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

author: Erik Demaine, Center for Future Civic Media, Massachusetts Institute of Technology, MIT
recorded by: Massachusetts Institute of Technology, MIT
published: Feb. 10, 2009,   recorded: September 2005,   views: 126766
released under terms of: Creative Commons Attribution Non-Commercial Share Alike (CC-BY-NC-SA)


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"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:

Comment1 peter, June 28, 2009 at 4:08 p.m.:


Comment2 ayaz, October 29, 2009 at 9:28 p.m.:

i want to know about recurences

Comment3 Sally, January 4, 2010 at 12:10 p.m.:

this helped me a lot... thank u Dr. Erik so much

Comment4 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:


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

Comment5 Oren, March 27, 2010 at 5:35 p.m.:

Thanks to Erik & MIT for sharing this and helping the world to get smarter!

Comment6 athn-john, October 26, 2010 at 4:16 p.m.:


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

thanks in advance !

Comment7 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!


Comment8 Yonatan, March 20, 2011 at 9:28 p.m.:

Thanks, this video helped me a lot.

Comment9 veera, January 20, 2012 at 9:12 p.m.:

thaliva vaalga

Comment10 Pytanie, June 30, 2012 at 10:02 p.m.:

Thanks for sharing! I learned a lot.

Comment11 KRIPANIDHI DAS, June 30, 2012 at 11:06 p.m.:


Comment12 ammara, March 17, 2015 at 11:23 a.m.:

I want to take ur lactures ,but unfortunately vidio is not starting ,em using net on cell

Comment13 derek, May 14, 2016 at 6:09 p.m.:

hi ,this was such a shit video. erik should take some teaching lessons. the class students itself was eager to leave the class.

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