MathPro Preferences

11-Jan-1995 Copyright \begin{matrix}c \\ ◯ \end{matrix} 1995 by MathPro Press, Inc. (http://www.mathpro.com/math/MathPro.html) Individuals may make copies for their own personal use. Inquiries to stan@MathPro.com.

Dialects

variation preferred form notes
acknowledgement acknowledgment prefer American to British spelling
centre  center  prefer American to British spelling
cheque  check  prefer American to British spelling
circumcentre  circumcenter  prefer American to British spelling
colour  color  prefer American to British spelling
incentre  incenter  prefer American to British spelling
labelled  labeled  prefer American to British spelling
litre  liter  prefer American to British spelling
metre  meter  prefer American to British spelling
neighbour  neighbor  prefer American to British spelling
travelled  traveled
travelling  traveling  prefer American to British spelling

Hyphenated Words

variation  preferred form  notes
co-prime  coprime  relatively prime
co-set  coset
n-th  nth
non-equivalent  nonequivalent
non-isosceles  nonisosceles
non-negative  nonnegative
non-obtuse  nonobtuse
non-singular  nonsingular
non-zero  nonzero
preimage  pre-image
semi-annual  semiannual
semi-circumference  semicircle
square free  square-free
torsion free  torsion-free
well known  well-known  when used as an adjective: the well-known theorem
well-known  well known  But: This theorem is well known.
X-axis  x-axis
XY plane xy-plane Code as $xy$-plane
x-y plane  xy-plane
This—and that—are fine. This — and that — are fine. Space around em-dash
3,4,5 triangle 3-4-5 triangle Use hyphen, not minus sign (do not use math mode)
three-digit  3-digit
a score of -1  a score of −1  Use $-1$

Words

variation  preferred form  notes
Abelian  abelian  named after Abel, but common practice prevails
aeroplane  airplane
angle of reflexion  angle of reflection
angular points of a triangle vertices of a triangle
solid sphere ball balls are solid; spheres are hollow
anticlockwise  counterclockwise
biquadrate  perfect fourth power
cartesian Cartesian named after Descartes
Tchebychef  Chebyshev
checkerboard chessboard board with black and white squares
circumscribable polygon  cyclic polygon
concyclic cyclic can be inscribed in a circle
inscriptible  cyclic
diophantine equation  Diophantine equation named after Diophantus
disk disc A circle and its interior.
dominos  dominoes
end point  endpoint
Erd\H os                 Erd\H{o}s  Do not have any spaces within a name.
Erd{\H o}s               Erd\H{o}s  Do not have any spaces within a name.
euclidean Euclidean named after Euclid
factorized  factored
iff  if and only if
median point of a triangle centroid of a triangle
mid point  midpoint
middle point  midpoint
point of bisection  midpoint
counting numbers  natural numbers
parallelopiped  parallelepiped
per cent  percent  prefer “%” after number
6 percent interest  6% interest  prefer “%” after number
pythagorean  Pythagorean  named after Pythagoras
hollow ball  sphere  balls are solid; spheres are hollow
circular ring  torus  or annulus if in two dimensions
right-angled triangle  right triangle
U. S.  U.S.
which that If both sound correct, use “that”
zeroes  zeros

Punctuation

variation  preferred form  notes
A widget is called a “foobar.”  A widget is called a “foobar”.  Use logical rather than traditional quoting rules.
They are “foo,” “bar,” and “gluk.” They are “foo”, “bar”, and “gluk”. Unrelated punctuation goes outside the quotes.
Tom said, “Where are you?”.  Tom said, “Where are you?”  In dialogue, use traditional quoting rules.
Tom said, “I am here”.  Tom said, “I am here.”  In dialogue, use traditional quoting rules.
The length is 3 in..  The length is 3 in.  Consecutive punctuation characters merge.
Is the length 3 in?  Is the length 3 in.?  Different punctuation characters remain distinct.
ten’s digit  tens digit
unit’s digit  units digit
$7000  $7,000  Use commas with money.
in ratio 1, 3, 5  in ratio 1 : 3 : 5  Use $1:3:5$
3: 1  3 : 1  Use $3:1$
a : b :: c : d  a : b = c : d  Use “=” with proportions
temperature was 65^{∘}F  temperature was 65^{∘}F

Phrases

variation  preferred form  notes
Tom, Dick and Harry  Tom, Dick, and Harry  Use comma before “and” in list of 3 or more.
find the chance that  find the probability that
Given n points. Given are n points. Use full sentences.
pick a point in the circumference pick a point on the circumference
a point in the surface of a circle a point inside a circle
a point in the base of a triangle a point on the base of a triangle
if a line be drawn  if a line is drawn
in a plane triangle  in a triangle
M.S. Klamkin M. S. Klamkin Leave space between first and middle names.
13-sided polygon  13-gon
Let x, y be real numbers.  Let x and y be real numbers.  But: “for x, y ∈ S” is okay.
Jordan curve theorem  Jordan Curve Theorem  initial caps on names of theorems
by the Pythagorean theorem  by the Pythagorean Theorem  initial caps on names of theorems
Mr. A plays a game.  Mr. A plays a game.  Even better: Andy plays a game.
city A and city B  city A and city B  Use roman for names of things.

Numbers

variation  preferred form  notes
4\frac{1}{2}  4^{1}/_{2}  Use $4\frac 1/2$ for mixed fractions
\frac{a}{b}  a/b  for very small, simple fractions appearing in-line
P/_{4}  P/4  Don’t use \frac when variables are involved.
12, 345  12,345  Use $12{,}345$
x + y = 12,345  x + y = 12345  Don’t use commas inside numbers in equations.
John has 1000 apples.  John has 1,000 apples. Use commas in numbers in normal text.
Mary has 3 apples.  Mary has three apples Numbers from 1 to 9 used as adjectives are spelled out
Mary has thirteen apples. Mary has 13 apples  adjectives 10 or larger use numerals
If 20 is divided by three If 20 is divided by 3  numbers used as nouns are always numerals
It took three hours.  It took 3 hours.  Units of measurement are always numerals.
1/3 = .333 ⋯  1/3 = .333 …  Use \ldots

Integrals

variation  preferred form  notes
∫ g(x)dx  ∫ g(x) dx  Use $\int g(x)\,dx$.

Add thin space before dx if not already present.

        ∫_{a}^{b} ∫_{a}^{b} g(x) dxdy  ∫_{a}^{b}∫_{a}^{b} g(x) dxdy  Use $\int _a^b\kern -3pt\int _a^b g(x)\,dxdy$.

∫ ∫ ∫ g(x) dxdydz ∫∫∫ g(x) dxdydz Kern multiple integrals closer together.

Dots

variation  preferred form  notes
a < b < … < x  a < b < ⋯ < x  Use $a<b<\cdots <x$
a + b + … + x  a + b + ⋯ + x  Use $a+b+\cdots +x$
a · b … x  a · b ⋯ x  Use $a\cdot b\cdots x$
Let a, b, c, …, z be Let a, b, c, …, z be Use $a$, $b$, $c,\ldots ,z$
for n = 1, 2, . . ..  for n = 1, 2, ….  Use $n=1,2,\ldots \ .$

Expressions

variation preferred form notes
$\varepsilon $        $\epsilon $  We will control how this looks (probably ε).
triangle abc  triangle ABC  prefer capital letters for names of points
φ  ϕ  Use \phi rather than \varphi
lim_{x↑a} f(x)  lim_{x→a−} f(x)
lim_{x↓a} f(x)  lim_{x→a+} f(x)

a by b  a × b  Use $a\times b$

A(x) := f(x)  A(x) = f(x)
all integers < n all integers less than n math symbols are not abbreviations for English words
If A then B. Prove this. Prove that if A then B.
A is a point on side BC Let A be a point on side BC Don’t start a sentence with mathematics.
A and B flip a coin  Players A and B flip a coin  Don’t start a sentence with mathematics.

f : A → B  f: A → B  Use $f\colon A\to B$

3|81  3 | 81  Use $3\mid 81$
{x|x > a}  {x | x > a}  Use $\{x\mid x>a\}$
\overline{lim}  lim sup  Use $\limsup $
{x : x > a}  {x | x > a}  Use $\{x\mid x>a\}$. Prefer “|” to “:”
{x | |x| > a}  {x : |x| > a}  Use $\{x:|x|>a\}$. Use “:” if “|” would be awkward.
\underline{lim}  lim inf  Use $\liminf $
∑_{k=1}^{⌊ \frac{n}{2} ⌋}  ∑_{k=1}^{⌊n/2⌋}  Use $\{\lfloor n/2\rfloor \}$ in exponent.
R_{+}  R^{+}  Use $\R ^+$ for positive real numbers
N = {0, 1, 2, …}  N = {1, 2, 3, …}  Natural numbers begin with 1.
N ∪ {0}  N_{0}  Nonnegative integers
Z^{+}  N  Positive integers (natural numbers)
triangle △ABC  triangle ABC  or △ABC (not both)
3 | a + b  3 | (a + b)
cos ABC  cos^{}A̸BC

Functions

variation preferred form notes
nC_{k}  \binom{n}{k}  Binomial coefficient; use \{n\choose k\}
nP_{r}  _{n}P_{r}  number of permutations of n things taken r at a time

                 [x]  ⌊x⌋  Use $\lfloor x\rfloor $

(m, n) = d gcd(m, n) = d Use $\gcd (m,n)=d$
[m, n] = d lcm[m, n] = d Use $\lcm [m,n]=d$
ℜ(z)  Re(z)  Use $\Re (z)$
ℑ(z)  Im(z)  Use $\Im (z)$
tg x  tan x  Use $\tan x$
ctg x  cot x  Use $\cot x$
sh x  sinh x  Use $\sinh x$
ch x  cosh x  Use $\cosh x$
Apea-tg  arctan

Additional preferences for “Homothety” book

variation preferred form notes
The midpoints of AB and CD are respectively P and Q. The midpoints of AB and CD are P and Q, respectively.
in view of (1)  in view of equation (1)
chord AB in circle C  chord AB of circle C
Let P be a point of circle C.  Let P be a point on circle C.
point P of segment AB  point P on segment AB
right triangle of hypotenuse AB  right triangle with hypotenuse AB
line meets the circles consecutively at A, B, C, and D  line meets the circles at A, B, C, and D in succession
the greater circle  the larger circle
f maps A to B  f maps A into B
lines AB, CD, and EF have a common point  lines AB, CD, and EF are concurrent
homothety of coefficient k  homothety with coefficient k
homothety of center M  homothety with center M
circle of center P  circle with center P
circle of radius r  circle with radius r
center of incircle  incenter
circle circumscribed about △ABC  circumcircle of △ABC
isogonal conjugate to the point M  isogonal conjugate of the point M
Put x = ab.  Set x = ab.
coefficient of similarity  ratio of similitude
midpoint of the arc AB  midpoint of arc AB
inscribed in the triangle ABC  inscribed in triangle ABC
touches the side AB  touches side AB
incircle of the triangle ABC  incircle of triangle ABC
Find the area of the triangle ABC.  Find the area of triangle ABC.
In the same time, we find that  At the same time, we find that
altitudes to the respective sides  altitudes to the corresponding sides

Additional preferences for “Vermont” book

variation preferred form notes
Give the value of  Find the value of
Write the value of  Find the value of
Given a square ABCD. Let ABCD be a square. Use full sentences with verbs.
Divide x^{2} − y^{2} by x − y.  Find the quotient when x^{2} − y^{2} is divided by x − y.
The sides of a triangle are 3, 4, 5. The lengths of the sides of a triangle are 3, 4, and 5. The variation is also acceptable.
A 3” rod.  A 3" rod.  Even better: A three inch rod.
Arcsin x  arcsin x  Code as $\arcsin x$.
AB = 6 units  AB = 6
16 sq. in.  16 in^{2}
1st  first
6th  sixth
angle ABC contains 15^{∘}  ^{}A̸BC = 15^{∘}
find the altitude find the length of the altitude But: “find the radius” is okay.
Solve the equation for x:  Solve for x:
degree measurement of angle A  degree measure of angle A

Additional preferences for the Monthly

variation preferred form notes
Show that a = b holds.  Show that a = b.
Describe a circle so that  Construct a circle such that
the angular points of a rhombus the vertices of a rhombus
a horse is tethered to a goat is tethered to Use goats with tether problems.
a section of a cube  a cross section of a cube
a tower AB = a  a tower AB of length a
at each point of a parabola  at each point on a parabola
fracture a rod  cut a rod
United States bond  US bond
x^{2} + y^{2} = square x^{2} + y^{2} = Use \square
true to six decimal places  correct to six decimal places
consecutive integers 1 to n  consecutive integers from 1 to n

Additional preferences for ARML book

variation  preferred form  notes
T NY W R  TNYWR  The Number You Will Receive. (Use \tt .)
[Let T = TNYWR]  Let T = TNYWR.  Don’t forget period at end of sentence.
a ≡ b(MAD c)  a ≡ b (MAD c)  space before open parenthesis
\underline{Hint}:  Hint:  roman
\underline{Note}:  Note:  roman
Note:  Note:  roman
the “Greatest Integer Function” the Greatest Integer Function
⌊x⌋  [x]  special for ARML book only
A⃗B  \overrightarrow{AB}  ray from A to B; use \overrightarrow
The 3-digit number \underline{1} \underline{A} \underline{4}  The 3-digit number 1A4  Use typewriter font for digits
The 3-digit number \underline{1}\underline{A}\underline{4}  The 3-digit number 1A4  Use typewriter font for digits
[T = 8]  We have T = 8.  At start of relay problems.
[T = 8,S = 7]  We have T = 8 and S = 7.  At start of relay problems.
a + 1 = b + 1 → a = b.  From a + 1 = b + 1, we get a = b. or “The equation a + 1 = b + 1 implies a = b.”
a + 1 = b + 1 ⇒ a = b.  From a + 1 = b + 1, we get a = b. or “Since a + 1 = b + 1, we see that a = b.”
\overleftrightarrow{AB}  \overleftrightarrow{AB}  Line through A and B
a ∗ b  a ⋆ b  Use \star for special operator