Lecture

Comp 25Math & Logic

Discussion

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.