Teaching info.
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Spring 2010 Teaching.
Math 4730: Set Theory
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 |
Lectures
| 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 |
Homeworks
| 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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Subjects for Basic Notions Quiz Feb 15
- Truth tables for basic connectives (and/or/if X, then Y/not/iff).
- Form of argument by contradiction.
- Form of argument by contrapositive.
- Form of standard argument to prove $\exists x. P(x)$.
- Form of standard argument to prove $\forall x. P(x)$.
- Form of standard argument to prove $A \Rightarrow B$.
- The axioms (up to and including the 8th).
- Definition of union of sets (pairs and families).
- Definition of intersection of sets (pairs and families).
- Definition of $\{x \in A \mid P(x)\}$.
- Definition of $\{a,b\}$.
- Definition of $\{a\}$.
- Definition of $\emptyset$.
- Definition of disjoint.
- Standard argument for use of disjunction.
- Standard argument for equality of sets.
- Definition of $(a,b)$, and its key property.
- Definition of Domain.
- Definition of Range.
- Definition of (binary) relation.
- Definition of inverse relation.
- Definition of image of a set under a relation.
- Definition of function.
- Definition of surjection (onto function).
- Definition of injection (one-to-one function).
- Definition of cartesian product of a system of sets.
- Definition of equivalence relation.
- Definition of partition.
- Definitions of the different properties of orders.
- Definition of the principle of complete induction.
- Definition of $\omega$.
pdf file is also available.