Algebraic combinatorics | Polyhedral combinatorics
In algebraic combinatorics, the h-vector of a simplicial polytope is a fundamental invariant of the polytope which encodes the number of faces of different dimensions and allows one to express the Dehn–Sommerville equations in a particularly simple form. A characterization of the set of h-vectors of simplicial polytopes was conjectured by Peter McMullen and proved by Lou Billera and Carl W. Lee and Richard Stanley (g-theorem). The definition of h-vector applies to arbitrary abstract simplicial complexes. The g-conjecture stated that for simplicial spheres, all possible h-vectors occur already among the h-vectors of the boundaries of convex simplicial polytopes. It was proven in December 2018 by Karim Adiprasito. Stanley introduced a generalization of the h-vector, the toric h-vector, which is defined for an arbitrary ranked poset, and proved that for the class of Eulerian posets, the Dehn–Sommerville equations continue to hold. A different, more combinatorial, generalization of the h-vector that has been extensively studied is the flag h-vector of a ranked poset. For Eulerian posets, it can be more concisely expressed by means of a noncommutative polynomial in two variables called the cd-index. (Wikipedia).
Vector Calculus 1: What Is a Vector?
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Vector Calculus
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
This video explains how to determine a unit vector given a vector. It also explains how to determine the component form of a vector in standard position that intersects the unit circle. http://mathispower4u.yolasite.com/
From playlist Vectors
A short refresher on vectors. Before I introduce vector-based functions, it's important to look at vectors themselves and how they are represented in python™ and the IPython Notebook using SymPy.
From playlist Life Science Math: Vectors
Linear Algebra for Computer Scientists. 1. Introducing Vectors
This computer science video is one of a series on linear algebra for computer scientists. This video introduces the concept of a vector. A vector is essentially a list of numbers that can be represented with an array or a function. Vectors are used for data analysis in a wide range of f
From playlist Linear Algebra for Computer Scientists
Determine the Magnitude of a Vector Given a Vector in Component Form (Ex 1)
This video explains how to determine the magnitude of a vector. http://mathispower4u.com
From playlist Vectors in 2D
This shows an small game that illustrates the concept of a vector. The clip is from the book "Immersive Linear Algebra" at http://www.immersivemath.com
From playlist Chapter 2 - Vectors
Finding the Unit Vector of a Vector in Standard Form
Learn how to determine the unit vector of a vector in the same direction. The unit vector is a vector that has a magnitude of 1. The unit vector is obtained by dividing the given vector by its magnitude. #trigonometry#vectors #vectors
From playlist Vectors
What is a vector? We gently introduce the i and j basis vectors and the idea of a column vector is presented. The algebra of addition, subtraction and scalar multiplication is discussed. Free ebook Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Take a sh
From playlist Introduction to Vectors
Linear Algebra - Lecture 27 - Subspaces of R^n
This video lecture contains definitions and examples of subspaces of R^n.
From playlist Linear Algebra Lectures
Parallel Lines with Geometric Vectors (Ch1 Pr1)
In this video we look at vectors in the plane formed by a 3 by 3 grid of equally spaced parallel lines. This is Chapter 1 Problem 1 of the UNSW MATH1141 Algebra notes. Presented by Norman Wildberger of the School of Mathematics and Statistics, UNSW.
From playlist Mathematics 1A (Algebra)
Random Matrix Theory and its Applications by Satya Majumdar ( Lecture 2 )
PROGRAM BANGALORE SCHOOL ON STATISTICAL PHYSICS - X ORGANIZERS : Abhishek Dhar and Sanjib Sabhapandit DATE : 17 June 2019 to 28 June 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore This advanced level school is the tenth in the series. This is a pedagogical school, aimed at bridgin
From playlist Bangalore School on Statistical Physics - X (2019)
Geometric Algebra Applications - Kepler Problem (Part 2)
In this video, we show that the trajectories of masses moving under an inverse-square law are conic sections using geometric algebra. We will not be solving any differential equations, but instead showing that a special vector, the Laplace-Runge-Lenz vector, is a conserved quantity of moti
From playlist Math
Derivative of a position vector valued function | Multivariable Calculus | Khan Academy
Visualizing the derivative of a position vector valued function Watch the next lesson: https://www.khanacademy.org/math/multivariable-calculus/line_integrals_topic/position_vector_functions/v/differential-of-a-vector-valued-function?utm_source=YT&utm_medium=Desc&utm_campaign=Multivariable
From playlist Advanced derivatives | AP Calculus BC | Khan Academy
5. Error correction, syndrome decoding
MIT 6.02 Introduction to EECS II: Digital Communication Systems, Fall 2012 View the complete course: http://ocw.mit.edu/6-02F12 Instructor: George Verghese This lecture continues to explore error correction through a closer look at the generator matrix and the parity check matrix. Syndrom
From playlist MIT 6.02 Introduction to EECS II: Digital Communication Systems, Fall 2012
4. Spin One-half, Bras, Kets, and Operators
MIT 8.05 Quantum Physics II, Fall 2013 View the complete course: http://ocw.mit.edu/8-05F13 Instructor: Barton Zwiebach In this lecture, the professor talked about spin one-half states and operators, properties of Pauli matrices and index notation, spin states in arbitrary direction, etc.
From playlist 8.05 Quantum Physics II - Prof. Barton Zwiebach
Multivariable Calculus | The notion of a vector and its length.
We define the notion of a vector as it relates to multivariable calculus and define its length. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Vectors for Multivariable Calculus