Ptolemy's theorem and generalizations | Rational Geometry Math Foundations 131 | NJ Wildberger
The other famous classical theorem about cyclic quadrilaterals is due to the great Greek astronomer and mathematician, Claudius Ptolemy. Adopting a rational point of view, we need to rethink this theorem to state it in a purely algebraic way, without resort to `distances' and the correspon
From playlist Math Foundations
Classical Mechanics | Lecture 7
(November 7, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he focuses on Liouville's Theorem, which he describes as one of the basis for Hamiltonian mechanics. He works to prove the reversibility of classical mechanics. This cour
From playlist Lecture Collection | Classical Mechanics (Fall 2011)
Lecture 4 | Modern Physics: Statistical Mechanics
April 20, 2009 - Leonard Susskind explains how to calculate and define pressure, explores the formulas some of applications of Helm-Holtz free energy, and discusses the importance of the partition function. Stanford University: http://www.stanford.edu/ Stanford Continuing Studies P
From playlist Lecture Collection | Modern Physics: Statistical Mechanics
Entropy: Origin of the Second Law of Thermodynamics
How did Clausius create entropy and why? I read his original papers to follow how possibly the most confusing concept in Classical Physics was created. My Patreon Page (thanks!): https://www.patreon.com/user?u=15291200 The music is from the awesome Kim Nalley of course www.KimNalley.
From playlist Laws of Thermodynamics: History
Local Correction of Codes and Euclidean Incidence Geometry - Avi Wigderson
Avi Wigderson Institute for Advanced Study March 5, 2012 A classical theorem in Euclidean geometry asserts that if a set of points has the property that every line through two of them contains a third point, then they must all be on the same line. We prove several approximate versions of t
From playlist Mathematics
On the connection between wave resonance, shear .. by Anirban Guha
DATES Monday 23 May, 2016 - Saturday 23 Jul, 2016 VENUE Madhava Lecture Hall, ICTS, Bangalore APPLY This program is first-of-its-kind in India with a specific focus to provide research experience and training to highly motivated students and young researchers in the interdisciplinary field
From playlist Summer Research Program on Dynamics of Complex Systems
Max Planck Biography with Depth and Humor
Max Planck was loved by the people who knew him, learn about this influential scientist and why he was so admired. My Patreon Page (thanks!): https://www.patreon.com/user?u=15291200 The music is from the awesome Kim Nalley of course www.KimNalley.com
From playlist Max Planck Biographies
Open questions in turbulent stratified mixing:Do we even know what we do not know? by C.P. Caulfield
ABSTRACT: Understanding how turbulence leads to the enhanced irreversible transport of heat and other scalars (such as salt and pollutants) in density-stratified fluids is a fundamental and central problem in geophysical and environmental fluid dynamics. There is a wide range of highly im
From playlist ICTS Colloquia
Qin Li - Multiscale inverse problem, from Schroedinger to Newton to Boltzmann - IPAM at UCLA
Recorded 11 April 2022. Qin Li of the University of Wisconsin-Madison, Mathematics, presents "Multiscale inverse problem, from Schroedinger to Newton to Boltzmann" at IPAM's Model Reduction in Quantum Mechanics Workshop. Abstract: Inverse problems are ubiquitous. People probe the media wit
From playlist 2022 Model Reduction in Quantum Mechanics Workshop
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
The Schrodinger Equation is (Almost) Impossible to Solve.
Sure, the equation is easily solvable for perfect / idealized systems, but almost impossible for any real systems. The Schrodinger equation is the governing equation of quantum mechanics, and determines the relationship between a system, its surroundings, and a system's wave function. Th
From playlist Quantum Physics by Parth G
Classical Mechanics | Lecture 1
(September 26, 2011) Leonard Susskind gives a brief introduction to the mathematics behind physics including the addition and multiplication of vectors as well as velocity and acceleration in terms of particles. This course is the beginning of a six course sequence that explores the theor
From playlist Lecture Collection | Classical Mechanics (Fall 2011)
Euler-Lagrange equation explained intuitively - Lagrangian Mechanics
Lagrangian Mechanics from Newton to Quantum Field Theory. My Patreon page is at https://www.patreon.com/EugeneK
From playlist Physics
The Fundamental Theorem of Calculus of vector fields -- Calculus III
This lecture is on Calculus III. It follows Part III of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus III
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Stability and Variability - Joel Lebowitz
Joel Lebowitz Rutgers, The State University of New Jersey September 27, 2013 More videos on http://video.ias.edu
From playlist Dreams of Earth and Sky
Statistical Mechanics Lecture 5
(April 29, 2013) Leonard Susskind presents the mathematical definition of pressure using the Helmholtz free energy, and then derives the famous equation of state for an ideal gas: pV = NkT. Originally presented in the Stanford Continuing Studies Program. Stanford University: http://www.s
From playlist Course | Statistical Mechanics
Field Equations Helmholz Decomposition [Redux]
[Redux: Errata fixed from previous version of this lecture. I corrected the expression for the Laplacian and gradient in spherical coordinates and repaired my execution of the delta function's volume integral.] In this lesson we prove the theorem which tells us that any vector field can b
From playlist QED- Prerequisite Topics
Konrad Polthier (7/27/22): Boundary-sensitive Hodge decompositions
Abstract: We provide a theoretical framework for discrete Hodge-type decomposition theorems of piecewise constant vector fields on simplicial surfaces with boundary that is structurally consistent with decomposition results for differential forms on smooth manifolds with boundary. In parti
From playlist Applied Geometry for Data Sciences 2022
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One