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Last edited 4/15/2008 2:44:00 PM

 

ALPHABETS  incomplete

Table of contents

Alphabets. 1

The Greek alphabet 1

Fraktur 4

Type styles  to be written. 4

Boldface. 4

Blackboard bold. 4

 

Alphabets

The Greek alphabet  

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. 

Pronunciation key

. 

Stress is indicated by an apostrophe after the stredded syllable, for example , .

 

Text Box: The pronunciations given here are based on Western scholarly tradition. Most Greek letters are pronounced differently in modern Greek; β for example is pro¬nounced (last vowel as "a" in father).   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 (Br.)  ).  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 (Br.)  ).

 

  theta (  or (Br.)  ).  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.