About: This page contains information and links related to my teaching.
The first exam has been moved to Friday February 26.
| Office hours | M 8:00-8:50, W 12:00-12:50, F 10:00-10:50 |
| Class times | MWF 9:00-9:50 |
| Class location | ECCR 118 |
| Book | Notes handed out in class |
| Date | |
| Monday January 11 |
Introduction.
Basic ideas about logic: truth tables and standard arguments (section introduction) |
| Wednesday January 13 |
The first axioms: meaning and some use. (section 1)
the key idea about axioms is that they don't describe what a set is, but what a universe of sets is. |
| Friday January 15 |
Axioms, defined properties, and how to write a proof (section 1)
the key idea in writing a proof is often using the standard methods to get down to the hart of the matter, and then reasoning very carefully. |
| Monday January 18 | No class: MLK day. |
| Wednesday January 20 |
Ordered pairs and relations (section 2)
The key point was the idea that notions that a priori are not about sets, can be "implemented" in sets. They should then have the main properties of the original notions, but will often also "accidentally" have more properties. |
| Friday January 22 |
Functions (section 3, a small start)
We discussed the reason for developing the axioms the way we are, not too strong, not too weak. We also discussed what the axioms are describing. |
| Monday January 25 |
Functions (section 3)
Worked some of the theorems in the section emphasizing the role of definitions, that they are not randomly chosen, but need to fit our intuitions. Side effects are to be expected though. |
| Wednesday January 27 |
Functions (section 3)
The axiom of choice was introduced and explained. |
| Friday January 29 |
replacement procedure (section 3)
Equivalence relations and partitions (section 4) |
| Monday February 1 |
Finishing equivalence relations (section 4)
Pictures of relations: easy way of obtaining examples. Definition and (non-)examples of wellorders (section 5) |
| Wednesday February 3 |
Induction: for any well order (section 5) and on N
defining N (section 6) |
| Friday February 5 |
Properties of N (section 6):
Induction and some basic properties of our implementation. |
| Monday February 8 |
Doing inductive proofs
The Recursion Theorem |
| Wednesday February 10 | Proof of the recursion theorem |
| Friday February 12 |
Defining addition.
Properties of addition. |
| Mon Feb 15-Feb19 | Essentially finish Chapter 6 |
| Monday February 22 | On the proof of the closure theorem. |
| Wednesday February 24 | On proving existence choice functions from AC. |
| Friday February 26 | First midterm |
| Monday March 1 | The ideas surrounding ordinals and cardinals. |
| Wednesday March 2 | Discussed the exercise on the recursion theorem in great detail. |
| Friday March 5 | Definition cardinals and some properties (Chapter 7) |
| Monday March 8 | Properties of cardinals (Chapter 7) |
| Due | Assignment | |||
| Friday January 22 |
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| Friday January 29 |
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| Friday February 5 |
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| Friday February 12 |
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| Friday February 19 |
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| Friday March 5 |
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| Friday March 12 |
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pdf file is also available.