Zorn's lemma

Zorn's Lemma, The Well-Ordering Theorem, and Undefinability (Version 2.0)

Zorn's Lemma and The Well-ordering Theorem are seemingly straightforward statements, but they give incredibly mind-bending results. Orderings, Hasse Diagrams, and the Ordinals / set theory will come up in this video as tools to get a better view of where the "proof" of Zorn's lemma comes f

From playlist The New CHALKboard

Zorn's Lemma, The Well-Ordering Theorem, and Undefinability | Nathan Dalaklis

Zorn's Lemma and The Well-ordering Theorem are seemingly straightforward statements, but they give incredibly mind-bending results. Orderings, Hasse Diagrams, and the Ordinals will come up in this video as tools to get a better view of where the proof of Zorn's lemma comes from. ***Corre

From playlist The First CHALKboard

Zorn’s Lemma and Basis

Why every vector space (not necessarily finite dimensional) has a basis, feat. Zorn's Lemma and the actual definition of a basis Check out my set theory playlist: Set theory https://www.youtube.com/playlist?list=PLJb1qAQIrmmDr_RYAtqY1MNgTgVNMJNIf Check out my vector space playlist: https

From playlist Vector Spaces

Zermelo Fraenkel Powerset

This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the powerset axiom, the strongest of the ZF axioms, and explain why the notion of a powerset is so hard to pin down precisely. For the other lectures in the course see https://www.youtube.com

From playlist Zermelo Fraenkel axioms

Zermelo Fraenkel Introduction

This lecture is part of an online course on the Zermelo Fraenkel axioms of set theory. This lecture gives an overview of the axioms, describes the von Neumann hierarchy, and sketches several approaches to interpreting the axioms (Platonism, von Neumann hierarchy, multiverse, formalism, pra

From playlist Zermelo Fraenkel axioms

Commutative algebra 32 Zariski's lemma

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We state and prove Zariski's lemma: Any field that is a finitely generated algebra over a field is a finitely generated modu

From playlist Commutative algebra

Set Theory (Part 2): ZFC Axioms

Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their

From playlist Set Theory by Mathoma

Lecture 5: Zorn’s Lemma and the Hahn-Banach Theorem

MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=KlAjiDivJoQ&list=PLUl4u3cNGP63micsJp_

From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021

Proof of Lemma and Lagrange's Theorem

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div

From playlist Abstract Algebra

Learn Topology with this Little Book for Beginners

In this video I go over a really little book on topology. This was he book I used when I first learned topology. The book is called Elements of Point Set Topology and it was written by John D. Baum. This is the book on amazon: https://amzn.to/3iC6FhY or https://amzn.to/361n8qE Note the

From playlist Book Reviews

3 Key Ideas for Math Tutors

I discuss 3 key ideas for tutoring. Do you have any advice? If so, please leave a comment. The Serge Lang Book: https://amzn.to/3lUYiUh Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affiliate links) ***********Math, Physics, and Comp

From playlist Inspiration and Advice

Foundations S2 - Seminar 6 - Filters and ultrafilters

A seminar series on the foundations of mathematics, by Will Troiani and Billy Snikkers. In this lecture Billy introduces filters and ultrafilters and proves that a filter is maximal iff. it is an ultrafilter. The webpage for this seminar is https://metauni.org/foundations/ You can join t

From playlist Foundations seminar

Homological algebra 6: Injective modules

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We study to following problem: are there enough injective modules, in the sense that every module is a submodule of an injecti

From playlist Commutative algebra

Commutative algebra 14 (Irreducible subsets of Spec R)

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we show that the irreducible closed subsets of Spec R are just the closures of points. We do this using the

From playlist Commutative algebra

Generating digraphs with derangements by Daniel Horsley

CMSA Combinatorics Seminar, 15 July 2020

From playlist CMSA Combinatorics Seminar

Burnside's Lemma (Part 2) - combining math, science and music

Part 1 (previous video): https://youtu.be/6kfbotHL0fs Orbit-stabilizer theorem: https://youtu.be/BfgMdi0OkPU Burnside's lemma is an interesting result in group theory that helps us count things with symmetries considered, e.g. in some situations, we don't want to count things that can be

From playlist Traditional topics, explained in a new way

Rings 6 Prime and maximal ideals

This lecture is part of an online course on rings and modules. We discuss prime and maximal ideals of a (commutative) ring, use them to construct the spectrum of a ring, and give a few examples. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj5

From playlist Rings and modules

Orders on Sets: Part 1 - Partial Orders

This was recorded as supplemental material for Math 115AH at UCLA in the spring quarter of 2020. In this video, I discuss the concept and definition of a partial order.

From playlist Orders on Sets