Math 89 Winter 2012
Set Theory - Syllabus

Syllabus is subject to change. More specific textbook readings will be added as the quarter progresses.

Week 1
Weds 4 JanWhat is set theory? Introduction to sets.Chapter 1
Fri 6 JanSets, relations.Sections 1.3, 2.2
Week 2
Mon 9 JanRelations, functions.Chapter 2
Weds 11 JanRelations, natural numbers.Chapter 2-3
Fri 13 JanNatural numbers, recursion.Chapter 3
Week 3
Mon 16 JanMartin Luther King, Jr. Day - no classes
Weds 18 JanRecursion, arithmetic.Sections 3.3, 3.4, 3.5
Fri 20 JanStructures, first-order languages, cardinality.Sections 3.5, 4.1, bits of later 4.
Week 4
Mon 23 JanFinite and countable sets.Sections 4.2, 4.3
Weds 25 JanCountable sets and linear orders.Sections 4.3, 4.4
Fri 27 JanLinear orders and uncountable sets.Sections 4.5, 4.6
Week 5
Mon 30 JanCompletion and uncountability loose ends, cardinal arithmetic.Sections 4.5, 4.6, 5.1
Weds 1 FebCardinal arithmetic and the continuum.Sections 5.1, 5.2
Weds 1 FebMidterm I distributed. Covers through chapter 5.
Fri 3 FebOrdinal numbers and arithmetic.Sections 6.2, 6.5
Week 6
Mon 6 FebUniqueness of ordinals, transfinite recursion, Replacement.Sections 6.1-6.4
Weds 8 FebJustifying transfinite recursion, beginning alephs.Sections 6.4, 7.1
Weds 8 FebMidterm I due.
Fri 10 FebWinter Carnival - no classes.

Office hours cancelled today.
Week 7
Mon 13 FebAlephs arithmetic, the Axiom of Choice.Sections 7.2, 8.1
Weds 15 FebPerfect subsets of R^n and the Cantor-Bendixson theorem.not from book
Fri 17 FebThe Axiom of Choice and cardinal arithmetic; cofinalitySections 9.1, 9.2
Week 8
Mon 20 FebCofinality, regular and singular cardinals.Section 9.2
Weds 22 FebHereditary cardinality.not from book
Fri 24 FebTopics: Combinatorics.Sections 12.1, 12.2
Week 9
Mon 27 FebTopics: Combinatorics.Sections 12.1, 12.2
Mon 27 FebMidterm II distributed.
Weds 29 FebTopics: Failure of the Axiom of Choice.
Fri 2 MarTopics: Failure of the Axiom of Choice.
Week 10
Mon 5 MarTopics: Failure of the Axiom of Choice.
Mon 5 MarMidterm II due.
Weds 7 MarPresentations.