**Algebra** is a part of mathematics which deals with symbols and the rules for manipulating those symbols. In algebra, those symbols represent quantities without fixed values, called as variables. Just how sentences describe relationships between specific words, in algebra, equations describe relationships between variables.

Math can be difficult for allot of people out there. However, it is crucial to recognize that even symbols, used in algebra, have names, and those names are made up of letters and words.

Symbol | Symbol Name | Meaning / definitio | Example |

≡ |
equivalence | identical to | |

x |
x variable | unknown value to find | when 2x = 4, then x = 2 |

:= |
equal by definition | equal by definition | |

≜ |
equal by definition | equal by definition | |

≈ |
approximately equal | approximation | sin(0.01) ≈ 0.01 |

~ |
approximately equal | weak approximation | 11 ~ 10 |

∞ |
lemniscate | infinity symbol | |

∝ |
proportional to | proportional to | y ∝ x when y = kx, k constant |

≫ |
much greater than | much greater than | 1000000 ≫ 1 |

≪ |
much less than | much less than | 1 ≪ 1000000 |

[ ] |
brackets | calculate expression inside first | [(1+2)*(1+5)] = 18 |

( ) |
parentheses | calculate expression inside first | 2 * (3+5) = 16 |

⌊x⌋ |
floor brackets | rounds number to lower integer | ⌊4.3⌋= 4 |

{ } |
braces | set | |

x! |
exclamation mark | factorial | 4! = 1*2*3*4 = 24 |

⌈x⌉ |
ceiling brackets | rounds number to upper integer | ⌈4.3⌉= 5 |

f (x) |
function of x | maps values of x to f(x) | f (x) = 3x+5 |

| x | |
single vertical bar | absolute value | | -5 | = 5 |

(a,b) |
open interval | (a,b) = {x | a < x < b} | x ∈ (2,6) |

(f ∘g) |
function composition | (f ∘g) (x) = f (g(x)) | f (x)=3x, g(x)=x-1 ⇒(f ∘g)(x)=3(x-1) |

∆ |
delta | change / difference | ∆t = t1 – t0 |

[a,b] |
closed interval | [a,b] = {x | a ≤ x ≤ b} | x ∈ [2,6] |

∑ |
sigma | summation – sum of all values in range of series | ∑ xi= x1+x2+…+xn |

∆ |
discriminant | Δ = b2 – 4ac | |

∑∑ |
sigma | double summation | \(\sum_{j=1}^{2} \sum_{i=1}^{8} xi,j = \sum_{i=1}^{8}xi,j + \sum_{i=1}^{8} xi,2\) |

e |
e constant / Euler’s number | e = 2.718281828… | e = lim (1+1/x)x , x→∞ |

∏ |
capital pi | product – product of all values in range of series | ∏ xi=x1∙x2∙…∙xn |

γ |
Euler-Mascheroni constant | γ = 0.527721566… | |

π |
pi constant | π = 3.141592654…
is the ratio between the circumference and diameter of a circle |
c = π·d = 2·π·r |

φ |
golden ratio | golden ratio constant |

Symbol | Symbol Name | Meaning / definition | Example |

× |
cross | vector product | a × b |

∙ | dot | scalar product | a ∙ b |

\(\left \langle x,y \right \rangle\) |
inner product | ||

A⊗B |
tensor product | tensor product of A and B | A ⊗ B |

[ ] |
brackets | matrix of numbers | |

( ) |
parentheses | matrix of numbers | |

det(A) |
determinant | determinant of matrix A | |

| A | |
determinant | determinant of matrix A | |

A T |
transpose | matrix transpose | (AT)ij = (A)ji |

|| x || |
double vertical bars | norm | |

A † |
Hermitian matrix | matrix conjugate transpose | (A†)ij = (A)ji |

A -1 |
inverse matrix | A A-1 = I | |

dim(U) |
dimension | dimension of matrix A | rank(U) = 3 |

rank(A) |
matrix rank | rank of matrix A | rank(A) = 3 |