Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
5. Recurrence Relations
We have already encountered a number of recurrence relations when we talked about
recursion. Now we look at more situations in which they arise and techniques for getting
expli
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
7.2 Eulerian Paths
Definition 1. An Eulerian path is one that uses every edge in a graph exactly once. An
Eulerian circuit is an Eulerian path that is a cycle, i.e. it ends at the same vertex that it
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
6. Relations
When we were talking about logic earlier we considered predicates. These were rules (or
functions) that took one or more objects and returned a value of true or false depending
on whether
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
5.3 Second Order Recurrence Relations
In the previous section we saw how to solve first order linear recurrence relations. This
is when an is given by a linear formula of an1, i.e.
an = pnan1 + sn
w
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
7. Graphs
A graph is the same as a relation, only with different terminology. Graph terminology
(instead of relation terminology) tends to be used with applications to real world
situations, which wil
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
6.2 Partial Orderings
In the previous section we talked about equivalence relations which were generalizations
of equality. In this section we consider partial orderings which are generalizations of
l
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
4
Permuatations and Combinations
This chapter is concerned with counting the number of ways one can do something. A typical example is
how many ways can one form a committee of three people who are ch
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
7.3 Shortest Paths
In this section we discuss an algorithm to find a shortest path from one vertex to another
in a graph where the edges have weights.
Example 1. A company has offices in the eight cit
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
4.3 Combinations
Application to Binomials. Combinations arise when we expand a power (a + b)n of a
binomial a + b. Here is the case n = 2.
(a + b)2 = (a + b)(a + b) = a(a + b) + b(a + b)
=
= a2 + + b2