CS 2102
Discrete Mathematics
David L. Edwards
Rice Hall 420
434-982-2253
[email protected]
1
Course Foci
Discrete Mathematics
&
Its Applications
2
Course Information
See and read syllabus
Web site on Collab
See syllabus for details of semester grading,
Number Theory
Integers and Division
Integers and Division: Whats
Important
Divides: a | b
Mod: a mod m; a b (mod m)
GCD(a,b): greatest common divisor
LCM(a,b): least common multiple
for a given integer & each
(Prime) Factors Unique
integers prime factors
Propositions
1
Specification Problem
Consider the following fragment of a
specification written in natural language:
There are two types of command that can be
entered into the computer system.
The command types are the USER commands and
the ADMINISTRA
Predicates
1
Specification Problem
Consider the following fragment of a specification
written in natural language:
All files that are larger than 1,000 blocks are to be
moved to tape provided that they have not been
referenced within the last 100 days a
Relations
Specification Fragment
Software is required to maintain a database of telephone numbers
within an organization.
Users will be known by last name and can have more than one
telephone number.
Four digit telephone number extensions must be stored.
Proofs
1
Logic
If "experts" could always be trusted to make the right moral decision,
then public participation would not be necessarybut they cannot be,
and so it is.
Source: Keay Davidson, Carl Sagan: A Life, John Wiley & Sons, 1999, p. xv.
- http:/www.
Sets
1
Specification Problem
Consider the following fragments of specification
written in natural language:
Software is required to maintain details of the users of
a computer system. Users will be people who are
permitted to use the computer system.
S