Department of Mathematical Sciences
Binghamton University

Math 330: Number Systems
Syllabus

Section 01, Zaslavsky

This syllabus is subject to change. Stay tuned.

Summary of Topics

• Logic, sets and operations
• Logic
• Sets and binary operations
• The Integers and Induction
• Axioms for the integers
• Sets and functions
• Quantifiers
• The natural numbers
• Ordering the Integers
• More on sets
• Defining things by induction: Binomial Theorem
• Well-Ordering Principle and an alternative form of induction
• Base ten representation of integers
• Factoring positive integers
• Equivalence relations
• Modular arithmetic
• The Real Numbers
• Axioms for the real numbers
• Injective functions and the relationship between Z and R
• Completeness of R
• Rational numbers
• Decimals
• Rationals and repeating decimals
• Countable and Uncountable Sets
• More on functions: cardinal number
• Q is countable, R is uncountable

"Where shall I begin?" he asked. "Begin at the beginning," the King said, "and stop when you get to the end."
—Lewis Carroll, Alice in Wonderland