Mathematical Symbols and Abbreviations mccp-matthews-symbols-001 This leaflet provides information on symbols and notation commonly used in mathematics. It is designed to enable further information to be found from resources in mathcentre(). In the table below, the symbol or notation is given in column one. It is not always obvious how the combination of characters used in mathematical notation is said, so where appropriate this information is given in column two. Column three explainstheuseofthesymbolandanexamplemaybegivenforfurtherexplanationincolumnfour.thelastcolumncontainsaphrasetobeentered as a search topic in mathcentre if further details are required. Care should be taken as context is important. Identical mathematical symbols and notation are used in different circumstances to convey very different ideas. sigma Represents summation Sigma notation Parallel In the same direction as The gradient of a straight line segment (vertical lines, eithersideofanumber or variable) A det(a) Modulus, absolute value Determinant of matrix A Determinant of matrix A The size of a number, ignoring the sign 3 = 3, 3 = 3 Modulus Determinant of matrix A Determinant of matrix A Determinants Determinants
% Percent, Percentage ± Plus or minus, positive or negative ± Plus or minus, positive or negative () brackets Used in many different contexts e.g. to Expanding or removing show multiplication, to define points, to de- brackets, fine functions Represents a fraction with the denominator of 100 Represents two numbers, one positive and one negative Used to indicate a range 25 100 π pi Represents the ratio of the circumference of acircletoitsdiameter. π = circumference diameter Removing brackets = 25% Percentages ±5 indicates +5 and 5 Mathematical language 10 ±2 indicates the range starting from 10 2 to 10 + 2i.e. 8, 9, 10, 11, 12 π is equal to 3.14159... Mathematical language Substitution& Formulae e The exponential constant e is approximately equal to 2.718 Infinity Used to represent infinity The exponential constant e
x Commonly used as a variable θ theta Commonly used as a variable to indicate an See Greek alphabet in angle Mathematical language Facts& Formulae Leaflet (x, y) Point xy encouraging A point with academics co-ordinates toxshare and y maths support resources x-y plots P(x, y) Point xylabeledp ApointPwithco-ordinates xand y x-yplots m Gradient or slope of a curve Equation of a straight line c y-axis intercept or a constant of unknown value e.g. the constant of integration Equation of a straight line Integration as the reverse of differentiation (dot above a digit) Recurring Indicates a digit continues to recur 0. 3 = 0.3333... Decimals ẋ (dot above variable x dot Differentiate function x with respect to t x) (time) Superscript To the power of A digit or letter placed above and slightly to therightofanotherdigitorletter. Usedto 2 3 = 2 2 2 Mathematical language, Indices or powers indicate multiplications of the same number Subscript A digit or letter placed below and slightly to therightofaletter. Usedtodistinguishbetween variables x 1, x 2, x 3,..., x m, x n Mathematicallanguage
Proportional to Proportional to y x means y = kx wherekisaconstant right < Lessthan Valueontheleftislessthanvalueonthe encouraging Valueontheleftislessthanorequaltovalue academics to share maths support resources Inequalities Less than or Inequalities equal to ontheright > Greaterthan Valueontheleftisgreaterthanvalueonthe Inequalities right Greater than or Valueontheleftisgreaterthanorequalto Inequalities equal to valueontheright = Equal to Equal to Not equal to Not equal to Mathematical language Approximately Approximately equal to Mathematical language equal to Equivalent to Equivalent for all values 2x + x 3x, equivalent forallvaluesof x Implies Calculations on left of symbol imply those on the right Implies Calculations on either side of symbol imply thoseontheother
Therefore Therefore right angle to, perpendicular to At 90 to,perpendicularto,normalto Thegradientofastraight line segment! Factorial Used to indicate the multiplication of consec- 6!= 6 5 4 3 2 1 Factorials encouraging utive wholeacademics numbers to share maths support resources log, log b x Logtothebase bof Logarithm log 2 8 = 3 Logarithms x ln lin Naturallogarithmdefinedas log e i.e. logarithmtothebasee Logarithms δ delta Represents a small change δx is a small change in the variable x Differentiation from first principles delta Represents a small change x is a small change in the variable x f(x) fof x function fofvariable x Whatisafunction? f 1 (x) ftotheminus1of x Inverse of function f(x) Inverse functions
dy dx dee y dee x Differentiate function y with respect to x Differentiation from first principles d 2 y dx 2 Double differentiate function y with respect to x, Differentiation dee 2 y dee x squared second derivative of function y f (x) fdashof x Differentiatefunction f(x)withrespectto x, equivalentto dy if y = f(x) dx from first principles y ydash Differentiatefunction y,equivalentto dy dx y = f(x) f (x) fdoubledashof x Differentiatefunction f(x)withrespectto x twice, Second derivative of function f(x) f (x) ftripledashof x Differentiatefunction f(x)withrespectto x three times, Third derivative of function f(x) f(x)dx Integrate fof xdee x Find the indefinite integral of function f(x) withrespectto x Differentiation from first principles Integration as summation Integration as the reverse of differentiation
b a f(x)dx Integrate fof xdee x between the limits aand b Find the definite integral of function f(x) withrespectto x Evaluating definite integrals Integration as summation AB, AB Vector AB Vector with direction from point A to point Introduction to vectors a Vector a B encouraging Vector academics to share maths support resources All mccp a resources are released under a Creative Commons licence Introduction to vectors a a bar, vector a Vector a Introduction to vectors a a underline, vector Vector a Introduction to vectors a â a hat Unit vector in the direction of vector a Introduction to vectors z Complex conjugate Complex conjugate of complex number z, The complex conjugate of z used in the division of complex numbers Squareroot Indicatesasquareroot-anumberthatmay 9 = ±3as 3 3 = 9 Surds and roots be multiplied by itself to achieve the value and 3 3 = 9 shown inside the square root symbol 3 Cuberoot Indicatesacuberoot-anumberthatmaybe 3 8 = 2as 2 2 2 = 8 Surdsandroots multiplied by itself three times to achieve the value shown inside the symbol
i or i i Represents 1(squarerootofminus1)and used interchangeably with j Unitvectorinthedirection ofthepositive x-axis Represents 1(squarerootofminus1)and j used interchangeably with i, usually by engineers or j Unitvectorinthedirection ofthepositive y-axis k or k Unitvectorinthedirection ofthepositive z-axis sin(θ) sine theta The trigonometric function sine abbreviated assin cos(θ) cos theta The trigonometric function cosine abbreviatedascos cosine theta tan(θ) tan theta The trigonometric function tangent abbreviatedastan Motivating the study of complex numbers Vectors Motivating the study of complex numbers Vectors Vectors
cosec(θ) cosec theta The trigonometric function cosecant abbreviatedascosecanddefinedas 1 sin(θ) sec(θ) sec theta The trigonometric function secant abbrevi- 1 atedassecanddefinedas cos(θ) cot(θ) cot theta The trigonometric function cotangent abbreviatedascotanddefinedas 1 tan(θ) Cosecant Secant Cotangent sin 1 (x) cos 1 (x) tan 1 (x) d.p s.f sinetotheminus1 θ=sin 1 (x)istheinverseoffunction of x x=sin(θ) costotheminus1 θ=cos 1 (x)istheinverseoffunction of x x=cos(θ) tantotheminus1 θ=tan 1 (x)istheinverseoffunction of x x=tan(θ) Decimal places Indicates the number of decimal places after thedecimalpointtowhichanumbershould be rounded Significant figures Indicates how a number should be displayed by stating the number of non-zero digits that should be shown counting from the left 12.357 = 12.36(2d.p) Decimals 0.05653 = 0.06(1s.f) 0.05653 = 0.0565(3s.f) Decimals