Miscellaneous Lecture Notes:

• Notes

Catalog Description

• Basic Set Theory and Symbolic logic. Methods of proof, including Mathematical Induction. Relations, Partitions, Partial Orders, Functions, and Graphs. Modular arithmetic. Prerequisite --PHI 251.

• The Objective of this course is to equip participants with a way of thinking and seeing based upon logic and the fundamental building blocks of mathematics: sets, relations, and functions. The course also will equip students with the skills to critically and analytically read mathematically technical textual material (books and papers)
• The Purpose of this way of seeing is to empower one to engineer anything in the design space that is the mathematical universe, the only limits being those imposed by logical consistency.

• The mathematical universe displays extreme consilience; in particular, that means the structure and function of any part of it impacts the structure and function of every other part.
• Artifacts of technology as well as the the virtual worlds of computing are realizations of structures in the mathematical universe.
• Therefore, the greater one's powers to roam at will through the design space that is the mathematical universe, the greater will be one's powers to create and to wield artifacts of technology and the virtual worlds of computing.
• The course material is essential to a deep understanding of much of computer science course work. However, a more important reason to study this subject, especially the logic and methods of proofs, is to develop mathematical maturity. The subject enhances one's ability to reason and to present a coherent, mathematically accurate, argument. Our goal is to emphasize this aspect of the course throughout the semester. How does one acquire such skill? By always insisting on proof, proof, and more proof. By insisting of yourself that you are not done until you see. The secret is: practice, practice, practice. After a while it becomes routine.

• To be able to construct mathematical proofs.
• Understand logical arguments. logical constructs.
• Understand sets, functions, and relations.
• Acquire ability to describe computer programs in a formal mathematical manner.

• Discrete Mathematics and Its Applications, (Sixth Edition), Author: Kenneth H. Rosen, Publisher: McGraw Hill, 2006.
•   -- available at Follett's Books, Marshall Square Mall

• Coverage: We will cover Chapters 1 through 5 and Chapters 8 and 9.