Math Symbols

Summation

The addition of a sequence of numbers

$$\sum _{i=1}^{100}(2i+1)$$

def summation(start,end):
    running_sum = 1
    for i in range(start,end):
        running_sum += (2*i) + 1
    return running_sum
print(summation(1,100))

Big PI

The multiplication of a sequence of numbers

$$\prod _{i=1}^{6}i$$

def pi(start,end):
        running_product = 1
        for i in range(start, end + 1):
            running_product *= i
        return r
print(pi(1,6))

Dot Product

Combine two vectors

$a\cdot b=\sum _{i=1}^n(a_i{b}_i)=a_i{b}_i+a_1{b}_1+a_2{b}_2+\dots +a_n{b}_n$

def dot_product(self,a, b):
        dp = 0
        for i in range(len(a)):
            dp += (a[i]*b[i])
        return dp

vector1 = [1,2,3,4,5]
vector2 = [2,1,1,1,1]

print(dot_product(vector1, vector2))

Piece Wise

A function built from pieces of different functions over different intervals

$$f(x)=\{\begin{array}{ll}\frac{x^2-x}{x,}& \text{if }x\text{ >= 1}\\ 0,& \text{otherwise}\end{array}$$

def f(x):
  if (x >= 1):
    return (math.pow(x, 2) - x) / x
  else:
    return 0

Math As Code

https://github.com/Experience-Monks/math-as-code/blob/master/PYTHON-README.md

Slope formula logrithms matrix math dot product algebra basics

MathJax

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When $a\ne 0$, there are two solutions to $(a{x}^2+bx+c=0)$ and they are

$$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

Maxwell's equations:

equation	description
$\mathrm{\nabla }\cdot \overrightarrow{\mathbf{B}}=0$	divergence of $\overrightarrow{\mathbf{B}}$ is zero
$\mathrm{\nabla }\times \overrightarrow{\mathbf{E}}+\frac{1}{c}\frac{\partial \overrightarrow{\mathbf{B}}}{\partial t}=\overrightarrow{\mathbf{0}}$	curl of $\overrightarrow{\mathbf{E}}$ is proportional to the rate of change of $\overrightarrow{\mathbf{B}}$
$\mathrm{\nabla }\times \overrightarrow{\mathbf{B}}-\frac{1}{c}\frac{\partial \overrightarrow{\mathbf{E}}}{\partial t}=\frac{4\pi }{c}\overrightarrow{\mathbf{j}}\mathrm{\nabla }\cdot \overrightarrow{\mathbf{E}}=4\pi \rho$	wha?

More Jax

followed by a display style equation:

$$V_{sphere} = \frac{4}{3}\pi r^3$$

$$V_{sphere}=\frac{4}{3}\pi r^3$$

$$f(a) = \frac{1}{2\pi i} \oint\frac{f(z)}{z-a}dz$$

$$f(a)=\frac{1}{2\pi i}\oint \frac{f(z)}{z-a}dz$$

$$\sigma = \sqrt{ \frac{1}{N} \sum_{i=1}^N (x_i -\mu)^2}$$

$$\sigma =\sqrt{\frac{1}{N}\sum _{i=1}^N(x_i-\mu {)}^2}$$

$$\vec{\nabla} \times \vec{F} =
            \left( \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} \right) \mathbf{i}
          + \left( \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \right) \mathbf{j}
          + \left( \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right) \mathbf{k}$$

$$\overrightarrow{\mathrm{\nabla }}\times \overrightarrow{F}=(\frac{\partial F_z}{\partial y}-\frac{\partial F_y}{\partial z})\mathbf{i}+(\frac{\partial F_x}{\partial z}-\frac{\partial F_z}{\partial x})\mathbf{j}+(\frac{\partial F_y}{\partial x}-\frac{\partial F_x}{\partial y})\mathbf{k}$$

$$\sigma = \sqrt{ \frac{1}{N} \sum_{i=1}^N (x_i -\mu)^2}$$

$$\sigma =\sqrt{\frac{1}{N}\sum _{i=1}^N(x_i-\mu {)}^2}$$

Limits

$\lim\limits_{x\mapsto 1}\dfrac1x$

$\underset{x\mapsto 1}{lim}{\displaystyle \frac{1}{x}}$

Matrices

$\begin{bmatrix}
    i&j&k\\x_1&y_1&z_1\\x_2&y_2&z_2\\x_3&y_3&z_3
\end{bmatrix}$

$\left[\begin{array}{ccc}i& j& k\\ x_1& y_1& z_1\\ x_2& y_2& z_2\\ x_3& y_3& z_3\end{array}\right]$

Derivatives

$\displaystyle \frac{d\hat{\mathbf r}}{d\theta}$

${\displaystyle \frac{d\hat{\mathbf{r}}}{d\theta }}$

Integrals

$\displaystyle \int_{y_0}^{y_1} \int_{x_0}^{x_1} f(x, y) \,dx\,dy$

${\displaystyle {\int }_{y_0}^{y_1}{\int }_{x_0}^{x_1}f(x,y)dxdy}$

Piecewise

$$f(n) =\begin{cases} 
    n/2,  &\text{if $n$ is even} \\ 
    3n+1, &\text{if $n$ is odd}
\end{cases}$$

$$f(n)=\{\begin{array}{ll}n/2,& \text{if }n\text{ is even}\\ 3n+1,& \text{if }n\text{ is odd}\end{array}$$

Determinant

$$\begin{vmatrix}
1 & x_{0} & x_{0}^{2} & \dots & x_{0}^{n} \\ 
1 & x_{1} & x_{1}^{2} & \dots & x_{1}^{n} \\
\hdotsfor{5} \\
1 & x_{n} & x_{n}^{2} & \dots & x_{n}^{n}
\end{vmatrix}$$

$$\left|\begin{array}{ccccc}1& x_0& x_0^2& \dots & x_0^n\\ 1& x_1& x_1^2& \dots & x_1^n\\ \text{hdotsfor}5\\ 1& x_n& x_n^2& \dots & x_n^n\end{array}\right|$$

Logarithm

$log_{b}m$

$lo{g}_{b}m$

Superscripts and Subscripts

$x_i^3+3x_i^2x_j+3x_ix_j^2+x_j^3$

$x_i^3+3x_i^2{x}_j+3x_i{x}_j^2+x_j^3$

Fractions

$\frac{n(n+1)}{2}$

$\frac{n(n+1)}{2}$

Reading Papers

Resources

• https://medium.com/@sourov.roy/mathjax-basic-quick-reference-eeba0f59b1b7
• 🎥 How to Read Math