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 is available online here! Also, sections of Bollobass
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 weeks.
Specifically, we took a concept from electrical engi
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 revolutionized the mathematical field of game theory before
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 something thats a fairly natural transition from our wor
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 that you have a set of choices A = cfw_, , , . . .. Given
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 quarter; weve seen how graphs interact with physics, Dirich
CCS Discrete III
Professor: Padraic Bartlett
Lecture 5: Toroidal Graphs
Week 10
UCSB 2015
(Relevant source material: Chapter 6 of Douglas Wests Introduction to Graph Theory; Section V.3 of Bela Bollob
ass Modern Graph Theory; Part IV of Alexander Soifers
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 Petersen graph into a circuit as follows: Pick any two nonadja
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 of R2 with equilateral triangles with side
length 1. Pic
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 lemma:
Lemma. Suppose that V is a vector space, and th