## Lecture 2: Asymptotic Notation, Recurrences, Substitution, Master Method

recorded by: Massachusetts Institute of Technology, MIT

published: Feb. 10, 2009, recorded: September 2005, views: 32723

released under terms of: Creative Commons Attribution No Derivatives (CC-BY-ND)

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# Description

*"My name is Erik Demaine. You should call me Erik. Welcome back to 6.046. This is Lecture 2. And today we are going to essentially fill in some of the more mathematical underpinnings of Lecture 1. So, Lecture 1, we just sort of barely got our feet wet with some analysis of algorithms, insertion sort and mergesort. And we needed a couple of tools. We had this big idea of asymptotics and forgetting about constants, just looking at the lead term. And so, today, we're going to develop asymptotic notation so that we know that mathematically. And we also ended up with a recurrence with mergesort, the running time of mergesort, so we need to see how to solve recurrences. And we will do those two things today. Question? Yes, I will speak louder. Thanks. Good..."*

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## Reviews and comments:

peter, June 28, 2009 at 4:08 p.m.:test

ayaz, October 29, 2009 at 9:28 p.m.:i want to know about recurences

Sally, January 4, 2010 at 12:10 p.m.:this helped me a lot... thank u Dr. Erik so much

mark, February 2, 2010 at 10:09 p.m.:Beware of "f(n) = O(g(n)" since it is NOT really true.

Instead, the "belongs to" symbol ("∈") should be used.

Please take a look at:

http://en.wikipedia.org/wiki/O_notati...

where it states:

'Note that "=" is not meant to express "is equal to" in its normal mathematical sense, but rather a more colloquial "is" [...]'

Oren, March 27, 2010 at 5:35 p.m.:Thanks to Erik & MIT for sharing this and helping the world to get smarter!

athn-john, October 26, 2010 at 4:16 p.m.:hello,

how do i prove that if f=O(g) then g=Ω(f)?

thanks in advance !

Summer, November 13, 2010 at 4:11 a.m.:Thanks a lot, this is a great service.

Erik gives a very good explanation of recurrences, now I understand!

(:

Yonatan, March 20, 2011 at 9:28 p.m.:Thanks, this video helped me a lot.

veera, January 20, 2012 at 9:12 p.m.:thaliva vaalga

Pytanie, June 30, 2012 at 10:02 p.m.:Thanks for sharing! I learned a lot.

KRIPANIDHI DAS, June 30, 2012 at 11:06 p.m.:ALL MIT STUDENTS JOIN MY SITE.

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