> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/900-index/970-links/videos.md). # Math on YouTubel Video Playlists ## HoTT and its Foundations by Matt Erbst Homological Algebra, Higher Category Theory *Thierry Coquand - Logic and Topology*\ The logic of topos is naturally described using intuitionistic higher-order logic, an intuitionistic version of a simple theory of types, a formal system designed by A. Church (1940). Two important axioms of this formal system are the axiom of extensionality and the axiom of description. Recently, Voevodsky formulated the axiom of univalence, which can be seen as a natural generalization of the axiom of extensionality, and showed that this axiom is valid in a model where a type is interpreted as a Kan simplicial set. This model uses classical logic in an essential way. We present a variation of this model which is carried out in an intuitionistic meta-theory and explain how the axiom of description is validated in this model. ## Foundations of Pure Mathematics * Last updated on Mar 30, 2015 * University of Nottingham * * The first class in Dr Joel Feinstein's `G11FPM Foundations of Pure Mathematics` module covers motivation for pure mathematical thinking (definitions, proofs and examples) illustrated by looking at some introductory puzzles with voting. * Dr Feinstein's blog may be viewed at: * Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. ## Set Theory * Set Theory (Part 1): Notation and Operations * Mar 15, 2015 * * by Mathoma * In this video series, we'll explore the basics of set theory. I assume no experience with set theory in the video series and anyone who's "been around town" in math should understand the videos. To make sure we're on common ground, I introduce the common set and logical symbols and operations such as subset, power set, union, intersection, and relative complement. ## FM 20 1.1 Making Conjectures Inductive Reasoning * Sep 6, 2017 * by Mr. MathWell * Foundations of Math 20 - section 1.1 * Making conjectures using Inductive reasoning! * FM 20 1.1 Making Conjectures Inductive Reasoning - YouTube * *** Algebraic Structures: Groups, Rings, and Fields - YouTube bt James Hamblin Axiomatics and the least upper bound property (I) | Real numbers and limits Math Foundations 120 - YouTube Introduction to Foundations of Pure Mathematics - Dr Joel Feinstein - YouTube