Sierpinski (<1K) Glossary of Mathematical Notations
    "Math is like love -- a simple idea but it can get complicated."  - R. Drabek.
   
Symbol  UseDescriptionDefinition/Example
ººDefined equalDefined to be equal to
ººAbreviated notationÑx ¦(x) º Ѧ
»»Approximately equal
==Light-based Unit Equivalence (given c,h, and kB)
¥¥InfinityCardinality(Z)
x-1x-1(1,1,...,1)[x-1]i=1
ååi=mn f(i)Sum from i=m to n of f(i)åi=13 i2=12+22+32
ò òabf(x) dxIntegral from x=a to b f(x), LimN ® ¥ åi=0N-1 f(a+i(b-a)/N)(a-b)/N
d/dx(d/dx)f(x)Derivative of f(x) (aka f '(x)) Limd ® 0 d-1(f(x+d)-f(x))
'¦'(x)Derivative of function Limd ® 0 (f(x+d)-f(x))/d
[x| Highest integer not above xMax { z Î Z : z £ x } [-3.6| = -4 ; aka floor(x)
Int(x)
?,?xy,zConditionaly if x=0, z else. NB: differs from C definition
!Factorialn! = n(n-1)...14!=24
nCrBinomial coefficientn! / ((r!(n-r)!)Number of unordered r-selections from n
Functions
Sin() Sin(x)x-1 sin(x)     aka. sinc(x) or sine cardinal
Tan()Tan(x)x-1 tanx
xExponentiation ex = åi=0¥ i!-1 xi
xLogarithm ln(x) (base e)
Vectors and Matrices
DimDim(a)Dimension of aDim((0,4,6)) = 3
| ||x|Absolute value of x|-5.4|=5.4
|a|Euclidean length of aÖ(åi=1Dim(a) ai2)
|A|Determinant of a square matrixSi,j,..sei,j,..s a1,i a2,j... a_N,s
TATTranspose of matrix(aTi,j) where aTj,i=ai,j
| |¥|a|¥Infinity normMax{ |ai| : 1 £ i £ Dim(a) }
| |+|a|+Vector traceåi=1Dim(a) |ai|
~a~Normalised vectora/|a|
.a.bScalar Vector "Dot" Productåi=1Dim(a) aibi
abVector Vector "Cross" Product[ab]i=åj k=1Dim(a) ei j kajbk
abMatrix Vector Product(ab)i j = aibj
ÄaÄbSkewed matrix Vector ProductaÄb = a.bI - abT
·a·bCoordinatewise product(a1,a2)·(b1,b2)=(a1b1,a2b2)
*a*bInversive product(a.b) / (|a||b|)
qÐqÐ(a,b)Subtended angle cos-1(a*b)
ÑÑ f(x)Gradient(Ñ f(x))i = df/dxi
ÐÐxa ¦(x)Directed dervivative(Ñ * a)¦(x)
ïïf=0 Evaluated at¦(x) ïx0 = ¦(x0)
Complex Numbers
^z^Complex conjugatex-iy
+|z|+Complex modulus(zz^)½ = (x2+y2)½
Multivectors
<i>a<i>i-vector component
ÙaÙbOuter product(akÙbm = (ab)<m+k>
¿a¿bContractive inner productak¿bm = (ab)<m-k>
.a.bSemi-Symmetric inner productak.bm = (ab)<|m-k|> m,k¹ 0 ; 0 else
×a×bCommutator product½(ab-ba)
~a~bAntiCommutator product½(ab+ba)
*a*bInversive product(a¿b) / (|a||b|)
DaDbDelta Product(ab)<Max>
¨a¨bGeneric linear productRepresents any one of Ù,¿,.,× or geometric products
¨+a¨+bForced Euclidean geometric product
*a*Dualai-1
#a#Main involutionåi(-1)ia<i>
§a§Reverseåi(-1)½ i(i-1)a<i>
©a©Clifford conjugationa§#
§a§Mitian conjugatione(p+1)..NaeN..(p+1)
aHermitian conjugationa§§#
~a~Normaliseda/|a| or similar, according to context
¯¯b(a)Projection(a¿b)b-1
^^b(a)Rejectiona - ¯b(a)
Îa Î bContained within¯b(a) = a
ÈaÈbJoinSee text
ÇaÇbMeetSee text
|A|s|a|sSelf scaleSee text
[-]¦[-](a,b)Skewsymmetroll¦[-](a,b) º ¦(a,b) - ¦(b,a)
ѦÑp(a)Differential¦Ñp(a) º (a.Ñp)¦(p)
D¦Dp(a)Adjoint¦Dp(a) º Ñp(a.¦(p))
ÄaÄbLie productÐab - Ðba
[a,b,..,f]Algebra generated by {a,b,..,f}   
Sets   and Logic
:Such that
Îx Î Xx is element of X 5 Î Primes
ÈA È BSet union{ x : x Î A OR  x Î B }
ÇA Ç BSet intersection{ x : x Î A AND x Î B }
"" x Î XFor all x in X" x Î { 1,2,3} : x < 4
$$ x Î XThere exists an x in X$ x Î { 1,2,3} : x > 2
fEmpty Set{}
NNatural numbers{ 1,2,3,...}
ZIntegers{ 0,1,-1,2,-2,...}
Z+Nonnegative Integers{ 0,1,2,...}
ZNNonnegative Integers below N{ 0,1,2,..,N-1 }
QRational numbers{ p/q : p Î Z, q Î N}
ÂReal numbers
CComplex ("Imaginary") numbers{ x + iy : x,y Î Â }
Intervals
[a,b]{ r Î Â : a £ r £ b }
[a,b){ r Î Â : a £ r < b }
(a,b]{ r Î Â : a < r £ b }
(a,b){ r Î Â : a < r < b }
Physical Constants
cSpeed of light
kCCoulomb Constant(4pe0)
hPlanck Constant 2pEw-1 photonic energy:frequency ratio
hReduced Planck Constant "h bar"(2p)-1h
hReduced Planck Pseudoscalr (2p)-1hi in Â4,1
kBBoltzman constantMolecular energy:temperature ratio
Me-Electron mass-energy
Qe-Electron charge

Abbreviation  MeaningExample
MostSigMost SignificantMostSig 8 bits
LeastSigLeast SignificantLeastSig bit
_LUTLook Up Table
iffIf and only-if (Û)
whennWhen and only-when
akaalso known as
ie.id est (that is)
eg.exampli gratia (for example)



Glossary   Contents   Author
Copyright (c) Ian C G Bell 1998
Web Source: www.iancgbell.clara.net/maths or www.bigfoot.com/~iancgbell/maths
Latest Edit: 18 May 2007.