In mathematical logic, an abstract logic is a formal system consisting of a class of sentences and a satisfaction relation with specific properties related to occurrence, expansion, isomorphism, renaming and quantification. Based on Lindström's characterization, first-order logic is, up to equivalence, the only abstract logic that is countably compact and has Löwenheim number ω. (Wikipedia).

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