Appendix;!
Pronunciation of letters of the alphabet
English alphabet
a	/«/	g		m	/cm/	t	/ti:/
b	/bi:/	h	/eitj/	n	/en/	u	/ju:/
c	/si:/	i	/«/	o	/*>/	V	/vi:/
d	mi	j	/d3«/	P	/Pi:/	w	/'dAblju:/
c	M	t	/k«/	q	/kju:/	X	/eks/
f	/ef/	1	/el/	r	/off	y	/wai/
				s	/«/	z	/zed/ AmE/zi:/
Greek alphabet
Letters		Name	Pron.
Capital	Small		
A	a	alpha	/'alfa/
B	P*	beta	/'birta/
r	Y	gamma	/'gema/
A	5	delta	/'delta/
E	e	epsilon	/'epsdan/
Z	c	zeta	/'zirta/
H		eta	/'i:t»/
e	e	theta	/'Giita/
i	i	iota	/ai'auta/
K	K	kappa	Asps/
A	k	lambda	/'laemda/
M		mu	/mju:/
Letters		Name	Pron.
Capital	Small		
N	V	nu	/nju:/
3	4	xi	/ksai/
O	o	omicron	/'aumikran/
n	71	Pi	/pai/
p	P	rho	/rau/
i		sigma	/"sigma/
T	1	tau	/tau/
Y	V	upsilon	/'jupsilan/
*	<ť	phi	/fai/
X	X	chi	/kai/
4*		psi	/psai/
£1	(0	omega	/'aumiga/
Appendix II
Pronunciation of some common mathematical expressions
Individual mathematicians often have their own way of pronouncing mathematical expressions and in many cases there is no generally accepted 'correct* pronunciation.
Distinctions made in writing are often not made explicit in speech; thus the sounds fx /'ef eks/ may be interpreted as any of: fx, fl(x), f^, FX, FX. The difference is usually made clear by the context; it is only when confusion may occur, or where he wishes to emphasise the point, that the mathematician will use the longer forms: f multiplied by x, the function of x, f subscript x, line FX, vector FX.
Similarly, a mathematician is unlikely to make any distinction in speech {except sometimes a difference in intonation or length of pauses) between pairs such as the following:
■x+^y+z) and (x + y) + z ^/ax + b and ^/(ax+b) a"-l       and a"-1
The most common pronunciations are given in the list below. In general, the shortest versions are preferred (unless greater precision is necessary).
x + 1 x-1 x±l xy
(x-y)(x+y) x
y
x = 5 x = y x > y x ž y x <y 0 <x < 1 0 <.x ^ 1
x* x"
X-"
h
^x
(x+y)2
III"
n!
*%
00
x ocy
á
á
f(x) f'(x)
x plus one
x minus one
x plus or minus one
xy / x multiplied by y
x mínus y, x plus y
x over y
x equals 5 / x is equal to 5
x is equivalent to y / x is identical with y
x is greater than y
x is greater than or equal to y
x is less than y
zero is less than x is less than 1
zero is less than or equal to x is less than or equal to 1
x squared
x cubed
x to the fourth / x to the power four
x to the n /x to the nth/ x to the power n
x to the minus n / x to the power minus n
root x / square root x / the square root of x \T
cube root x t
fourth root x f
nth root x /'enG ru:t 'eks/
x plus y all squared
x over y all squared
n factorial / factorial n x per cent /'eks pa "sent/ infinity
x varies as y / x is (directly) proportional to y
a dot /'ei dot/
a double dot /'ei 'dAbl dot/
fx /f of x/ the function of x
f dash x / the (first) derivative of f with respect to x
f double-dash x / the second derivative of f with respect to x
f"(x)	
	
	
m	
	
d&2	
w.r.t.	
r	
Jo It	
I i-1	
lim	
	
	►
Lt	
	
grad	
div	
'og.y	
]-y	
ÖÄorÖA	
xeA	
x*A	
Ac B	
A<= B	
B n A	
B vjA	
cosx	
sinx	
tanx	
secx	
co sec x	
sinhx	
coshx	
tanhx	
m.	
x!+x2 + x3	
x	
,-f triple-dash x / f treble-dash x / the third derivative of f with respect to x
f four x / the fourth derivative of f with respect to x
the partial derivative of v with respect to 8
d two v by d theta squared / the second partial derivative of v with respect to 0 with respect to
the integral from zero to infinity
the sum from i equals one to n
the limit as delta x approaches zero
the limit as delta x tends to zero
gradient divergence
log y to the base e / log to the base e of y / natural log (of) y log y to the base e / log to the base e of y / natural log (of) y OA/vector OA
.x belongs to A / x is a member of A / x is an element of A x does not belong to A / x is not a member of A / x is not an element of A
A is contained in B / A is a proper subset of B
A is contained in B / A is a subset of B
B intersection A
B union A
fkos eks/
/sam eks/
/taen eks/
/sek eks/
/'kousek eks/
/ Jam eks/ or /sint J eks/
/kojeks/
/(ten eks/ or /taent J eks/ ma / m subscript a / m suhu a . (usually) x one plus x two plus x three, etc. mod x / modulus x
Appendix HI
Units
S.I. Units
S.I. Units (S.I. = systeme international) have now been adopted by most countries of the world and should always be used. Points to note are:
a) There is no full stop after abbreviations (except, of course, at the end of a sentence).
eg  10 cm long  NOT   10 cm. long
b) The abbreviations do not change in the plural.
eg  10 cm        NOT 10 cms When written in full, however, the units do take the plural -s, (eg 10 centimetres) except when used as adjectives (eg a ten-centimetre line).
c) No unit is written with a capital letter, even when its abbreviation is written with a capital letter
eg  Inewton  NOT  1 Newton
d) Note the preferred spellings:
gramme rather than gram metre     rather than meter
e) Numbers with more than three digits are separated into groups of three with spaces, not commas or full-stops.
eg  one million is written   1 000 000
NOT  1,000,000  andNOT 1.000.000
f) Figures after the decimal point are separated in the same way.
eg  2-732 981 326
g) The decimal point is written as a point and not as a comma.
eg 3-141  NOT  3,141  (three point one four one)
The following are the more important S.I. units for mathematics:
Quantity	Unit	Pronunciation	Symbol
length	metre	/'mktaf/	m
mass	kilogramme	/'kilagram/	kg
time	second	/'sek and/	s
temperature	kelvin*	/'kelvin/	K
plane angle	radian	/'reidian/	rad
solid angle	steradian	/ste'reidian/	sr
area	square metre	/.skwea 'mi:ty/	m1 :
volume	cubic metre	/,kju:bik 'mi:t3r/	m3    - J
speed	metre per second	/'mi:ta pa 'sek and/	ms"' '
acceleration	metre per second per second	/'mi:tapa 'sek and pa 'sekand/	ms"1
density	kilogramme per cubic metre	/'kilagrsem pa ,kju:btk 'miita/	kgm-J
force	newton**	/'njuitan/	N
pressure	newton per square metre	/'njuitan pa ,skwea 'mi:ta/	Nm"2
energy	joule	/d3u:l/	J
Notes: * °C = °K - 273-15. The degree Celsius will continue to be widely used. **one newton = one kilogramme metre per second per second (IN= Ikgrns"2)			
SYMBOLS AND NOTATION USED IN THIS BOOK
This notation is based on that indicated by the International Organisation for Standardisation.
TV          the set of positive integers and zero, {0,1,2,3, ......>
Z the set of integers,   {0, ±1. ±2, ±3.......}
Z + the set of positive integers,   {1, 2. 3.......}
Q the set of rational numbers
Q + the set of positive rational numbers,
{arjxeO, x>0}
St the set of real numbers
the set of positive real numbers, {x|ar€.», *>0}
CJ the set of complex numbers,
{a + in j o, b € $t]
x a complex number
z * the complex conjugate of z
\z\ the modulus of z
arg z the argument of z
Re ^ the real part of z
Im z the imaginary part of z
[xi.xz.....}    the set with dements xj, X2,.....
n{A) the mmiber of elements in the finite set A
j.... ox {2::     the- set of all ar such that
€ is on element of
£ is not an element of
0 the empty (null) set
U the universal set
U onion
O intersection ......'
A' the complement of (he set A
an , a to the power of ^, nth root of a
(if 0 > 0 then #a 5s 0)
a5, v/a       a to the power      square root of a
(if a > 0 then y/a #s 0)
|:r| the modulus or absolute value of x, that is
f 3; for a: 0 xE$l \ — x for !S < 0    x € #
» identity   or   is equivalent to
sor= is approximately equal to
> is greater than
> or ^ is greater than or equal to
< < or <
it [a.b]
r
SU
"DO Tl
(?)
is less than
is less than or equal to is not greater (han is not less than
the closed interval  a ^ b
the open interval  a < x < b
the nth term of a sequence or series
the common difference of an arithmetic sequence
the common ratio of a geometric sequence
the sum of die first n terms of a sequence, «1 +-U2 +.....4- u«
the sum to infinity of a sequence,
ttl +V2 +.....
Uj +•.....+ Vn
fit
B
/(*) lira /(x)
*—*a.
cis2 /"<*) d"y
/<">(*)
b
In x
rt(n-r)l
f is a function under which each element of set ^4 has im image in set D
j is a function under which x is mapped to y
the image of x tinder the fiinctioa /
the inverse function of the function /
the composite function of / and g
the limit of f(x) as x tends to n
tie derivative of y with respect to x the derivative of /(x) with respect to x
the second derivative of y with respect to x
the second derivative of /{x) with respect to
the nth derivative of y with respect to x
the nth deriviative of /(*) with respect to x the indefinite integral of y with respect to x
the definite integral of y with respect to x
between the limits x = o and x = 6
exponential function of x
logarithm to the base a of x
the natural logarithm of 1,   log,, x
* continued next page
Set operators
e	in, membership	a € {a, b, c}
u	union	{o, 6, c} U {a, d} — {a, b, c, d}
	... over an index set	\JieNsi = s0us1us2u---
n	intersection	{a, b, c} n {a, d} = {a}
	... over an index set	
\	difference	{a, b, c} \ {a, d} = {b, c}
D	strict superset	ZDN
D	superset	
c	strict subset	NcZ
c	subset	NCN
2A	power set of A	if A = {a, b, c}, then 2A = {0, {a}, {b}, {c}, {a, b}, {a, c}( {b, c}, A}
String, grammar, and formal language notation
A	empty string (at times, e is used instead of A)	Aa =	a
*	Kleene star, zero or more occurrences	a* =	{e, a, aa, aaa,..,}
+	one or more occurrences	a+ -	{a, aa, aaa,...}
1 1	string length	|abc|	= 3, \an\ = n, \e\ = 0
	A goes to x (grammar production)		
A x	A derives x		
A x	A derives x in some number of steps		
A =^> x	A derives x according to G		
A x	A derives x according to G in some number of steps		
(qt aa) h (p, a)	(q, aa) yields (p, a) in one step		
* (q, aa) h (p, a)	(q, aa) yields (p, a) in some number of steps		
(q,aa) h (p,a) M	(q, aa) yields (p, a) in one step according to M		
* (q,aa) h (p,a) m	{q, aa) yields (p, a) in some number of steps according to M		
M \ uj	the Turing machine M halts on string w		
M /* w	the Turing machine does not M halt on string w		
And remember...
0! = 1_
Vn € Z, Vm eN,m>0=>n=(n div m)m + (n mod m)
LJTßXsource available at http://ww.cs.ucr.edu/~ciardo/teaching/Notation.tex
A partial list of mathematical symbols and how to read them
Greek alphabet
A	a	alpha	B	ß	beta	r	7	gamma	A	6	delta	E	«, e	epsilon
Z	C	zeta	H		eta	e	0, i?	theta	I	L	iota	K	K	kappa
A	X	lambda	M	M	mu	N	v	nu			xi	0	0	omicron
n		Pi	P	P, Q	rho	S	v, í	sigma	T	T	tau	T	V	upsilon
	(j), <p	phi	X	X	chi	\P		psi		U)	omega			
Important sets
0    empty set		
	natural numbers	{0,1,2,...}
N+	positive integer numbers	{1,2,...}
Z	integer numbers	{...,-2,-1,0,1,2,...}
Q	rational numbers	{m/n :m€Z,n6 N+}
R	real numbers	(-00, +00)
R+	positive real numbers	(0, +oo)
C	complex numbers	{x + iy : x, y € E}         (i is the imaginary unit, i2 = —1)
Logical operators
V	for all, universal quantifier	VneN,n>0	
3	exists, there is, existential quantifier	3n £ N, n > 7	
3!	there is exactly one	3!n e N, n < 1	
A	and	(3 > 2) A (2 > 1)	
	... over an index set	/\ieNBi = BQAB1 ABjA-	
V	or	(2 > 3) V (2 > 1)	
	... over an index set	\fi€NBi = B0V Bi Vß2V---	
	implication, if-then	Va,í>eE, (a = b) =*» (a > b)	
	biimplication, if-and-only-if	Va, b G K, (a = b) <í=> (b = a)	
—1	negation, not	-i(2 > 3)	
	alternative notations for negation	(2 > 3), 2 jť 3	
Arithmetic operators			
II	absolute value	|-7| = |7| = 7	
i:	summation		
n	product		
	factorial	7! = l- 2- 3- 4- 5- 6- 7 = 5040	
( m	j    7i choose m, combinatorial number	/ íl\_ 7i! V m y (n-m)!m!	
mod	modulo, remainder	7 mod 3 = 1, -8 mod 5 = 2	
div	integer quotient	7 div 3 = 2, -8 div 5 = -2