Symbol  Name  Explanation  Examples 

Read as  
Category  
=
 equality  x = y means x and y represent the same thing or value.  1 + 1 = 2 
is equal to; equals  
everywhere  
≠
<> !=  inequation  x ≠ y means that x and y do not represent the same thing or value. (The symbols != and <> are primarily from computer science. They are avoided in mathematical texts.)  1 ≠ 2 
is not equal to; does not equal  
everywhere  
<
> ≪ ≫  strict inequality  x < y means x is less than y. x > y means x is greater than y. x ≪ y means x is much less than y. x ≫ y means x is much greater than y.  3 < 4 5 > 4 0.003 ≪ 1000000 
is less than, is greater than, is much less than, is much greater than  
order theory  
≤
<= ≥ >=  inequality  x ≤ y means x is less than or equal to y. x ≥ y means x is greater than or equal to y. (The symbols <= and >= are primarily from computer science. They are avoided in mathematical texts.)  3 ≤ 4 and 5 ≤ 5 5 ≥ 4 and 5 ≥ 5 
is less than or equal to, is greater than or equal to  
order theory  
<·
 cover  x <• y means that x is covered by y.  {1, 8} <• {1, 3, 8} among the subsets of {1, 2, …, 10} ordered by containment. 
is covered by  
order theory  
∝
 proportionality  y ∝ x means that y = kx for some constant k.  if y = 2x, then y ∝ x 
is proportional to; varies as  
everywhere  
+
 addition  4 + 6 means the sum of 4 and 6.  2 + 7 = 9 
plus  
arithmetic  
disjoint union  A_{1} + A_{2} means the disjoint union of sets A_{1} and A_{2}.  A_{1} = {1, 2, 3, 4} ∧ A_{2} = {2, 4, 5, 7} ⇒ A_{1} + A_{2} = {(1,1), (2,1), (3,1), (4,1), (2,2), (4,2), (5,2), (7,2)}  
the disjoint union of ... and ...  
set theory  
−
 subtraction  9 − 4 means the subtraction of 4 from 9.  8 − 3 = 5 
minus  
arithmetic  
negative sign  −3 means the negative of the number 3.  −(−5) = 5  
negative; minus; the opposite of  
arithmetic  
settheoretic complement  A − B means the set that contains all the elements of A that are not in B. ∖ can also be used for settheoretic complement as described below.  {1,2,4} − {1,3,4} = {2}  
minus; without  
set theory  
×
 multiplication  3 × 4 means the multiplication of 3 by 4.  7 × 8 = 56 
times  
arithmetic  
Cartesian product  X×Y means the set of all ordered pairs with the first element of each pair selected from X and the second element selected from Y.  {1,2} × {3,4} = {(1,3),(1,4),(2,3),(2,4)}  
the Cartesian product of ... and ...; the direct product of ... and ...  
set theory  
cross product  u × v means the cross product of vectors u and v  (1,2,5) × (3,4,−1) = (−22, 16, − 2)  
cross  
vector algebra  
·
 multiplication  3 · 4 means the multiplication of 3 by 4.  7 · 8 = 56 
times  
arithmetic  
dot product  u · v means the dot product of vectors u and v  (1,2,5) · (3,4,−1) = 6  
dot  
vector algebra  
÷
⁄  division  6 ÷ 3 or 6 ⁄ 3 means the division of 6 by 3.  2 ÷ 4 = .5 12 ⁄ 4 = 3 
divided by  
arithmetic  
quotient group  G / H means the quotient of group G modulo its subgroup H.  {0, a, 2a, b, b+a, b+2a} / {0, b} = {{0, b}, {a, b+a}, {2a, b+2a}}  
mod  
group theory  
quotient set  A/~ means the set of all ~ equivalence classes in A.  If we define ~ by x ~ y ⇔ x − y ∈ ℤ, then ℝ/~ = {{x + n : n ∈ ℤ} : x ∈ (0,1]}  
mod  
set theory  
±
 plusminus  6 ± 3 means both 6 + 3 and 6  3.  The equation x = 5 ± √4, has two solutions, x = 7 and x = 3. 
plus or minus  
arithmetic  
plusminus  10 ± 2 or equivalently 10 ± 20% means the range from 10 − 2 to 10 + 2.  If a = 100 ± 1 mm, then a ≥ 99 mm and a ≤ 101 mm.  
plus or minus  
measurement  
∓
 minusplus  6 ± (3 ∓ 5) means both 6 + (3  5) and 6  (3 + 5).  cos(x ± y) = cos(x) cos(y) ∓ sin(x) sin(y). 
minus or plus  
arithmetic  
√
 square root  $sqrt\{x\}$ means the positive number whose square is $x$.  $sqrt\{4\}=2$ 
the principal square root of; square root  
real numbers  
complex square root  if $z=r,exp(iphi)$ is represented in polar coordinates with $pi\; <\; phi\; le\; pi$, then $sqrt\{z\}\; =\; sqrt\{r\}\; exp(i\; phi/2)$.  $sqrt\{1\}=i$  
the complex square root of … square root  
complex numbers  
…
 absolute value or modulus  x means the distance along the real line (or across the complex plane) between x and zero.  3 = 3 –5 = 5 = 5  i  = 1  3 + 4i  = 5 
absolute value (modulus) of  
numbers  
Euclidean distance  x – y means the Euclidean distance between x and y.  For x = (1,1), and y = (4,5), x – y = √([1–4]^{2} + [1–5]^{2}) = 5  
Euclidean distance between; Euclidean norm of  
Geometry  
Determinant  A means the determinant of the matrix A  $begin\{vmatrix\}$1&2 2&4end{vmatrix} = 0  
determinant of  
Matrix theory  
Cardinality  X means the cardinality of the set X.  {3, 5, 7, 9} = 4.  
cardinality of  
set theory  

 divides  A single vertical bar is used to denote divisibility. ab means a divides b.  Since 15 = 3×5, it is true that 315 and 515. 
divides  
Number theory  
Conditional probability  A single vertical bar is used to describe the probability of an event given another event happening. P(AB) means a given b.  If P(A)=0.4 and P(B)=0.5, P(AB)=((0.4)(0.5))/(0.5)=0.4  
Given  
Probability  
!
 factorial  n! is the product 1 × 2 × ... × n.  4! = 1 × 2 × 3 × 4 = 24 
factorial  
combinatorics  
^{T}
^{tr}  transpose  Swap rows for columns  If $A\; =\; (a\_\{ij\})$ then $A^mathrm\{T\}\; =\; (a\_\{ji\})$. 
transpose  
matrix operations  
~
 probability distribution  X ~ D, means the random variable X has the probability distribution D.  ''X ~ N(0,1), the standard normal distribution 
has distribution  
statistics  
Row equivalence  A~B means that B can be generated by using a series of elementary row operations on A  $begin\{bmatrix\}$1&2 2&4end{bmatrix} sim begin{bmatrix} 1&2 0&0end{bmatrix}  
is row equivalent to  
Matrix theory  
same order of magnitude  m ~ n means the quantities m and n have the same order of magnitude, or general size. (Note that ~ is used for an approximation that is poor, otherwise use ≈ .)  2 ~ 5 8 × 9 ~ 100 but π^{2} ≈ 10  
roughly similar; poorly approximates  
Approximation theory  
asymptotically equivalent  f ~ g means $lim\_\{ntoinfty\}\; frac\{f(n)\}\{g(n)\}\; =\; 1$.  x ~ x+1  
is asymptotically equivalent to  
Asymptotic analysis  
Equivalence relation  a ~ b means $b\; in\; [a]$ (and equivalently $a\; in\; [b]$).  1 ~ 5 mod 4  
are in the same equivalence class  
everywhere  
≈
 approximately equal  x ≈ y means x is approximately equal to y.  π ≈ 3.14159 
is approximately equal to  
everywhere  
isomorphism  G ≈ H means that group G is isomorphic to group H.  Q / {1, −1} ≈ V, where Q is the quaternion group and V is the Klein fourgroup.  
is isomorphic to  
group theory  
◅
 normal subgroup  N ◅ G means that N is a normal subgroup of group G.  Z(G) ◅ G 
is a normal subgroup of  
group theory  
ideal  I ◅ R means that I is an ideal of ring R.  (2) ◅ Z  
is an ideal of  
ring theory  
∴
 therefore  Sometimes used in proofs before logical consequences.  All humans are mortal. Socrates is a human. ∴ Socrates is mortal. 
therefore  
everywhere  
∵
 because  Sometimes used in proofs before reasoning.  3331 is prime ∵ it has no positive factors other than itself and one. 
because  
everywhere  
⇒
→ ⊃  material implication  A ⇒ B means if A is true then B is also true; if A is false then nothing is said about B. → may mean the same as ⇒, or it may have the meaning for functions given below. ⊃ may mean the same as ⇒, or it may have the meaning for superset given below.  x = 2 ⇒ x^{2} = 4 is true, but x^{2} = 4 ⇒ x = 2 is in general false (since x could be −2). 
implies; if … then  
propositional logic, Heyting algebra  
⇔
↔  material equivalence  A ⇔ B means A is true if B is true and A is false if B is false.  x + 5 = y +2 ⇔ x + 3 = y 
if and only if; iff  
propositional logic  
¬
˜  logical negation  The statement ¬A is true if and only if A is false. A slash placed through another operator is the same as "¬" placed in front. (The symbol ~ has many other uses, so ¬ or the slash notation is preferred.)  ¬(¬A) ⇔ A x ≠ y ⇔ ¬(x = y) 
not  
propositional logic  
∧
 logical conjunction or meet in a lattice  The statement A ∧ B is true if A and B are both true; else it is false. For functions A(x) and B(x), A(x) ∧ B(x) is used to mean min(A(x), B(x)). (Old notation) u ∧ v means the cross product of vectors u and v.  n < 4 ∧ n >2 ⇔ n = 3 when n is a natural number. 
and; min  
propositional logic, lattice theory  
∨
 logical disjunction or join in a lattice  The statement A ∨ B is true if A or B (or both) are true; if both are false, the statement is false. For functions A(x) and B(x), A(x) ∨ B(x) is used to mean max(A(x), B(x)).  n ≥ 4 ∨ n ≤ 2 ⇔ n ≠ 3 when n is a natural number. 
or; max  
propositional logic, lattice theory  
⊕ ⊻
 exclusive or  The statement A ⊕ B is true when either A or B, but not both, are true. A ⊻ B means the same.  (¬A) ⊕ A is always true, A ⊕ A is always false. 
xor  
propositional logic, Boolean algebra  
direct sum  The direct sum is a special way of combining several modules into one general module (the symbol ⊕ is used, ⊻ is only for logic).  Most commonly, for vector spaces U, V, and W, the following consequence is used: U = V ⊕ W ⇔ (U = V + W) ∧ (V ∩ W = {0})  
direct sum of  
Abstract algebra  
∀
 universal quantification  ∀ x: P(x) means P(x) is true for all x.  ∀ n ∈ ℕ: n^{2} ≥ n. 
for all; for any; for each  
predicate logic  
∃
 existential quantification  ∃ x: P(x) means there is at least one x such that P(x) is true.  ∃ n ∈ ℕ: n is even. 
there exists  
predicate logic  
∃!
 uniqueness quantification  ∃! x: P(x) means there is exactly one x such that P(x) is true.  ∃! n ∈ ℕ: n + 5 = 2n. 
there exists exactly one  
predicate logic  
:=
≡ :⇔  definition  x := y or x ≡ y means x is defined to be another name for y (Some writers use ≡ to mean congruence). P :⇔ Q means P is defined to be logically equivalent to Q.  cosh x := (1/2)(exp(x)+exp(x)) 
is defined as  
everywhere  
$triangleq$
 delta equal to  $triangleq$ means equal by definition. When $triangleq$ is used, equality is not true generally, but rather equality is true under certain assumptions that are taken in context. Some writers prefer ≡.  $p(x\_1,x\_2,...,x\_n)\; triangleq\; prod\_\{i=1\}^n\; p(x\_i\; \; x\_\{pi\_i\})$. 
equal by definition  
everywhere  
≅
 congruence  △ABC ≅ △DEF means triangle ABC is congruent to (has the same measurements as) triangle DEF.  
is congruent to  
geometry  
≡
 congruence relation  a ≡ b (mod n) means a − b is divisible by n  5 ≡ 11 (mod 3) 
... is congruent to ... modulo ...  
modular arithmetic  
{ , }
 set brackets  {a,b,c} means the set consisting of a, b, and c.  ℕ = { 1, 2, 3, …} 
the set of …  
set theory  
{ : }
{  }  set builder notation  {x : P(x)} means the set of all x for which P(x) is true. {x  P(x)} is the same as {x : P(x)}.  {n ∈ ℕ : n^{2} < 20} = { 1, 2, 3, 4} 
the set of … such that  
set theory  
∅
{ }  empty set  ∅ means the set with no elements. { } means the same.  {n ∈ ℕ : 1 < n^{2} < 4} = ∅ 
the empty set  
set theory  
∈
∉  set membership  a ∈ S means a is an element of the set S; a ∉ S means a is not an element of S.  (1/2)^{−1} ∈ ℕ 2^{−1} ∉ ℕ 
is an element of; is not an element of  
everywhere, set theory  
⊆
⊂  subset  (subset) A ⊆ B means every element of A is also element of B. (proper subset) A ⊂ B means A ⊆ B but A ≠ B. (Some writers use the symbol ⊂ as if it were the same as ⊆.)  (A ∩ B) ⊆ A ℕ ⊂ ℚ ℚ ⊂ ℝ 
is a subset of  
set theory  
⊇
⊃  superset  A ⊇ B means every element of B is also element of A. A ⊃ B means A ⊇ B but A ≠ B. (Some writers use the symbol ⊃ as if it were the same as ⊇.)  (A ∪ B) ⊇ B ℝ ⊃ ℚ 
is a superset of  
set theory  
∪
 settheoretic union  A ∪ B means the set of those elements which are either in A, or in B, or in both.  A ⊆ B ⇔ (A ∪ B) = B (inclusive) 
the union of … or … union  
set theory  
∩
 settheoretic intersection  A ∩ B means the set that contains all those elements that A and B have in common.  {x ∈ ℝ : x^{2} = 1} ∩ ℕ = {1} 
intersected with; intersect  
set theory  
∆
 symmetric difference  A ∆ B means the set of elements in exactly one of A or B.  {1,5,6,8} ∆ {2,5,8} = {1,2,6} 
symmetric difference  
set theory  
∖
 settheoretic complement  A ∖ B means the set that contains all those elements of A that are not in B. − can also be used for settheoretic complement as described above.  {1,2,3,4} ∖ {3,4,5,6} = {1,2} 
minus; without  
set theory  
( )
 function application  f(x) means the value of the function f at the element x.  If f(x) := x^{2}, then f(3) = 3^{2} = 9. 
of  
set theory  
precedence grouping  Perform the operations inside the parentheses first.  (8/4)/2 = 2/2 = 1, but 8/(4/2) = 8/2 = 4.  
parentheses  
everywhere  
f:X→Y
 function arrow  f: X → Y means the function f maps the set X into the set Y.  Let f: ℤ → ℕ be defined by f(x) := x^{2}. 
from … to  
set theory,type theory  
o
 function composition  fog is the function, such that (fog)(x) = f(g(x)).  if f(x) := 2x, and g(x) := x + 3, then (fog)(x) = 2(x + 3). 
composed with  
set theory  
ℕ
N  natural numbers  N means { 1, 2, 3, ...}, but see the article on natural numbers for a different convention.  ℕ = {a : a ∈ ℤ, a ≠ 0} 
N  
numbers  
ℤ
Z  integers  ℤ means {..., −3, −2, −1, 0, 1, 2, 3, ...} and ℤ_{+} means {1, 2, 3, ...} = ℕ.  ℤ = {p, p : p ∈ ℕ} ∪ {0} 
Z  
numbers  
ℚ
Q  rational numbers  ℚ means {p/q : p ∈ ℤ, q ∈ ℕ}.  3.14000... ∈ ℚ π ∉ ℚ 
Q  
numbers  
ℝ
R  real numbers  ℝ means the set of real numbers.  π ∈ ℝ √(−1) ∉ ℝ 
R  
numbers  
ℂ
C  complex numbers  ℂ means {a + b i : a,b ∈ ℝ}.  i = √(−1) ∈ ℂ 
C  
numbers  
arbitrary constant  C can be any number, most likely unknown; usually occurs when calculating antiderivatives.  if f(x) = 6x² + 4x, then F(x) = 2x³ + 2x² + C, where F'(x) = f(x)  
C  
integral calculus  
𝕂
K  real or complex numbers  K means the statement holds substituting K for R and also for C. 

K  
linear algebra  
∞
 infinity  ∞ is an element of the extended number line that is greater than all real numbers; it often occurs in limits.  $lim\_\{xto\; 0\}\; frac\{1\}$ 
infinity  
numbers  
…
 norm   x  is the norm of the element x of a normed vector space.   x + y  ≤  x  +  y  
norm of length of  
linear algebra  
∑
 summation  $sum\_\{k=1\}^\{n\}\{a\_k\}$ means a_{1} + a_{2} + … + a_{n}. 
$sum\_\{k=1\}^\{4\}\{k^2\}$ = 1^{2} + 2^{2} + 3^{2} + 4^{2}

sum over … from … to … of  
arithmetic  
∏
 product  $prod\_\{k=1\}^na\_k$ means a_{1}a_{2}···a_{n}. 
$prod\_\{k=1\}^4(k+2)$ = (1+2)(2+2)(3+2)(4+2)

product over … from … to … of  
arithmetic  
Cartesian product 
$prod\_\{i=0\}^\{n\}\{Y\_i\}$ means the set of all (n+1)tuples
 $prod\_\{n=1\}^\{3\}\{mathbb\{R\}\}\; =\; mathbb\{R\}timesmathbb\{R\}timesmathbb\{R\}\; =\; mathbb\{R\}^3$  
the Cartesian product of; the direct product of  
set theory  
∐
 coproduct  
coproduct over … from … to … of  
category theory  
′
^{•}  derivative  f ′(x) is the derivative of the function f at the point x, i.e., the slope of the tangent to f at x. The dot notation indicates a time derivative. That is $dot\{x\}(t)=frac\{partial\}\{partial\; t\}x(t)$.  If f(x) := x^{2}, then f ′(x) = 2x 
… prime derivative of  
calculus  
∫
 indefinite integral or antiderivative  ∫ f(x) dx means a function whose derivative is f.  ∫x^{2} dx = x^{3}/3 + C 
indefinite integral of the antiderivative of  
calculus  
definite integral  ∫_{a}^{b} f(x) dx means the signed area between the xaxis and the graph of the function f between x = a and x = b.  ∫_{a}^{b} x^{2 } dx = b^{3}/3  a^{3}/3;  
integral from … to … of … with respect to  
calculus  
∮
 contour integral or closed line integral  Similar to the integral, but used to denote a single integration over a closed curve or loop. It is sometimes used in physics texts involving equations regarding Gauss's Law, and while these formulas involve a closed surface integral, the representations describe only the first integration of the volume over the enclosing surface. Instances where the latter requires simultaneous double integration, the symbol ∯ would be more appropriate. A third related symbol is the closed volume integral, denoted by the symbol ∰. The contour integral can also frequently be found with a subscript capital letter C, ∮_{C}, denoting that a closed loop integral is, in fact, around a contour C, or sometimes dually appropriately, a circle C. In representations of Gauss's Law, a subscript capital S, ∮_{S}, is used to denote that the integration is over a closed surface.  If C is a Jordan curve about 0, then $oint\_C\; \{1\; over\; z\},dz\; =\; 2pi\; i$. 
contour integral of  
calculus  
∇
 gradient  ∇f (x_{1}, …, x_{n}) is the vector of partial derivatives (∂f / ∂x_{1}, …, ∂f / ∂x_{n}).  If f (x,y,z) := 3xy + z², then ∇f = (3y, 3x, 2z) 
del, nabla, gradient of  
vector calculus  
divergence  $nabla\; cdot\; vec\; v\; =\; \{partial\; v\_x\; over\; partial\; x\}\; +\; \{partial\; v\_y\; over\; partial\; y\}\; +\; \{partial\; v\_z\; over\; partial\; z\}$  If $vec\; v\; :=\; 3xymathbf\{i\}+y^2\; zmathbf\{j\}+5mathbf\{k\}$, then $nabla\; cdot\; vec\; v\; =\; 3y\; +\; 2yz$.  
del dot, divergence of  
vector calculus  
curl  $nabla\; times\; vec\; v\; =\; left(\{partial\; v\_z\; over\; partial\; y\}\; \; \{partial\; v\_y\; over\; partial\; z\}\; right)\; mathbf\{i\}$ $+\; left(\{partial\; v\_x\; over\; partial\; z\}\; \; \{partial\; v\_z\; over\; partial\; x\}\; right)\; mathbf\{j\}\; +\; left(\{partial\; v\_y\; over\; partial\; x\}\; \; \{partial\; v\_x\; over\; partial\; y\}\; right)\; mathbf\{k\}$  If $vec\; v\; :=\; 3xymathbf\{i\}+y^2\; zmathbf\{j\}+5mathbf\{k\}$, then $nablatimesvec\; v\; =\; y^2mathbf\{i\}\; \; 3xmathbf\{k\}$.  
curl of  
vector calculus  
∂
 partial differential  With f (x_{1}, …, x_{n}), ∂f/∂x_{i} is the derivative of f with respect to x_{i}, with all other variables kept constant.  If f(x,y) := x^{2}y, then ∂f/∂x = 2xy 
partial, d  
calculus  
boundary  ∂M means the boundary of M  ∂{x : x ≤ 2} = {x : x = 2}  
boundary of  
topology  
δ
 Dirac delta function  $delta(x)\; =\; begin\{cases\}\; infty,\; \&\; x\; =\; 0\; 0,\; \&\; x\; ne\; 0\; end\{cases\}$  δ(x) 
Dirac delta of  
hyperfunction  
Kronecker delta  $delta\_\{ij\}\; =\; begin\{cases\}\; 1,\; \&\; i\; =\; j\; 0,\; \&\; i\; ne\; j\; end\{cases\}$  δ_{ij}  
Kronecker delta of  
hyperfunction  
<:
 subtype  T_{1} <: T_{2} means that T_{1} is a subtype of T_{2}.  If S <: T and T <: U then S <: U (transitivity). 
is a subtype of  
type theory  
⊤
 top element  x = ⊤ means x is the largest element.  ∀x : x ∨ ⊤ = ⊤ 
the top element  
lattice theory  
top type  The top or universal type; every type in the type system of interest is a subtype of top.  ∀ types T, T <: ⊤  
the top type; top  
type theory  
⊥
 perpendicular  x ⊥ y means x is perpendicular to y; or more generally x is orthogonal to y.  If l ⊥ m and m ⊥ n in the plane then l  n. 
is perpendicular to  
geometry  
coprime  x ⊥ y means x has no factor in common with y.  34 ⊥ 55.  
is coprime to  
number theory  
bottom element  x = ⊥ means x is the smallest element.  ∀x : x ∧ ⊥ = ⊥  
the bottom element  
lattice theory  
bottom type  The bottom type (a.k.a. the zero type or empty type); bottom is the subtype of every type in the type system.  ∀ types T, ⊥ <: T  
the bottom type; bot  
type theory  
comparability  x ⊥ y means that x is comparable to y.  {e, π} ⊥ {1, 2, e, 3, π} under set containment.  
is comparable to  
Order theory  

 parallel  x  y means x is parallel to y.  If l  m and m ⊥ n then l ⊥ n. In physics this is also used to express $x\; \; y\; Leftrightarrow\; frac\{1\}\{x^\{1\}\; +\; y^\{1\}\}$ 
is parallel to  
geometry, physics  
incomparability  x  y means x is incomparable to y.  {1,2}  {2,3} under set containment.  
is incomparable to  
order theory  
exact divisibility  p^{f}  n means p^{f} exactly divides n.  2^{3}  360.  
exactly divides  
number theory  
⊧
 entailment  A ⊧ B means the sentence A entails the sentence B, that is in every model in which A is true, B is also true.  A ⊧ A ∨ ¬A 
entails  
model theory  
⊢
 inference  x ⊢ y means y is derivable from x.  A → B ⊢ ¬B → ¬A 
infers or is derived from  
propositional logic, predicate logic  
〈,〉
( ) < , > · :  inner product  〈x,y〉 means the inner product of x and y as defined in an inner product space. For spatial vectors, the dot product notation, x·y is common. For matrices, the colon notation may be used.  The standard inner product between two vectors x = (2, 3) and y = (−1, 5) is: 〈x, y〉 = 2 × −1 + 3 × 5 = 13 $A:B\; =\; sum\_\{i,j\}\; A\_\{ij\}B\_\{ij\}$ 
inner product of  
linear algebra  
⊗
 tensor product, tensor product of modules  $V\; otimes\; U$ means the tensor product of V and U. $V\; otimes\_R\; U$ means the tensor product of modules V and U over the ring R.  {1, 2, 3, 4} ⊗ {1, 1, 2} = {{1, 2, 3, 4}, {1, 2, 3, 4}, {2, 4, 6, 8}} 
tensor product of  
linear algebra  
*
 convolution  f * g means the convolution of f and g.  $(f\; *\; g\; )(t)\; =\; int\; f(tau)\; g(t\; \; tau),\; dtau$ 
convolution, convolved with  
functional analysis  
$bar\{x\}$
x̄  mean  $bar\{x\}$ (often read as "x bar") is the mean (average value of $x\_i$).  $x\; =\; \{1,2,3,4,5\};\; bar\{x\}\; =\; 3$. 
overbar, … bar  
statistics  
$overline\{z\}$ $z^ast$  complex conjugate  $overline\{z\}\; =\; z^ast$ is the complex conjugate of z.  $overline\{3+4i\}\; =\; (3+4i)^ast\; =\; 34i$ 
conjugate  
complex numbers 