Mathematical notation | Analysis of algorithms | Asymptotic analysis

Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a invented by Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation. The letter O was chosen by Bachmann to stand for Ordnung, meaning the order of approximation. In computer science, big O notation is used to classify algorithms according to how their run time or space requirements grow as the input size grows. In analytic number theory, big O notation is often used to express a bound on the difference between an arithmetical function and a better understood approximation; a famous example of such a difference is the remainder term in the prime number theorem. Big O notation is also used in many other fields to provide similar estimates. Big O notation characterizes functions according to their growth rates: different functions with the same growth rate may be represented using the same O notation. The letter O is used because the growth rate of a function is also referred to as the order of the function. A description of a function in terms of big O notation usually only provides an upper bound on the growth rate of the function. Associated with big O notation are several related notations, using the symbols o, Ω, ω, and Θ, to describe other kinds of bounds on asymptotic growth rates. (Wikipedia).

Big O notation is simpler than you might think

Big O notation is a very popular topic, in contexts such as algorithms and P vs NP. In this video, I attempt to explain big O notation using only basic arithmetic, so that these other topics can be enjoyed by everyone! Timestamps: Intro: 00:00 Eventuality: 00:28 Deltas: 03:54 Stolz-Ces

From playlist Summer of Math Exposition Youtube Videos

Truly Understanding Big O Notation: An introduction to analysing algorithm efficiency #SoME2

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Introduction to Big-O Notation

This video introduces Big-O notation. http://mathispower4u.com

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Big O: How Code Slows as Data Grows

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Big O Zoo (Acing Your Coding Interview) : Data Science Basics

The *most* commonly seen Big-O notations and how to spot them! Dictionaries / Hash Tables Video: https://www.youtube.com/watch?v=_WG-TJc24Ks Binary Search Video: https://www.youtube.com/watch?v=BZzdnqSEGa8

From playlist Data Science Basics

In this video, we are trying to get a better intuition for what it means if some algorithm has particular time or space requirements in big O notation. In doing so, we will learn what time complexity means, look at typical running times of algorithms and consider if there might be alternat

From playlist All About Algorithms

From playlist Algorithms 1

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In this video we look at to how to compare ressource requirements of algorithms, independently from hardware, implementation etc. In doing so we will come across a useful, but infamous tool from the field of algorithms: big O notation 00:00 Ressource requirements and the scalability of al

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A coding interview question to explain Big O Notation! Gaussian sum formula: https://www.mathwords.com/a/arithmetic_series.htm

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From playlist Algorithms 1

Introduction to big-O notation. Sources: 1/ Algorithms by Dasgupta, Papadimitriou & Vazirani [https://code.google.com/p/eclipselu/downloads/detail?name=algorithms.pdf] 2/ http://pages.cs.wisc.edu/~paton/readings/Complexity/#bigO 3/ http://bigocheatsheet.com/ LinkedIn: https://www.linked

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