MATH-013* Lecture 6 (February 26, 2008)
Todays main lesson:
To learn basic notions of graph theory.
some terminology
Eulers theorems
Some terminology
Graphs are pictures consisting of dots called vertices and lines between vertices called
edges (A sing
MATH-013* Lecture 3 (January 22, 2008) Further Note
1. Suppose that there are N players in a weighted voting system.
The number of sequential coalitions involving all N players is given by
N (N 1) 2 1 = N ! (N factorial).
I have noticed that I forgot to
MATH-013* Lecture 7 (March 4, 2008)
Todays main lesson:
Hamilton paths and Hamilton circuits
Complete graphs
Algorithms associated with the traveling-salesman problem
Hamilton paths and Hamilton circuits
A Hamilton path is a path that passes through a
MATH-013* Lecture 3 (January 22, 2008)
Todays main lesson:
To learn two ways to describe the powers of players in a weighted voting system.
the Banzhaf power index
the Shapley-Shubik power index
Dictators, dummies and players with veto power
In a weigh
MATH-013* Lecture 1 (January 8, 2008)
Todays main lesson is:
to learn a few methods to nd the winner of an election, together with two fairness
criteria for elections.
Methods to nd the winner of an election
We will assume that voters pick candidates in
MATH-013* Lecture 2 (January 15, 2008)
Todays main lessons:
To learn another method of nding the winner of an election, and to introduce two
more fairness criteria.
To learn how to rank all candidates (choices) according to the same methods used
for ndi
MATH-013* Lecture 8 (March 11, 2008)
Todays main lesson:
Trees and their properties
Kruskals algorithm
Trees and their properties
A tree is a graph satisyng the following:
a tree is a connected graph.
a tree has no circuits.
Property 1
(a) If a graph
MATH-013* Lecture 10 (March 25, 2008)
Todays main lesson:
digraphs and some terminology
project digraphs
Digraphs and some terminology
A digraph, or directed graph, is a graph in which directions are assigned for all edges
(the directions are indicated
MATH-013* Lecture 4 (January 29, 2008)
Todays main lessons:
To understand the concept of fair division.
To learn two fair-division methods.
The divider-chooser method (a method for 2 players)
The lone-divider method (a method for 3 or more players)
Fa
MATH-013* Lecture 9 (March 18, 2008)
Todays main lesson:
the converse, the inverse and the contraposition of a statement
bipartite graphs
colourings of graphs
The converse, the inverse and the contraposition of a statment
Given a statement S:If P, then