Permutation Groups and Symmetric Groups | Abstract Algebra
We introduce permutation groups and symmetric groups. We cover some permutation notation, composition of permutations, composition of functions in general, and prove that the permutations of a set make a group (with certain details omitted). #abstractalgebra #grouptheory We will see the
From playlist Abstract Algebra
Permutation matrices | Lecture 9 | Matrix Algebra for Engineers
What is a permutation matrix? Define 2x2 and 3x3 permutation matrices. 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/jch
From playlist Matrix Algebra for Engineers
Abstract Algebra: (Linear Algebra Required) The symmetric group S_n is realized as a matrix group using permutation matrices. That is, S_n is shown to the isomorphic to a subgroup of O(n), the group of nxn real orthogonal matrices. Applying Cayley's Theorem, we show that every finite gr
From playlist Abstract Algebra
301.5C Definition and "Stack Notation" for Permutations
What are permutations? They're *bijective functions* from a finite set to itself. They form a group under function composition, and we use "stack notation" to denote them in this video.
From playlist Modern Algebra - Chapter 16 (permutations)
matrix choose a matrix. Calculating the number of matrix combinations of a matrix, using techniques from linear algebra like diagonalization, eigenvalues, eigenvectors. Special appearance by simultaneous diagonalizability and commuting matrices. In the end, I mention the general case using
From playlist Eigenvalues
What is a Tensor? Lesson 25: Review of Determinants
What is a Tensor? Lesson 25: Review of Determinants This lesson is purely a review of a mathematical topic that we will need for our upcoming work regarding exterior product spaces and the exterior algebra. If you are solid on determinants then you can skip this lesson
From playlist What is a Tensor?
AMMI Course "Geometric Deep Learning" - Lecture 5 (Graphs & Sets I) - Petar Veličković
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July-August 2021 by Michael Bronstein (Imperial College/Twitter), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 5: Learning on sets • Permutat
From playlist AMMI Geometric Deep Learning Course - First Edition (2021)
AMMI 2022 Course "Geometric Deep Learning" - Lecture 5 (Graphs & Sets) - Petar Veličković
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July 2022 by Michael Bronstein (Oxford), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 5: Learning on sets • Permutations • Permutation invari
From playlist AMMI Geometric Deep Learning Course - Second Edition (2022)
36 entangled officers of Euler: A quantum solution to a classically... by Arul Lakshminarayan
Colloquium: 36 entangled officers of Euler: A quantum solution to a classically impossible problem Speaker: Arul Lakshminarayan (IIT Madras, Chennai) Date: Mon, 06 June 2022, 15:30 to 17:00 Venue: Online and Madhava Lecture Hall Abstract The 36 officers problem of Euler is a well-known i
From playlist ICTS Colloquia
From playlist Plenary talks One World Symposium 2020
Vertex gluings and Demazure products by Nathan Pflueger
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Alexander HULPKE - Computational group theory, cohomology of groups and topological methods 2
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Learning from ranks, learning to rank - Jean-Philippe Vert, Google Brain
Permutations and sorting operators are ubiquitous in data science, e.g., when one wants to analyze or predict preferences. As discrete combinatorial objects, permutations do not lend themselves easily to differential calculus, which underpins much of modern machine learning. In this talk I
From playlist Statistics and computation
This project was created with Explain Everything™ Interactive Whiteboard for iPad.
From playlist Modern Algebra - Chapter 16 (permutations)
Theoretical Foundations of Graph Neural Networks
Deriving graph neural networks (GNNs) from first principles, motivating their use, and explaining how they have emerged along several related research lines. Computer Laboratory Wednesday Seminar, 17 February 2021 Slide deck: https://petar-v.com/talks/GNN-Wednesday.pdf Link at Talks.cam: h
From playlist Talks
Topics in Combinatorics lecture 7.4 --- The Marcus-Tardos theorem
We say that a permutation pi of {1,2,...,k} is contained in a permutation sigma of {1,2,...,n} if we can find k elements of {1,2,...,n} that are reordered by sigma in the way that pi reorders {1,2,...,k}. For instance, the permutation 2413 (meaning that 1 goes to 2, 2 goes to 4, 3 goes to
From playlist Topics in Combinatorics (Cambridge Part III course)
From playlist Sample Midterm