Disclaimer: I am not a mathematician, not even a math major. So, this table may contain some misconceptions and I would be happy if anyone corrects me on them.
Accumulation Notation(a name I made up) | |||
Applications: Series, Probability | |||
Representation | Pronunciation | Interpretation | |
---|---|---|---|
Σ_{x=n}^{m} f(x) | Sigma | This is a summation, whic means means inputting all the integers from n to m into the function f, then taking the sum of the outputs | |
Π_{x=n}^{m} f(x) | Pi | input all the integers from n to m into the function f, then take the product of the outputs |
Calculus Notation | |||
Applications: Physics, Chemistry | |||
Representation | Pronunciation | Interpretation | |
---|---|---|---|
δx | differential of x | an infinitely small increment of a variable x. On a continuous line, the point right next to x = 1 is x = 1+δx | |
Δx | delta x | unlike the differential, this represents a finite increment of x as Δx = (x_{2}-x_{1}) | |
^{δx}⁄_{δy} | derivative of x with respect to y | This is how much x changes in one instant as y changes. On the function in the usual x and y graph, this would represent the exact slope at one specific point. | |
∫ f(x) δx | Integral of f(x) | An integral is like a summation for continuous functions. In this case, the integral equals the area beneath the line/curve. In other cases, it can also mean the length of the line/curve, or volume. | |
∮ | Contour Integral | This is an integral over a closed loop |
Set Notation | |||
Applications: Probability, Statistics | |||
Representation | Pronunciation | Interpretation | |
---|---|---|---|
X = {a,b,c} | set | a,b, and c are elements of set X | |
ℝ | all real numbers | include all rational and irrational numbers | |
ℤ | all integers | both positive and negative whole numbers | |
ℕ | all natural numbers | all positive integers, and sometimes 0 | |
ℚ | fractions | ratio of two integers | |
{p|q} | "such that" "given" |
the set of all p that follows the rules defined by q | |
x ∈ ℤ | "is within" | x is within a set of all integers | |
a ⊂ b | "subset" | a is a subset of b | |
b ⊄ a | "non-subset" | b is not a subset of a | |
C ∪ D | "union" | a set with all the elements from sets C and D, but with no repeating values | |
C ∩ D | "intersection" | a set with only elements in both sets C and D |
No comments:
Post a Comment