| Main page | Homework |
|---|
Syllabus is subject to change. More specific textbook readings will be added as the quarter progresses.
| Week 1 | ||
|---|---|---|
| Weds 4 Jan | What is set theory? Introduction to sets. | Chapter 1 |
| Fri 6 Jan | Sets, relations. | Sections 1.3, 2.2 |
| Week 2 | ||
| Mon 9 Jan | Relations, functions. | Chapter 2 |
| Weds 11 Jan | Relations, natural numbers. | Chapter 2-3 |
| Fri 13 Jan | Natural numbers, recursion. | Chapter 3 |
| Week 3 | ||
| Mon 16 Jan | Martin Luther King, Jr. Day - no classes | |
| Weds 18 Jan | Recursion, arithmetic. | Sections 3.3, 3.4, 3.5 |
| Fri 20 Jan | Structures, first-order languages, cardinality. | Sections 3.5, 4.1, bits of later 4. |
| Week 4 | ||
| Mon 23 Jan | Finite and countable sets. | Sections 4.2, 4.3 |
| Weds 25 Jan | Countable sets and linear orders. | Sections 4.3, 4.4 |
| Fri 27 Jan | Linear orders and uncountable sets. | Sections 4.5, 4.6 |
| Week 5 | ||
| Mon 30 Jan | Completion and uncountability loose ends, cardinal arithmetic. | Sections 4.5, 4.6, 5.1 |
| Weds 1 Feb | Cardinal arithmetic and the continuum. | Sections 5.1, 5.2 |
| Weds 1 Feb | Midterm I distributed. Covers through chapter 5. | |
| Fri 3 Feb | Ordinal numbers and arithmetic. | Sections 6.2, 6.5 |
| Week 6 | ||
| Mon 6 Feb | Uniqueness of ordinals, transfinite recursion, Replacement. | Sections 6.1-6.4 |
| Weds 8 Feb | Justifying transfinite recursion, beginning alephs. | Sections 6.4, 7.1 |
| Weds 8 Feb | Midterm I due. | |
| Fri 10 Feb | Winter Carnival - no classes. Office hours cancelled today. | |
| Week 7 | ||
| Mon 13 Feb | Alephs arithmetic, the Axiom of Choice. | Sections 7.2, 8.1 |
| Weds 15 Feb | Perfect subsets of R^n and the Cantor-Bendixson theorem. | not from book |
| Fri 17 Feb | The Axiom of Choice and cardinal arithmetic; cofinality | Sections 9.1, 9.2 |
| Week 8 | ||
| Mon 20 Feb | Cofinality, regular and singular cardinals. | Section 9.2 |
| Weds 22 Feb | Hereditary cardinality. | not from book |
| Fri 24 Feb | Topics: Combinatorics. | Sections 12.1, 12.2 |
| Week 9 | ||
| Mon 27 Feb | Topics: Combinatorics. | Sections 12.1, 12.2 |
| Mon 27 Feb | Midterm II distributed. | |
| Weds 29 Feb | Topics: Failure of the Axiom of Choice. | |
| Fri 2 Mar | Topics: Failure of the Axiom of Choice. | |
| Week 10 | ||
| Mon 5 Mar | Topics: Failure of the Axiom of Choice. | |
| Mon 5 Mar | Midterm II due. | |
| Weds 7 Mar | Presentations. | |
Last modified 2 Mar 2012.