Logic: The Structure of Reason
As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be
From playlist Logic & Philosophy of Mathematics
Lecture 2. Homomorphisms and ideals
From playlist Abstract Algebra 2
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
Equivalence relations -- Proofs
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Field Definition (expanded) - Abstract Algebra
The field is one of the key objects you will learn about in abstract algebra. Fields generalize the real numbers and complex numbers. They are sets with two operations that come with all the features you could wish for: commutativity, inverses, identities, associativity, and more. They
From playlist Abstract Algebra
Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.
From playlist Abstract algebra
What is Abstract Algebra? (Modern Algebra)
Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in t
From playlist Abstract Algebra
We start off by looking at the basics of sets.
From playlist Abstract algebra
10 Relations (still with the not-so-exciting-stuff)
This video introduces relations between pairs of elements.
From playlist Abstract algebra
What Are Numbers? Philosophy of Mathematics (Elucidations)
What is mathematics about and how do we acquire mathematical knowledge? Mathematics seems to be about numbers, but what exactly are numbers? Are numbers and other mathematical objects something discovered or invented? Daniel Sutherland discusses some of these issues in the philosophy of ma
From playlist Logic & Philosophy of Mathematics
God, Science, and Epistemology - A Conversation with Quentin Lee (Theism vs. Atheism)
Quentin Lee and I talk about epistemology, philosophy of science, and theology. To get in touch: Email: mathoma1517@gmail.com Twitter: @Math_oma Stuff mentioned in discussion: 1. "Five Proofs of the Existence of God" by Edward Feser: https://www.amazon.com/Five-Proofs-Existence-Edward-F
From playlist Conversations
Stanford Seminar - Safety (and Liveness!) of Robot Behaviors
Hadas Kress- Gazit, Professor Sibley School of Mechanical and Aerospace Engineering, College of Engineering - Princeton April 27, 2022 In this talk I will describe how formal methods such as synthesis – automatically creating a system from a formal specification – can be leveraged to desi
From playlist Stanford CS521 - AI Safety Seminar
Django Structure For Scale and Longevity
Django is great. But as we add new features, as our dev team grows, the software needs to be stable on production, things can get quite messy. We are going to look at some common patterns, derived from experience, on how to structure your Django project for scale and longevity. PUBLICATIO
From playlist Python
Wolfram Physics Project: Working Session Tuesday, Mar. 16, 2021 [Bibliographying Combinators]
This is a Wolfram Physics Project working session on bibliographying combinators. Begins at 4:33 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am
From playlist Wolfram Physics Project Livestream Archive
Ruby on Ales 2014 - Small Code
By Mark Menard To paraphrase Mark Twain, "I didn't have time to write some small classes, so I wrote a BIG ONE instead." Now what do you do? Refactor! In this talk we'll refactor some large classes into a series of smaller classes. We'll learn techniques to identify buried abstractions, wh
From playlist Ruby on Ales 2014
Lecture 8A: Logic Programming, Part 1
MIT 6.001 Structure and Interpretation of Computer Programs, Spring 2005 Instructor: Harold Abelson, Gerald Jay Sussman, Julie Sussman View the complete course: https://ocw.mit.edu/6-001S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE18841CABEA24090 Logic Programming, Part
From playlist MIT 6.001 Structure and Interpretation, 1986
Programming with Math (Exploring Type Theory)
As programs are getting more complex, it's time to go back to basics, to the old well tested approach to complexity called mathematics. Let compilers deal with the intricacies of Turing machines. Our strength is abstract thinking. Let's use it! EVENT: Øredev 2018 SPEAKER: Bartosz Milew
From playlist Software Development
IMS Public Lecture: Foundations of Mathematics: An Optimistic Message
Stephen G. Simpson, Pennsylvania State University, USA
From playlist Public Lectures
Category Theory 1.1: Motivation and Philosophy
Motivation and philosophy
From playlist Category Theory
Logical challenges with abstract algebra II | Abstract Algebra Math Foundations 215 | NJ Wildberger
There is a very big jump in going from finite algebraic objects to "infinite algebraic objects". For example, there is a huge difference, if one is interested in very precise definitions, between the concept of a finite group and the concept of an "infinite group". We illustrate this imp
From playlist Math Foundations