R. Johnsonbaugh,
Discrete Mathematics
5th edition, 2001
Chapter 2
The Language of Mathematics
Set Theory
Set: Collection of objects (elements)
a A
a is an element of A
a is a member of A
a A
a is not
R. Johnsonbaugh
Discrete Mathematics
5th edition, 2001
Chapter 11
Computational Geometry
11.1 The closest pair problem
Problem:
Given n points in the plane
find a closest pair
with distance measured i
R. Johnsonbaugh
Discrete Mathematics
5th edition, 2001
Chapter 10
Automata, Grammars
and Languages
Last chapter
Combinatorial circuits
The output depended only on the input
These circuits have no memo
R. Johnsonbaugh
Discrete Mathematics
5th edition, 2001
Chapter 8
Network models
The overview of this chapter
Network models make use of directed
graphs.
The network might be a transport network
throug
R. Johnsonbaugh
Discrete Mathematics
5th edition, 2001
Chapter 7
Trees
Chapter 7 Trees
7.1 Introduction
A (free) tree T is
A simple graph
such that for
every pair of
vertices v and w
there is a unique
R. Johnsonbaugh
Discrete Mathematics
5th edition, 2001
Chapter 6
Graph Theory
In the beginning
1736: Leonhard Euler
Basel, 1707-St. Petersburg, 1786
He wrote A solution to a problem concerning the geo
R. Johnsonbaugh
Discrete Mathematics
5th edition, 2001
Chapter 5
Recurrence Relations
Now its Time for
Recurrenc
e
Relations
5.1 Introduction
A recurrence relation for the sequence
cfw_an is an equati
R. Johnsonbaugh
Discrete Mathematics
5th edition, 2001
Chapter 4
Counting methods
and the pigeonhole principle
Basic Counting Principles
Counting
How
there?
problems are of the following kind:
many di
R. Johnsonbaugh,
Discrete Mathematics
5th edition, 2001
Chapter 3
Algorithms
Algorithms
What is an algorithm?
An algorithm is a finite set of precise
instructions for performing a computation or
for s
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4.1 ?
4.2 ?
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4.7 ?
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4. 1 ?
?
?(?): ? x ? y ?
?: < x, y > ? x ?
?, y ?
?
?: (1) ? x y ?, < x, y > < y, x >
(2) < x, y > = < u, v > ? x = u, y = v
(1)(2) ?
1