Preface

Prerequisites

Learning ethics

Introduction

What is an Algorithm?

Informally, an algorithm is a series of computational steps that takes an input and returns an output in a finite amount of time. The input and output relationship is a way to describe a computational problem. So, you use algorithms because you have a problem, but no upside down.

A mathematical reader can think is a little floppy definition and maybe you thought “your definition is not the correct way to found any science” —what the heck is a computational step?— and you are right, it is an easy way to definite an algorithm, but it is not the full answer. A more accurate definition is given to you later.

Different ways to describe an algorithm:

# Notation 1
f: x: T -> y: T1 -> z: T2 ... -> output: TN
f = computational steps

# Notation 2
f(x: T, y: T1, ...): output: TN = computational steps

# Notation 3
f(x: T, y: T1, ...): output: TN {
   computational steps
}

Some authors don’t write types when they write algorithms, but we do since they give precision.

We say with $x:T$ that x is a term with type T. A type has values and operations —interface. We explain more later.

Why do algorithms matter to you?

Perhaps you are here to build a Skynet —Artificial intelligence, to solve the problem NP=P —Research, work in a Big Tech company —Industry.

Algorithms are foundations for building great systems and for research too.