Math → Kotlin Cheatsheet

This is still very much a work-in-progress and I welcome any contributions. This cheat sheet was inspired by Jam3's Math as Code project.

I am using this online LaTeX equation editor to generate expressions, and if you want to learn MathJax notation here is a great resource.

While you are here, please rally this issue on Dokka to bring MathJax support to Kotlin Docs.

Summation

This symbol $\sum$ indicates you are summing a series of items. It is probably one of the most commonly used symbols in math to express iterative addition.

Math Expression	Kotlin Code
$\sum_{i=1}^{3}i$	`(1..3).sum()`
$\sum_{i=1}^{5}10i$	`(1..5).map { i -> 10*i }.sum()`
$\sum_{i=0}^{n}i^2$	`fun f(n: Int) = (0..n).map { it * it }.sum()`
$\sum_{i=1}^{100}3x^2 + 2i$	`fun f(x: Double) = (1..100).map { i -> 3 * Math.pow(x, 2.0) + (2*i) }.sum()`
$10 + 3\sum_{i=0}^{n}i^2$	`fun f(n: Int) = 10 + 3(0..n).map { it it }.sum()`
$\sum_{i=0}^{n} x_i + i$	`fun f(allX: List<Int>) = allX.mapIndexed { i,x -> x + i }.sum()`
$\sum_{i=1}^{10} \sum_{j=4}^{20} 2ij$	`(1..4).flatMap { i -> (4..20).map { j -> 2 i j } }.sum()`

Nested Summation

When you see more than one summation, this means they are nested summations. This is no different than summing with nested loops or flatmapped functional sequences.

$\sum_{i=1}^{10} \sum_{j=4}^{20} 2ij$

(1..4).flatMap { i -> (4..20).map { j -> 2 *i * j } }.sum()

Variables

Hopefully the concept of a variable (such as x) should be self-explanatory to a programmer. However, in mathematical notation it is common for subscripts to distinctly describe several instances of that variable. For instance, we can use old and new x values to measure a rate of change.

$change = \frac{x_{new} - x_{old}}{x_{old}}$

Here is a more iterative example. We can define 5 different variables all named , but notate them as $x_1, x_2, x_3, x_4, \text{and} x_5$ . Here is how we can notate an average operation.

$x_{average} = \frac{x_1 + x_2 + x_3 + x_4 + x_5}{5}$ .

val xValues = listOf(23, 65, 45, 23, 66)
val xAverage = allXs.sum() / 5 

// or 

val xAverage = allXs.average()

Mathematics and programming are similar in that they try to generalize. Instead of formulating an average for just 5 variables, we can notate it for any n number of variables.

$x_{average} = \frac{x_1 + x_2 + ... + x_n}{n}$

To maximize fanciness, we can go a step further and use a summation operator and just generalize each x value as . Note that n is the number of variables/elements we are averaging.

$x_{average} = \frac{1}{n}\sum_{i=1}^{n}x_i$

Naming Subscripted Variables in Kotlin

Trying to express subscripted variables like and $x_{old}$ can be a little awkward in code. In Kotlin, you can choose to stick with conventional camelCase or break style guidelines by using underscores.

val x1 = 12
val x_1 = 12

val xOld = 13
val x_old = 13

Hopefully you will not run into this decision often, as you may express variables as iterated elements in collections/sequences rather than give each one an explicit variable name.

Elements and Sets

Functions

Math Expression	Description	Kotlin Code
	Exponent of `e`	`exp(x)`
	Natural logarithm	`ln(x)`

krystianzybala/kotlin_math_cheatsheet