Lecture
Comp 25
Math & Logic
What is logic?
• Logic is the study of reason
• Focus is the method or process by
which an argument unfolds
• Aristotle was the founder of logic –
developed principles of inference
• “All men are mortal. Socrates is a
man. Therefore Socrates is mortal.”
Where are we Headed?
• COMP 25 satisfies the specific criteria of
Area III-B as follows:
– Principles of mathematics
– Principles of formal logic
Principles of Mathematics
– Number representations: Decimal, binary and
hexadecimal numbering systems in programming.
– Applications of algebra and their implementation:
demonstrated by applications in various computer
programming languages
– Development of theories of logic and set theory,
demonstrated through implementation of Access
database queries
Principles of Formal Logic
– Program structure, grammar and constructs:
demonstrated through HTML programming, CSS
and JavaScript
– General programming conditional constructs (IF,
IF-THEN-ELSE, FOR and WHILE loops, etc):
demonstrated through JavaScript programming
– Development of theories of logical formulas:
demonstrated through Excel spreadsheets
Students gain insights into through
“demonstration”
• How does the binary/hex number systems
works, then directly see how this applies to
the fundamental operation of modern
computers
• Learn how logic allows expressions to be
proved true or false, then directly see how
this is used in the construction of programs,
algorithms, and queries.
Insights through “demonstration”
• Learn how the languages of computers have
structures, then observe the necessity of
this structures in writing and debugging
programs
• Some “formal proofs”, such as the basic
laws and theorems of algebra, and students
can see how these laws and theorems apply
to computer programs and the operation of
the computer itself.
Course outline
• Comp 25 is divided into four sections:
– Computer Architecture and
Networking
– Programming Languages
– Logical formulas
– Database management systems
Computer Architecture &
Networking
• The necessary foundation material is discussed for the
course. This includes computer numbering systems, the
basic organization of a computer system (its architecture),
how data is represented stored, and some rudimentary
networking background.
• Networking principles with emphasis on the TCP/IP suite of
protocols, IP addressing systems, packet switching and
network troubleshooting.
Programming languages
• Programming is introduced: initially through
HTML (Hypertext Markup Language), CSS
(Cascading Style Sheets), JavaScript.
• All programming is accomplished using basic text
editors similar to using Windows Notepad or Max
TextEdit: no HTML editors are used.
Logical Formulas
• These formulas are presented using Excel
• Beyond basic math formulas into logical formulas
based on programming logic
• IF, THEN, ELSE, as well as nested IF statements,
IF AND and IF OR.
• These logical formulas are constructed using
algebra, allowing the computer to make
decisions based on the results of the formulas.
Database Management Systems
• The use of logical formulas developed in the previous
section allows the students to them move on to more
advanced decision-making using databases of
information.
• Complex logical expressions are built to form “queries”
which are then evaluated by the Access database
application.
• Apply formal logical principles in order to access
specific information stored in a database.