Sergei Yakovenko's blog: on Math and Teaching

Sunday, October 27, 2013

Lectures 1 and 2 (Oct. 22 & 29, 2013)

We start our course by first carefully walking in a zoo with several surprising, wonderful or dangerous beasts, all caught in the Jungle of Infinity. To tame them, we need to wear some protective gear made of ironclad formulas, operate from the safety of well defined sets and use the tools provided by functions 馃槈

The lecture notes (considerably updated and revised in comparison with the previous years) can be found here. Please report typos, errors and complain about obscure instances in the comments.

Please pay attention to the problems scattered over the text: they are mostly for self-control, but if you are not sure, you may write your solutions and submit them (e.g., in the comments to this post, but also directly to Inna, if you want to keep it private).

Sunday, November 13, 2011

Lecture 2. November 8, 2011

Infinity: first accurate steps

  1. Finite and infinite subsets of \mathbb N.
  2. Admissible infinite operations: infinite unions and intersections. Quantifiers.
  3. “Small” and “large” infinite subsets of \mathbb N.
  4. One-to-one maps as the means of comparison between various infinite sets.
  5. The first “paradox”: \mathbb N\times\mathbb N\simeq\mathbb N.

Download the pdf file for the complete exposition.

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