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
Business Math (1 of 1) Introduction
Visit http://ilectureonline.com for more math and science lectures! In this video I will introduce the topics that will be covered in Business Math – investments, interest, annuities, mortgages, functions in business, cost, revenue, profit, supply and demand, predictions, optimization, ma
From playlist BUSINESS MATH 1 - INTRODUCTION
Definitions, specification and interpretation | Arithmetic and Geometry Math Foundations 44
We discuss important meta-issues regarding definitions and specification in mathematics. We also introduce the idea that mathematical definitions, expressions, formulas or theorems may support a variety of possible interpretations. Examples use our previous definitions from elementary ge
From playlist Math Foundations
The problem with `functions' | Arithmetic and Geometry Math Foundations 42a
[First of two parts] Here we address a core logical problem with modern mathematics--the usual definition of a `function' does not contain precise enough bounds on the nature of the rules or procedures (or computer programs) allowed. Here we discuss the difficulty in the context of funct
From playlist Math Foundations
4 Calculating some interesting limits
Now that we have got the ball rolling, let's do some examples.
From playlist Life Science Math: Limits in calculus
In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were
From playlist An Introduction to the Arithmetic of Elliptic Curves
Michael R. Douglas - How will we do mathematics in 2030?
Abstract: We make the case that over the coming decade, computer assisted reasoning will become far more widely used in the mathematical sciences. This includes interactive and automatic theorem verification, symbolic algebra, and emerging technologies such as formal knowledge repositories
From playlist 2nd workshop Nokia-IHES / AI: what's next?
The decline of rigour in modern mathematics | Real numbers and limits Math Foundations 88
Rigour means logical validity or accuracy. In this lecture we look at this concept in some detail, describe the important role of Euclid's Elements, talk about proof, and examine a useful diagram suggesting the hierarchy of mathematics. We give some explanation for why rigour has declined
From playlist Math Foundations
Mathematical Knowledge Management software survey (paper review)
In this video I talk about the paper "The Space of Mathematical Software Systems — A Survey of Paradigmatic Systems" found here: https://arxiv.org/abs/2002.04955 My notes on the text and all links shown on in the video can be found here: https://gist.github.com/Nikolaj-K/87371836d1dd1abfba
From playlist Reviews
Inference: A Logical-Philosophical Perspective with Alexander Paseau
In this talk, Professor Alexander Paseau, Faculty of Philosophy, University of Oxford, will describe some of his work on inference within mathematics and more generally. Inferences can be usefully divided into deductive or non-deductive. Formal logic studies deductive inference, the obviou
From playlist Franke Program in Science and the Humanities
The Ultimate Guide to Propositional Logic for Discrete Mathematics
This is the ultimate guide to propositional logic in discrete mathematics. We cover propositions, truth tables, connectives, syntax, semantics, logical equivalence, translating english to logic, and even logic inferences and logical deductions. 00:00 Propositions 02:47 Connectives 05:13 W
From playlist Discrete Math 1
An introduction to the general types of logic statements
From playlist Geometry
MATH1081 Overview and Course Information
Director of First Year, Peter Brown, goes through the General information for 2014 Semester 2, MATH1081, Discrete Mathematics.
From playlist MATH1081 Discrete Mathematics
Sets, logic and graphs | Math Terminology | NJ Wildberger
In this lecture we review high school mathematics language and notation relating to sets, logic and basic graph theory. The first two topics are particularly important as they provide a language and notation that is common in many other areas of mathematics. SPECIAL NOTE: This is part of
From playlist MathTerminology for incoming Uni students
The History of Logic: The Logic of Aristotle
A few clips of Gabriele Giannantoni explaining Aristotelian logic, the logic of Aristotle. These clips come from the Multimedia Encyclopedia of the Philosophical Sciences. More Short Videos: https://www.youtube.com/playlist?list=PLhP9EhPApKE8v8UVlc7JuuNHwvhkaOvzc Aristotle's Logic: https:
From playlist Logic & Philosophy of Mathematics
Algebra and Artificial Intelligence
This is the audio from a talk I gave in May 2018 for the Melbourne logic seminar on the subject of algebra and artificial intelligence. The aim was to explain to an audience of logicians and mathematicians some of the recent progress in machine learning, and how events like the AlphaGo mat
From playlist Talks
Laurent Polynumbers and Leibniz's Formula for pi/4 | Algebraic Calculus One | Wild Egg
We can use the Fundamental Theorem of the Algebraic Calculus to give a new and simplified derivation of Leibniz's famous alternating series for "pi/4". To set this up, we take an applied point of view, going beyond the polynumber framework established so far, to more general quotient polyn
From playlist Old Algebraic Calculus Videos
Univalent Foundations Seminar - Steve Awodey
Steve Awodey Carnegie Mellon University; Member, School of Mathematics November 19, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
This video lists an explains propositional, predicate calculus axioms, as well as a set theoretical statement that goes with it, including ZF and beyond. Where possible, the explanations are kept constructive. You can find the list of axioms in the file discussed in this video here: https:
From playlist Logic