Math on YouTubel Video Playlists
HoTT and its Foundations
by Matt Erbst https://www.youtube.com/playlist?list=PLsRvhcI3lNd75hvq4-mIhMCeDbr7HPpji 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
https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa
The first class in Dr Joel Feinstein's
G11FPM Foundations of Pure Mathematicsmodule 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: http://explainingmaths.wordpress.com
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
https://www.youtube.com/watch?v=qgizzlTVxxs
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
https://www.youtube.com/watch?v=W_BmYEaV9Yo&list=PLuCnOyrHWa9FwnCmuG4dRTn2bKI5YuO15
Algebraic Structures: Groups, Rings, and Fields - YouTube https://www.youtube.com/watch?v=vfyUU_prh9s bt James Hamblin
Axiomatics and the least upper bound property (I) | Real numbers and limits Math Foundations 120 - YouTube https://www.youtube.com/watch?v=rCDRCGjmaO8
Introduction to Foundations of Pure Mathematics - Dr Joel Feinstein - YouTube https://www.youtube.com/watch?v=nORtCRDotZY&list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa
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