CCS Discrete III
Professor: Padraic Bartlett
Lecture 1: Electrical Networks and Random Walks
Weeks 1-2
UCSB 2015
(Relevant source material: Doyle and Snells Random walks and electrical networks,
which
CCS Discrete III
Professor: Padraic Bartlett
Lecture 2: The Max-Flow Min-Cut Theorem
Weeks 3-4
1
UCSB 2015
Flows
The concept of currents on a graph is one that weve used heavily over the past few week
CCS Discrete III
Professor: Padraic Bartlett
Lecture 6: Game Theory
Week 10
UCSB 2015
If youve seen A Beautiful Mind, youve heard of John Nash one of the brightest mathematicians of our time, who revo
CCS Discrete III
Professor: Padraic Bartlett
Lecture 3: Algebra and Graphs
Weeks 5-6
UCSB 2015
We turn here to a different aspect of graph theory; the intersection of graphs and
algebra! We start by s
CCS Discrete III
Professor: Padraic Bartlett
Lecture 7: Democracy and Arrows Theorem
Week 7
UCSB 2015
Consider the following problem, encountered by democracies all over the world:
Problem. Suppose th
CCS Discrete III
Professor: Padraic Bartlett
Lecture 4: Spectral Graph Theory
Weeks 7-9
UCSB 2015
Weve studied a number of different intersections of graph theory and other fields
throughout this quar
CCS Discrete III
Professor: Padraic Bartlett
Homework 1: Circuits and Random Walks
Due Friday, Week 1
UCSB 2015
Do one of the following three problems!
1. Consider the Petersen graph:
Turn the Peterse
CCS Discrete III
Professor: Padraic Bartlett
Homework 3: Current and Random Walks
Due Friday, Week 2
UCSB 2015
Do one of the following three problems!
1. Consider a graph G corresponding to a tiling o
CCS Discrete III
Professor: Padraic Bartlett
Homework 2: Linear Algebra and More Circuits
Due Friday, Week 2
UCSB 2015
Do three of the following five problems!
1. (a) Prove the following basis-trading