The SECRET to UNDERSTANDING math (Informal vs. Formal math)
Many people go through school thinking that they are not a “math person,” or that “math just isn’t for them,” or that they aren’t smart enough to learn math. But in most cases, this simply isn’t true; and I’m about to let you in on one of the best kept secrets in math, to show you why. L
From playlist Algebra 1 (Basics)
AlgTopReview: An informal introduction to abstract algebra
This is a review lecture on some aspects of abstract algebra useful for algebraic topology. It provides some background on fields, rings and vector spaces for those of you who have not studied these objects before, and perhaps gives an overview for those of you who have. Our treatment is
From playlist Algebraic Topology
Maths for Programmers: Introduction (What Is Discrete Mathematics?)
Transcript: In this video, I will be explaining what Discrete Mathematics is, and why it's important for the field of Computer Science and Programming. Discrete Mathematics is a branch of mathematics that deals with discrete or finite sets of elements rather than continuous or infinite s
From playlist Maths for Programmers
This video explains what is taught in discrete mathematics.
From playlist Mathematical Statements (Discrete Math)
Formal Definition of a Function using the Cartesian Product
Learning Objectives: In this video we give a formal definition of a function, one of the most foundation concepts in mathematics. We build this definition out of set theory. **************************************************** YOUR TURN! Learning math requires more than just watching vid
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
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
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
Quantum Mechanics -- a Primer for Mathematicians
Juerg Frohlich ETH Zurich; Member, School of Mathematics, IAS December 3, 2012 A general algebraic formalism for the mathematical modeling of physical systems is sketched. This formalism is sufficiently general to encompass classical and quantum-mechanical models. It is then explained in w
From playlist Mathematics
(IC 1.6) A different notion of "information"
An informal discussion of the distinctions between our everyday usage of the word "information" and the information-theoretic notion of "information". A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F Attribution for image of TV static:
From playlist Information theory and Coding
Gregory Chaitin - How is Mathematics Truth and Beauty?
When mathematicians speak about their craft, why do they use terms of philosophy and art? What is it about mathematics that can penetrate trivial truth and reveal fundamental “Truth?” What are the characteristics of fundamental truth? What is it about mathematics that can elicit the descri
From playlist How is Mathematics Truth and Beauty? - CTT Interview Series
Ideas for a Complex World - Anna Seigal
Science is full of smart tools for explaining the world around us. But those tools can sometimes feel far removed from the way the rest of us understand that world. How can we reconcile the two approaches? Oxford Mathematician Anna Seigal provides some pertinent answers in this Oxford Math
From playlist Oxford Mathematics Public Lectures
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
Using Algebra and Geometry in the Real World
You hear terms like “algebra” and “geometry” and these theories we memorized in high school start to dance a jig in our heads – a jig many of us weren’t overly interested in! But the past decade has seen an explosion of applications of algebra, geometry, and topology to the real world, lik
From playlist What is math used for?
ICM 2018 - Rio de Janeiro | http://www.icm2018.org © 2018 Rio ICM2018 & International Mathematical Union Os direitos sobre todo o material deste canal pertencem ao Instituto de Matemática Pura e Aplicada, sendo vedada a utilização total ou parcial do conteúdo sem autorização prévia e
From playlist Ceremonies ICM 2018
A conversation between Gregory Chaitin and Stephen Wolfram at the Wolfram Summer School 2021
Stephen Wolfram plays the role of Salonnière in this new, on-going series of intellectual explorations with special guests. Watch all of the conversations here: https://wolfr.am/youtube-sw-conversations Follow us on our official social media channels. Twitter: https://twitter.com/Wolfra
From playlist Conversations with Special Guests
Giulio Tononi - What is Information?
Free access to Closer to Truth's library of 5,000 videos: http://bit.ly/2UufzC7 Information is a common word but has technical meanings so important that our entire world depends on them. What are the kinds of information? How about the scientific definitions of information? How does info
From playlist What is Information? - CTT Interview Series
Oxford Mathematics Public Lectures: Sanjeev Goyal - The Law of the Few The study of networks offers a fruitful approach to understanding human behaviour. Sanjeev Goyal is one of its pioneers. In this lecture Sanjeev presents a puzzle: In social communities, the vast majority of individua
From playlist Oxford Mathematics Public Lectures
The Mathematics of Consciousness (Integrated Information Theory)
Entry for the #3Blue1Brown Summer of Math Exposition 2022 (#SoME2) by Rodrigo Coin Curvo & Alexander Maier Read more about Integrated Information Theory and the #neuroscience of #consciousness: http://www.scholarpedia.org/article/Integrated_information_theory Also, check out Rodrigo's e
From playlist Summer of Math Exposition 2 videos
What is Information? | Episode 1403 | Closer To Truth
What is information? Information is all the rage in science, changing how we think about fundamental questions. Information has many descriptions, some of them surprising. Why is Information so important to scientists and philosophers? Featuring interviews with Max Tegmark, Paul Davies, Se
From playlist Closer To Truth | Season 14
What is a number? | Arithmetic and Geometry Math Foundations 1 | N J Wildberger
The first of a series that will discuss foundations of mathematics. Contains a general introduction to the series, and then the beginnings of arithmetic with natural numbers. This series will methodically develop a lot of basic mathematics, starting with arithmetic, then geometry, then alg
From playlist Math Foundations