine divided by cosine, or opposite over adjacent in a right triangle. |
| tanh | Hyperbolic tangent | The ratio sinh x / cosh x, an S-shaped curve that rises smoothly from −1 to 1. |
| TFAE | The following are equivalent | Phrase introducing a theorem that lists several statements and asserts that each implies all of the others. |
| Thm | Theorem | Abbreviation for theorem in lecture notes, textbooks and slides, as in "Thm 3.2", where results are numbered by chapter and section. |
| tr | Trace | The sum of the diagonal entries of a square matrix, written tr A. |
| trig | Trigonometry | Clipped form of trigonometry, the branch of mathematics dealing with angles, triangles and periodic functions such as sine and cosine, and the everyday name for the… |
| WLOG | Without loss of generality | Phrase used in proofs to restrict attention to one representative case when the others follow by symmetry or relabeling. |
| WRT | With respect to | Introduces the topic a comment concerns, meaning "regarding" or "about." Engineers, scientists and office workers use it in emails and notes; in mathematics it… |
| WTS | Want to show | Shorthand in proofs, lecture notes and homework that states the goal of an argument, as in "WTS: f is continuous at a". |
| Z | Integers | Blackboard-bold ℤ names the set of integers, ..., −2, −1, 0, 1, 2, .... |
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