Math 330: Number Systems
Syllabus
Section 5, Zaslavsky · Fall 2021
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Textbook
Matthias Beck and Ross Geoghegan, The Art of Proof, Springer, New York, 2010.
Chapters 1–6, 8–11, 13–14.
(This list may be slightly 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
This list may be slightly 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
- Square roots
- Cardinality
- More on functions: cardinal number
- Countable and uncountable sets
- Q is countable, R is uncountable
- Many kinds of infinity
- [Omitted: §13.5, Indescribability]
Main class page | Schedule and homework | Announcements | Advice | Term Project | Syllabus