📄️ Some C++ features
- explicit keyword is used to prevent implicit conversion and copy-initialization. A quick example is that class with only one parameter constructor can be used as a type conversion. The following example
📄️ Function
We say the way transfer an element of a collection to the other collection as function. In mathematic, we always use function to transfer an element of a set to the other set. (Obviously set is a kind of collection.) Or sample space in statistics, or parameters in CS.
📄️ GCD && LCM
GCD
📄️ Matrix
Matrix is the extension of vector where from $n\times 1 \to n\times m$, but notice, the addition of matrix only perform when they are all the same $n\times m$ where they have the same number of rows and columns. For multiplication, we can only perform $A{n\times p} = B{n\times k} \cdot C_{k\times p}$
📄️ Modular Arithmetic
let m be a fixed natural number greater than 1. we say b modulo m if a - b is divisible by m. $a\equiv b\pmod m$
📄️ Sequence
$\forall n\in \mathbb$ we define the list number $\dots,xn,x{n+1},\dots$ then $\{xn\}$ is a sequence, or $(xn)$; some time we have multiple variable and we may have something like $(x{a,b}){a\in N}$ means this sequence focus on the changing of $a$
📄️ Set
Let $C$ be a collection. $\forall a\in C, \nexists b\in C\backslash \{a\}, a = b \implies C$ is a set.
📄️ Some Basic Discrete Math Definition
A variable is a logical variable like $x$,$y$, $p$, $q$.
📄️ Some Common Series Used
Arithmetic Progression:: $\sum\{i=k}^m i = (k + m)*(m - k)/2 = (m^2 - k^2)/2$; More specific, for all $i, \|a\ - a\{i}\| = d, d\in \R$ we have $(a\0 + a\_n)*(n+1)/2$
📄️ Some Short Form English
Formal
📄️ Vector
we first define vector which is a collection of data in $n\times1$ as $\beginx1\\ x2\\x3\\\vdots\\xn\end{bmatrix}$, and matrix is a collection of data in $n\times p$ as $\begin{bmatrix}x{11} & x{12} & \cdots & x{1p} \\ x{21} & x{22} & \cdots & x{2p} \\ \cdots & \cdots & \cdots & \cdots \\x{n1} & x{n2} & \cdots & x_{np}\end{bmatrix}$
📄️ Some Basic Knowledge
We may find some knowledge are common and very basic, I may organize to here :)