A final exam for this course will be scheduled by the registrar. Details will be posted on the course website as they become available.
Lecture # | Date | topics covered | reading/resources/comments |
1 | 05/09/23 | Course introduction, equinumerosity | Chapter 2 from textbook |
2 | 07/09/23 | equinumerosity, continued | Chapter 2 |
3 | 09/09/23 | countability of the rationals, uncountability of the reals | Chapter 2 |
4 | 12/09/23 | Algebraic numbers, Schroder-Bernstein Theorem | Chapter 2 |
5 | 14/09/23 | Russell's paradox, first six axioms of ZFC | Chapter 3 |
6 | 15/09/23 | continued | Chapter 3 |
7 | 19/09/23 | ordered pairs, cartesian product | Chapter 4 |
8 | 21/09/23 | relations, cardinals, cardinal arithmetic. | Chapter 4 |
9 | 23/09/23 | Peano Systems. Properties, existence | Chapter 5 |
10 | 26/09/23 | The Recursion Theorem, uniqueness of Peano Systems | Chapter 5 |
11 | 28/09/23 | Arithmetic operations, the well ordering of the natural numbers | Chapter 5 |
12 | 29/09/23 | continued, Assignment #1 due |
Chapter 5 |
13 | 03/10/23 | well orderings | Chapter 7 |
14 | 05/10/23 | well orderings | Chapter 7 |
15 | 06/10/23 | transfinite recursion, Assignment #2 due (deadline extended to 10/10/23) | Chapter 7 |
16 | 17/10/23 | midterm test | |
17 | 19/10/23 | transfinite recursion | Chapter 7 |
18 | 20/10/23 | Comparability of well orderings | Chapter 7 |
19 | 24/10/23 | Hartog's theorem | Chapter 7 |
20 | 26/10/23 | Hartog's theorem, The axiom of choice | Chapter 8 |
21 | 27/10/23 | The axiom of choice, Assignment #3 due | Chapter 8 |
22 | 31/10/23 | The axiom of choice | Chapter 8 |
23 | 02/11/23 | The axiom of choice | Chapter 8 |
24 | 03/11/23 | Choice's consequences | Chapter 9 |
25 | 07/11/23 | Cardinal arithmetic | Chapter 9 |
26 | 09/11/23 | best well orders, CxC = C in cardinality, cardinal arithmetic | Chapter 9 |
27 | 10/11/23 | Konig's Theorem, assignment #4 due | Chapter 9 |
28 | 14/11/23 | No class today | |
29 | 16/11/23 | Axiom of Replacement | Chapter 11 |
30 | 17/11/23 | Axiom of Foundation, Writing Project topic due today | Chapter 11 |
31 | 21/11/23 | ordinals |
Chapter 12 |
32 | 23/11/23 | ordinals |
Chapter 12 |
33 | 24/11/23 | cardinals |
Chapter 12 |
34 | 28/11/23 | cardinals, cumulative hierarchy |
Chapter 12 |
35 | 30/11/23 | cumulative hierarchy |
Chapter 12 |
36 | 01/12/23 | no class today |
|
37 | 05/12/23 | Kieran's lecture, course wrap up, writing
project due |