Nils Kürbis: Set Theory, King's College London, Autumn Term 2015
References to chapters, pages and exercises are to Herbert B Enderton: Elements of Set Theory.
Week 1
Lecture: Naïve Set Theory and Paradoxes, Axiomatic Set Theory and the Hierarchy of Sets
Reading: chapter 1
Homework: Exercises p.6f: 1-4, p.9: 5-7
Week 2
Lecture: Zermelo's Axioms for Set Theory
Reading: chapter 2 to p.26
Homework: Exercises, p.26: 1-10 (formative)
Week 3
Lecture: The Algebra of Sets, Ordered Pairs, Relations
Reading: chapter 2, p.27 to end, chapter 3 to p.42
Homework: Exercises p.32: 11, 14-22
Week 4
Lecture: Functions
Reading: chapter 3, p.42-52
Homework: exercises p.33: 24, 25, p.38: 1, 3, 4, p.41: 6-9 (formative)
Week 5
Lecture: Indexed Operations, Equivalence Relations, Ordering Relations
Reading: chapter 3, p.54 to end
Homework: Homework: exercises p.52ff: 13-15, 18, 19, 21, 22, 26, 29, p.61: 32, 34, 36 (formative)
Reading Week
Week 6
Lecture: The Natural Numbers
Reading: chapter 4, p.66-73
Homework: Catch Up
Week 7
Lecture: The Recursion Theorem and Arithmetic
Reading: chapter 4, p.73-83
Homework: exercises p.70: 1, p.73: 2, 3, 6, p.78: 8, p.83: 13, 14, p.88: 21, 26, 28 (formative)
Week 8
Lecture: More Arithmetic
Reading: chapter 4, p.83-87
Homework: continued from week 7
Week 9
Lecture: The Cardinal Numbers
Reading: chapter 6, 128-144
Homework: exercises p.133: 5, p.138: 8, 9, p.144: 12, p.150f: 15, 16, 17, p.158: 18, 19, 23
Week 10
Lecture: Ordering the Cardinals and the Axiom of Choice
Reading: chapter 6, 145-158
References to chapters, pages and exercises are to Herbert B Enderton: Elements of Set Theory.
Week 1
Lecture: Naïve Set Theory and Paradoxes, Axiomatic Set Theory and the Hierarchy of Sets
Reading: chapter 1
Homework: Exercises p.6f: 1-4, p.9: 5-7
Week 2
Lecture: Zermelo's Axioms for Set Theory
Reading: chapter 2 to p.26
Homework: Exercises, p.26: 1-10 (formative)
Week 3
Lecture: The Algebra of Sets, Ordered Pairs, Relations
Reading: chapter 2, p.27 to end, chapter 3 to p.42
Homework: Exercises p.32: 11, 14-22
Week 4
Lecture: Functions
Reading: chapter 3, p.42-52
Homework: exercises p.33: 24, 25, p.38: 1, 3, 4, p.41: 6-9 (formative)
Week 5
Lecture: Indexed Operations, Equivalence Relations, Ordering Relations
Reading: chapter 3, p.54 to end
Homework: Homework: exercises p.52ff: 13-15, 18, 19, 21, 22, 26, 29, p.61: 32, 34, 36 (formative)
Reading Week
Week 6
Lecture: The Natural Numbers
Reading: chapter 4, p.66-73
Homework: Catch Up
Week 7
Lecture: The Recursion Theorem and Arithmetic
Reading: chapter 4, p.73-83
Homework: exercises p.70: 1, p.73: 2, 3, 6, p.78: 8, p.83: 13, 14, p.88: 21, 26, 28 (formative)
Week 8
Lecture: More Arithmetic
Reading: chapter 4, p.83-87
Homework: continued from week 7
Week 9
Lecture: The Cardinal Numbers
Reading: chapter 6, 128-144
Homework: exercises p.133: 5, p.138: 8, 9, p.144: 12, p.150f: 15, 16, 17, p.158: 18, 19, 23
Week 10
Lecture: Ordering the Cardinals and the Axiom of Choice
Reading: chapter 6, 145-158