What is a Vector Space? (Abstract Algebra)
Vector spaces are one of the fundamental objects you study in abstract algebra. They are a significant generalization of the 2- and 3-dimensional vectors you study in science. In this lesson we talk about the definition of a vector space and give a few surprising examples. Be sure to su
From playlist Abstract Algebra
Giuseppe Rosolini: Triposes and Gödel's Dialectica Interpretation
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: In previous joint work with B. Biering, L. Birkedal, C. Butz, J.M.E. Hyland, J. van Oosten, and T. Streicher, the problem of a semantic presentation of the functional int
From playlist Workshop: "Proofs and Computation"
Paulo Oliva: On a Dialectica like version of Kleene numerical realizability
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Kleene's original notion of realizability (1945) makes use of all (partial) computable functions as potential realisers. Later Kreisel (1959) presented a "modified" notio
From playlist Workshop: "Proofs and Computation"
Makoto Fujiwara: Bar theorem and bar recursion for continuous functions with continuous modulus
The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: (joint work with Tatsuji Kawai) Bar induction is originally discussed by L. E. J. Brouwer under the name of “bar theorem” in his intuitionistic mathematics but first formali
From playlist Workshop: "Constructive Mathematics"
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
Amir Tabatabai Mining the Surface: Proof mining in the bounded world
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: A computational flow is a pair consisting of a sequence of computational problems of a certain sort and a sequence of computational reductions among them. In this talk we
From playlist Workshop: "Proofs and Computation"
Hugo Herbelin: Computing with Markov's principle
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Computing with Markov's principle via a realizability interpretation is standard, using unbounded search as in Kleene's realizability or by selecting the first valid wit
From playlist Workshop: "Proofs and Computation"
Metric space definition and examples. Welcome to the beautiful world of topology and analysis! In this video, I present the important concept of a metric space, and give 10 examples. The idea of a metric space is to generalize the concept of absolute values and distances to sets more gener
From playlist Topology
What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:
From playlist Science Unplugged: Physics
What is (a) Space? From Zero to Geo 1.5
What is space? In this video, we learn about the many different things that we might call "space". We come up with both a geometric and an algebraic definition, and the discussion also leads us to the important concept of subspaces. Sorry for how long this video took to make! I mention
From playlist From Zero to Geo
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
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From playlist Science Unplugged: Special Relativity
Dimensions (1 of 3: The Traditional Definition - Directions)
More resources available at www.misterwootube.com
From playlist Exploring Mathematics: Fractals
Vector spaces | Lecture 16 | Matrix Algebra for Engineers
Definition of a vector space. Join me on Coursera: https://www.coursera.org/learn/matrix-algebra-engineers Lecture notes at http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirmation=1
From playlist Matrix Algebra for Engineers
CGSR Seminar Series | War in Space: Strategy, Spacepower, Geopolitics
Speaker Biography Bleddyn Bowen primary research interests concern modern warfare, politics, and security in outer space, as well as classical strategic theory. Dr. Bowen provides research-led teaching in his 3rd year specialist module PL3144 Politics and War in Outer Space. He is the au
From playlist Center for Global Security Research
10. The Four Fundamental Subspaces
MIT 18.06 Linear Algebra, Spring 2005 Instructor: Gilbert Strang View the complete course: http://ocw.mit.edu/18-06S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8 10. The Four Fundamental Subspaces License: Creative Commons BY-NC-SA More information at http
From playlist MIT 18.06 Linear Algebra, Spring 2005
[Lesson 11] QED Prerequisites - Tensor Product Spaces
We take a detour from the Angular Momentum Mind Map to cover the important topic of Tensor Product spaces in the Dirac Formalism. In quantum mechanics, the notion of tensors is hidden under the hood of the formalism and this lesson opens that hood. The goal is to make us confident that we
From playlist QED- Prerequisite Topics
Nicolò Zava (3/17/23): Every stable invariant of finite metric spaces produces false positives
In computational topology and geometry, the Gromov-Hausdorff distance between metric spaces provides a theoretical framework to tackle the problem of shape recognition and comparison. However, the direct computation of the Gromov-Hausdorff distance between finite metric spaces is known to
From playlist Vietoris-Rips Seminar
We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the
From playlist Introducing linear algebra
CGSR Seminar Series | U.S. National Security Space Strategy: The Cold War to the Present
Talk Abstract At the present time, U.S. government officials are faced with the increasingly complex task of protecting critical national security space infrastructure in a rapidly evolving threat environment. When placed in a historical context, we find that anxiety about space security
From playlist Center for Global Security Research