mathcentrecommunityproject

1 Community project 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 explains the use of the symbol and an example may be given for further explanation in column four. The last column contains a phrase to be entered mathcentre community project as a search topic in mathcentre if further details are required. encouraging Care should be taken as context is important. academics to Identical mathematical shareand symbols maths notationsupport are used resources in different circumstances to convey very different All mccp resources are released under a Creative Commons licence ideas.

2 Symbol Say Means Example mathcentre Search Topic P. sigma Represents summation Sigma notation . k Parallel In the same direction as The gradient of a straight line segment . || Modulus, absolute The size of a number, ignoring the sign |3|= 3, | 3|= 3 Modulus (vertical lines, ei- value ther side of a num- ber or variable). |A| Determinant of Determinant of matrix A Determinants matrix A. det (A) Determinant of Determinant of matrix A Determinants matrix A. c Janette Matthews Tony Croft Loughborough University Loughborough University community project Mathematical Symbols and Abbreviations (continued). Symbol Say Means Example mathcentre Search Topic () brackets Used in many different contexts to Expanding or removing show multiplication, to define points, to de- brackets , % Percent, Percentage mathcentre community project fine functions Represents a fraction with the denominator 100.

3 Of 100. 25. = 25 %. Removing brackets . Percentages encouraging academics to share maths support resources Plus or minus, All mccp resources Represents are releasedone two numbers, underpositive a Creativeand Commons 5 licence indicates +5 and 5 Mathematical language . positive or negative one negative Plus or minus, Used to indicate a range 10 2 indicates the range Mathematical language . positive or negative starting from 10 2 to 10 + 2 8, 9, 10, 11, 12. pi Represents the ratio of the circumference of is equal to Substitution & Formulae . a circle to its diameter. = circumference diameter e The exponential constant e is approximately equal The exponential constant to e . Infinity Used to represent infinity c Janette Matthews Tony Croft Loughborough University Loughborough University community project Mathematical Symbols and Abbreviations (continued). Symbol Say Means Example mathcentre Search Topic x Commonly used as a variable theta Commonly used as a variable to indicate an See Greek alphabet in (x, y) Point xy mathcentre community project angle A point with co-ordinates and y maths support resources Mathematical language.

4 Facts & Formulae Leaflet . x-y plots . encouraging academics toxshare All mccp resources are released under a Creative Commons licence P(x, y) Point xy labeled P A point P with co-ordinates x and y x-y plots . m Gradient or slope of a curve Equation of a straight line . c y-axis intercept or a constant of unknown Equation of a straight line . value the constant of integration Integration as the reverse of differentiation . (dot above a digit) Recurring Indicates a digit continues to recur = Decimals x (dot above vari- x dot Differentiate function x with respect to t able x) (time). Superscript To the power of A digit or letter placed above and slightly to 23 = 2 2 2 Mathematical language , the right of another digit or letter. Used to Indices or powers . indicate multiplications of the same number Subscript A digit or letter placed below and slightly to x1 , x2 , x3 , .., xm , xn Mathematical language.

5 The right of a letter. Used to distinguish be- tween variables c Janette Matthews Tony Croft Loughborough University Loughborough University community project Mathematical Symbols and Abbreviations (continued). Symbol Say Means Example mathcentre Search Topic Proportional to Proportional to y x means y = kx where k is a constant <.. mathcentre community project Less than Less than or Value on the left is less than value on the right Value on the left is less than or equal to value Inequalities Inequalities encouraging academics to share maths support resources equal to All mccp on the right resources are released under a Creative Commons licence > Greater than Value on the left is greater than value on the Inequalities right Greater than or Value on the left is greater than or equal to Inequalities equal to value on the right = Equal to Equal to 6 = 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.

6 Equivalent for all values of x Implies Calculations on left of symbol imply those on the right Implies Calculations on either side of symbol imply those on the other c Janette Matthews Tony Croft Loughborough University Loughborough University community project Mathematical Symbols and Abbreviations (continued). Symbol Say Means Example mathcentre Search Topic Therefore Therefore right angle to, At 90 to, perpendicular to, normal to The gradient of a straight ! mathcentre community project perpendicular to Factorial Used to indicate the multiplication of consec- 6! = 6 5 4 3 2 1. utive wholeacademics numbers to share maths support resources line segment . Factorials encouraging All mccp resources are released under a Creative Commons licence log, logb x Log to the base b of Logarithm log2 8 = 3 Logarithms x ln lin Natural logarithm defined as loge loga- Logarithms rithm to the base e delta Represents a small change x is a small change in Differentiation from first the variable x principles.

7 Delta Represents a small change x is a small change in the variable x f (x) f of x function f of variable x What is a function? . f 1 (x) f to the minus 1 of Inverse of function f (x) Inverse functions . x c Janette Matthews Tony Croft Loughborough University Loughborough University community project Mathematical Symbols and Abbreviations (continued). Symbol Say Means Example mathcentre Search Topic dy dx dee y dee x Differentiate function y with respect to x Differentiation from first principles . mathcentre community project d2 y dx2. dee 2 y dee x Double differentiate function y with respect squared to x, second derivative encouraging academics of function y to share maths support resources All mccp resources are released under a Creative Commons licence f (x) f dash of x Differentiate function f (x) with respect to x, Differentiation from first dy equivalent to dx if y = f (x) principles.

8 Dy y y dash Differentiate function y, equivalent to dx if Differentiation from first y = f (x) principles . f (x) f double dash of x Differentiate function f (x) with respect to x twice, Second derivative of function f (x). f (x) f triple dash of x Differentiate function f (x) with respect to x three times, Third derivative of function f (x). R. f (x)dx Integrate f of x dee Find the indefinite integral of function f (x) Integration as summation . x with respect to x Integration as the reverse of differentiation . c Janette Matthews Tony Croft Loughborough University Loughborough University community project Mathematical Symbols and Abbreviations (continued). Rb f (x)dx Integrate f of x dee Find the definite integral of function f (x) Evaluating definite inte- a x between the limits with respect to x grals . a and b Integration as summation .. AB, AB. mathcentre community project Vector AB Vector with direction from point A to point B.

9 Introduction to vectors . a Vector a encouraging Vector a academics to share maths support resources Introduction to vectors . All mccp resources are released under a Creative Commons licence a a bar, vector a Vector a Introduction to vectors . a a underline, vector Vector a Introduction to vectors . a . a 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 . Square root Indicates a square root - a number that may 9 = 3 as 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 Cube root Indicates a cube root - a number that may be 3 8 = 2 as 2 2 2 = 8 Surds and roots multiplied by itself three times to achieve the value shown inside the symbol c Janette Matthews Tony Croft Loughborough University Loughborough University community project Mathematical Symbols and Abbreviations (continued).

10 I Represents 1 (square root of minus 1) and Motivating the study of used interchangeably with j complex numbers . i or i Unit vector in the direction of the positive Vectors . j mathcentre community project x-axis . Represents 1 (square root of minus 1) and used interchangeably Motivating the study of encouraging academicswith usually to i,share by engi- maths support resources complex numbers . neers All mccp resources are released under a Creative Commons licence j or j Unit vector in the direction of the positive Vectors y-axis k or k Unit vector in the direction of the positive Vectors z-axis sin( ) sine theta The trigonometric function sine abbreviated Trigonometric functions . as sin cos( ) cos theta The trigonometric function cosine abbrevi- Trigonometric functions . cosine theta ated as cos tan( ) tan theta The trigonometric function tangent abbrevi- Trigonometric functions.