Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 10, 2009
Lecture 1
Scribe: Jesse Geneson (2009)
Lecturer: Jonathan Kelner
1
Overview
The classs goals, requirements, and policies were introduced, and topics
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
October 20, 2009
Lecture 11
Lecturer: Jonathan Kelner
1
Scribe: Chaithanya Bandi
Outline
Today well introduce and discuss
Polar of a convex body.
Correspondence betwe
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
10/8/2009
18.409 An Algorithmists Toolkit
Lecture 9
Lecturer: Jonathan Kelner
At the end of the previous lecture, we began to motivate a technique called Sparsication. In this lecture,
we describe spa
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
October 22, 2009
Lecture 12
Scribes: Alex Levin (2009)
Lecturer: Jonathan Kelner
1
Outline
Today well go over some of the details from last class and make precise many
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 30, 2009
Lecture 7
Lecturer: Jonathan Kelner
1
Scribe: Alan Deckelbaum (2009)
Administrivia
There were two administrative announcements made at the beginning
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 29, 2009
Lecture 6
Lecturer: Jonathan Kelner
Scribe: Anthony Kim(2009)
Topics
Diameters and their relationship to 2
Expanders
Buttery networks
1
Diameters
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
November 3rd , 2009
18.409 An Algorithmists Toolkit
Lecture 15
Lecturer: Jonathan Kelner
1
Scribe: Justin Thaler
Outline
In this lecture we will design a method to randomly sample from a convex body,
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
10/29/09
Lecture 14
Lecturer: Jonathan Kelner
1
Approximating the volume of a convex b o dy
Exactly computing the volume a convex body is known to be #Phard, so the fa
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 15, 2007
Lecture 2
Scribe: Mergen Nachin 2009
Lecturer: Jonathan Kelner
1
Administrative Details
Signup online for scribing.
2
Review of Lecture 1
All of the
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 17, 2009
Lecture 3
Lecturer: Jonathan Kelner
1
Scribe: Andre Wibisono
Outline
Todays lecture covers three main parts:
CourantFischer formula and Rayleigh qu
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 10, 2009
Lecture 1
Scribe: Jesse Geneson (2009)
Lecturer: Jonathan Kelner
1
Overview
The classs goals, requirements, and policies were introduced, and topics
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 15, 2007
Lecture 2
Scribe: Mergen Nachin 2009
Lecturer: Jonathan Kelner
1
Administrative Details
Signup online for scribing.
2
Review of Lecture 1
All of the
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 17, 2009
Lecture 3
Lecturer: Jonathan Kelner
1
Scribe: Andre Wibisono
Outline
Todays lecture covers three main parts:
CourantFischer formula and Rayleigh qu
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 22, 2009
Lecture 4
Lecturer: Jonathan Kelner
1
Scribe: Dan Iancu (2009)
Random walks
Let G = (V, E ) be an undirected graph. Consider the random process that
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 24, 2009
Lecture 5
Lecturer: Jonathan Kelner
1
Scribe: Shaunak Kishore
Administrivia
Two additional resources on approximating the permanent
Jerrum and Sincl
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 24, 2009
Lecture 5
Lecturer: Jonathan Kelner
1
Scribe: Shaunak Kishore
Administrivia
Two additional resources on approximating the permanent
Jerrum and Sincl
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
10/15/2009
Lecture 10
Lecturer: Jonathan Kelner
In this lecture, we shall revisit the Spectral Sparsiers and see a slightly dierent proof from last time.
We will then b
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
September 22, 2009
Lecture 4
Lecturer: Jonathan Kelner
1
Scribe: Dan Iancu (2009)
Random walks
Let G = (V, E ) be an undirected graph. Consider the random process that
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
October 6, 2009
18.409 An Algorithmists Toolkit
Lecture 8
Lecturer: Jonathan Kelner
1
Scribe: Alessandro Chiesa (2009)
Administrivia
You should probably know that
the rst problem set (due October 15
Topics in Theoretical Computer Science: An Algorithmist's toolkit
MATH 18.409

Fall 2009
18.409 An Algorithmists Toolkit
October 27, 2009
Lecture 13
Lecturer: Jonathan Kelner
1
Scribe: Jonathan Pines (2009)
Outline
Last time, we proved the BrunnMinkowski inequality for boxes. Today well