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Set Theory

The theory of collections, from naive counting arguments to the axioms, cardinals and independence results that came out of them.

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A non-Noetherian local ring with finitely generated maximal ideal

2026NotesBogdan Zavyalov

A complete local ring with a finitely generated maximal ideal is Noetherian. Drop completeness and it fails: an ultraproduct construction gives a non-Noetherian local ring whose maximal ideal is principal.

Mathematical Analysis 1. Lecture 1

2026LectureСтанислав Шапошников

Naive set theory and Russell's paradox, Kuratowski's ordered pair and the Cartesian product, a function as a subset of a product, composition, injections, surjections and bijections, the group of bijections and the embedding of any group into it, equinumerosity and indicator functions, the Cantor–Bernstein and Cantor theorems.