Mathematical Terms and Symbols

Abbreviations     (Note:  Capitalization of some abbreviations is not standardized and may vary from author to author.)

Abbreviation                   Meaning

ACC                
adj                
Ai                 
Alt or An        
arccos          
arccossec or arccsc
arcot                         
arcosech or arcsch   
arcosh                    
arcoth                 
arcsec                
arcsin                 
arctan                   
arg                        
arg max                 
arg min                 
arsech                   
arsinh                          
artanh                         
Aut                        

Bi                               

Card                 
cdf                    
char              
Cl                              
cos                 
cosec or csc                
cosech or csch    
cosh                         
cot                             
coth                
cov        
curl or rot               
deg  or ∂                    
del                       
det                              
dim                    
div                    
dom                   
End                       
Ei                           
erf                       
erfc                           
exp                        
Ext                       
ext                       

FOL                         
Frob                    

Gal                         
gcd or hcf              
GL                          
grad                     

Hom                            
iff                        
Im                       
inf                        
int                      

Ker                   

lcm                        
lg                           
LHS                          
Li                           
li                            
lim                         
ln                          
log                          
LST                        
lub                       

max                       
min                        
mod                       
mx                          
NTS                         

ord                          

pdf                               
pf                            
PGL                          
pmf                              
Pr or P                 
PSL                      
   
ran                     
Re                          
rep                      
RHS                        
Rk                          
rng                          
RTP                          
sec                       
sech                      
seg                      
sgn                       
sin                          
sinh                       
SL                       
Sp                        
Spec                         
st                             
STP                          
sup                      
supp                        
Sym or Sn                  

tan                           
tanh                           
TFAE                  
Thm                    
Tor                  
Tr                        

var                 

walog                     
wff                          
wlog                        
WO                      
wrt                        
WTP                 
WTS                      
ZF                   
ZFC                         

Axiom of Choice
adjugate of a matrix
Airy function
alternating group
inverse cosine function
inverse cosecant function
inverse cotangent function
inverse hyperbolic cosecant function
inverse hyperbolic cosine function
inverse hyperbolic cotangent function
inverse secant function
inverse sine function
inverse tangent function
argument of a complex number
argument of the maximum
argument of the minimum
inverse hyperbolic secant function
inverse hyperbolic sine function
inverse hyperbolic tangent function
automorphism group

Airy function of the second kind

cardinality of a set
cumulative density function
characteristic of a ring
topological closure
cosine function
cosecant  function
hyperbolic cosecant function
hyperbolic cosine function
cotangent
hyperbolic
covariance of a pair of random variables
curl of a vector field
degree of a polynomial
del, a differential operator
determinant of a matrix or linear transformation
dimension of a vector space
divergence of a vector field
domain of a function (or, more generally, a relation)
categories of endomorphisms
exponential integral function
error function
complementary error function
exponential function
Ext functor
exterior

first-order logic
Frobenius endomorphism

Galois group
greatest / highest common divisor of two numbers
general linear group
gradient of a scolar field

Hom functor
if and only if
either image of a function or imaginary part of a complex number
infimum of a set
interior

kernel

lowest common multiple of two numbers
logarithm
left-hand side of an equation    
offset logarithmic integral function or linearly independent 
logarithmic integral function or linearly independent 
limit of a sequence or limit of a function
natural logarithm, loge
logarithm
language of set theory
least upper bound

maximum of a set
minimum of a set
modulo
matrix
need to show

ordinal numbers of a well-ordered set

probability density function                               
proof
projective general linear group
probability mass function
probability of an event
projective special linear group
   
range of a function
real part of a complex number
respectively
right-hand side of an equation
rank
non-unital ring
required to prove
secant function
hyperbolic secant function
initial segment of
signum function
sine function
hyperbolic sine function
special linear group
linear span of a set of vectors
spectrum of a ring
such that or so that
sufficient to prove
supremum of a set
support of a function
symmetric group

tangent function
hyperbolic tangent function
the following are equivalent
theorum
Tor functor
field trace or trace of a matrix or linear transformation

variance of a random variable

without any loss of generality
well-formed formula
without loss of generality
well-ordered set
with respect to or with regard to
want to prove
want to show
Zermelo-Fraenkel axioms of set theory
Zermelo-Fraenkel axioms (with the Axiom of Choice) of set theory

 

Symbols   

Symbol             Meaning

             
                
<              
>           
:=               
equals, is the same as
such that, under the condition
is less than
is greater than
is equal by definition to