How has the teaching of (undergraduate) Set Theory changed over time?

Question

I'm writing an Essay on Set Theory, and realized it was formulated quite recently, so I thought it might be cool to have some first person accounts. Russell's Paradox was discovered just around a century ago. So I'm guessing that some of the senior members of this community might have experienced a tumult learning curriculum. Most of the undergraduate books in diverse areas offer an introduction to Set Theory in the first chapter, which is pretty standardized. Again, I'm speculating that it might not have been that way before. Other important events that might have impacted how set theory was teach would be Paul Cohen's discovery of forcing. So, reformulating my question, In your lifetime, have you seen a noticeable difference in how Set Theory is taught at an undergraduate level? If the question is too broad, please tell me so that I can modify it accordingly. Thanks in advance

Answer 1

Besides the most basic "operational" topics, I don't think any standard for teaching set theory exists yet.

As soon as you starts really "doing set theory" things become non-trivial and not very accessible for undergrads. For weak evidence about this, here is my experience: when I was finishing my third year in my undergrad program (after measure theory and abstract algebra) we set with a classmate to read Halmos' Naive Set Theory. We gave up fairly soon, as it seemed impossible to follow for us. Then 27 years later I read it (last year), and it was so clear and easy to follow.