Math 330: Number Systems
Syllabus
Section 6 · Zaslavsky · Spring 2025
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Textbook
Matthias Beck and Ross Geoghegan, The Art of Proof, Springer, New York, 2010.
Chapters 1–6; 8, 9, 10?, 11?; and 13.
(This list will be modified as we go through the course. Stay tuned.)
"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
Tentative. This list will be modified as we go through the course.
- 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
- 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
- Limits
- Rational numbers
- Irrational numbers
- Cardinality
- More on functions: cardinal number
- Countable and uncountable sets
- Q is countable, R is uncountable
- Many kinds of infinity
Main class page | Schedule and homework | Announcements | Advice | Term Project