Last edited 4/15/2008 2:44:00 PM
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ALPHABETS incomplete
Every letter of the Greek alphabet except omicron is used in mathematics.
All the lowercase forms and all those uppercase forms that are not identical with the Roman alphabet are used.
Mathematicians pronounce these letters in various ways. There is a substantial difference between the
way American mathematicians pronounce them and they way English-speaking
mathematicians whose background is British pronounce them. (This is indicated below by (Br).)
Newcomers to abstract math often
don’t know the names of some of the letters, or mispronounce them if they
do. I have heard young
mathematicians pronounce and
in exactly the same way, and since they were
writing it on the board I doubt that anyone except language nuts like me
noticed that they were doing it. Another
one pronounced
as “
” and
as “
”.
Many Greek letters are used as proper names of mathematical objects. I have indicated the most widely known ones here. They are all discussed in MathWorld and in Wikipedia. Greek letters are widely used in other sciences, but I have not attempted to cover those uses here.
Mathematicians freely use Greek letters,
including , to many anything they want,
without regard to their use as a particular proper name.
.
Stress is indicated by an apostrophe after
the stredded syllable, for example ,
.

alpha (
).
beta (
or (Br)
). The
Euler Beta function is a function of two variables denoted by B. (The
capital beta looks just like a B but they write it that way and call it “beta”
anyway.) The Dirichlet beta function is
a function of one variable denoted by
.
gamma (
). Don’t refer to
as “r”, or snooty cognoscenti may ridicule
you. The Gamma function, denoted by
, has the property
that
delta (
). The
Dirac delta function and the Kronecker delta are denoted by
.
denotes the change or increment in x and
denotes the Laplacian of a multivariable function.
epsilon (
or
;
is occasionally heard). The
letter
is frequently used informally to denoted a
positive real number that is thought of as being small. The symbol
for elementhood is strictly
speaking not an epsilon, but many mathematicians use an epsilon for it anyway.
zeta (
or (
).
There are many functions called “zeta functions” and they are mostly
related to each other. The unproved
Riemann hypothesis concerns the Riemann
-function.
eta (
or (
).
theta (
or (
).
Lower case theta may also be written
. The letter
is commonly used to denote an angle. There is also a Jacobi
-function related to the Riemann
-function.