Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
3.4 Modular Arithmetic
There are three properties of mod that are useful both in computations with mod and
which also form the theoretical basis for the next two applications of mod which are to
two's complement representation of negative numbers and to c
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
1.9 Mathematical Induction
Mathematical induction is a way of establishing the correctness of formulas involving an
integer variable. It also applies to inequalities, algorithms and other assertions involving
an integer variable. Even more broadly it appl
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
2.2 Comparison of Algorithms
Suppose we have two algorithms to do the same thing. Let n be the amount of data that
the algorithms are working on. For example, these might be two algorithms that sort the
elements in an array and n is the number of items to
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
2. Algorithms and Their Complexity
In this chapter we shall be interested in comparing computer programs (or parts of
computer programs) that do the same task. A typical example is programs that sort an
array of names into alphabetical order. In particula
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
1.6 Lists
list = an ordered collection of items
Order is important in a list, as is the number of repetitions.
(1)
(John, 50000, 45000)
is an example of a list. It is has three items,
John
50000
45000
In this case John is an employee of NetCo, 50000 is hi
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
3.6 RSA Cryptography
Cryptography is the science of coding and decoding messages. Over the years many
methods for coding messages have been developed. Many of them involve converting
the text to numbers and using some algebraic method for coding the corre
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
1.6 Valid Arguments Involving Predicates
In the previous section we looked at establishing valid arguments of the form (P1P2
Pn) Q. If some of P1P2Pn and Q involve predicates and the operators for every and
there exists then to show (P1P2Pn) Q we need som
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
3.2 Summation
Sums arise frequently in a variety of situations. In this section we look at some simple
summation formulas, some of which you have probably seen in previous courses. Here is
an example to get started.
Example 1. You have a computer network
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
1.5 Rules of Inference and Valid Arguments
In this section we look at rules of inference (also called logical implications) which form
the basis of logical arguments. As in section 1.3, when we say expression we shall mean
a logical expression unless stat
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
1.10 Recursion
A recursive definition of a term is a definition that involves the term itself in the
definition of the term.
A recursive formula (or recursive function) is a formula (or function) that involves itself
in its definition.
A recursive functio
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
1.7 Sets
In the section we shall look at sets. Sets and set operation closely mirror logic and the
logical operations that we looked at in section 1.1.
1.7.1 Sets and Set Operations
A set is a collection of items.
There are similarities between sets and l
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
Chapter 10
Use the following to answer questions 126:
In the questions below fill in the blanks.
1. If T is a tree with 999 vertices, then T has _ edges.
Ans: 998.
2. There are _ nonisomorphic trees with four vertices.
Ans: 2.
3. There are _ nonisomorp