Kirchhoff's theorem

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)

What is the Riemann Hypothesis?

This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation

From playlist Mathematics

Maxim Kazarian - 1/3 Mathematical Physics of Hurwitz numbers

Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge num

From playlist ­­­­Physique mathématique des nombres de Hurwitz pour débutants

Maxim Kazarian - 3/3 Mathematical Physics of Hurwitz numbers

Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge num

From playlist ­­­­Physique mathématique des nombres de Hurwitz pour débutants

Maxim Kazarian - 2/3 Mathematical Physics of Hurwitz numbers

Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge num

From playlist ­­­­Physique mathématique des nombres de Hurwitz pour débutants

The Euler Mascheroni Constant

I define one of the most important constants in mathematics, the Euler-Mascheroni constant. It intuitively measures how far off the harmonic series 1 + 1/2 + ... + 1/n is from ln(n). In this video, I show that the constant must exist. It is an open problem to figure out if the constant is

From playlist Series

Weil conjectures 1 Introduction

This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie

From playlist Algebraic geometry: extra topics

EEVblog #820 - Mesh & Nodal Circuit Analysis Tutorial

Dave explains the fundamental DC circuit theorems of Mesh Analysis, Nodal Analysis, and the Superposition Theorem, and how they can be used to analyse circuits using Kirchhoff's Voltage and Current Laws we learned in the previous video here: https://www.youtube.com/watch?v=WBfAEeEzDlg The

From playlist Electronics Tutorial - DC Fundamentals

Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem

In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair

From playlist Introduction to Additive Combinatorics (Cambridge Part III course)

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

Applying reimann sum for the midpoint rule and 3 partitions

👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the

From playlist The Integral

Incidence Matrices of Graphs

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015 View the complete course: http://ocw.mit.edu/RES-18-009F15 Instructor: Gilbert Strang The incidence matrix has a row for every edge, containing -1 and +1 to show which two nodes are connec

From playlist MIT Learn Differential Equations

Lec 31 | MIT 18.085 Computational Science and Engineering I

Simplex method in linear programming A more recent version of this course is available at: http://ocw.mit.edu/18-085f08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.085 Computational Science & Engineering I, Fall 2007

Lec 3 | MIT Finite Element Procedures for Solids and Structures, Nonlinear Analysis

Lecture 3: Lagrangian continuum mechanics variables for analysis Instructor: Klaus-Jürgen Bathe View the complete course: http://ocw.mit.edu/RES2-002S10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT Nonlinear Finite Element Analysis

Electrical Engineering: Ch 11 AC Circuit Analysis (2 of 34) Overview of the Techniques (Part 1)

Visit http://ilectureonline.com for more math and science lectures! http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 In this video I will give an overview the top-level 6 techniques (strategies) to solve AC circuits or sinusoidally variant circuits. Part 1: tec

From playlist ELECTRICAL ENGINEERING 11 AC CIRCUIT ANALYSIS

Kirchhoff Formula

I derive the celebrated Kirchhoff Formula, which gives the solution of the wave equation in 3 dimension, enjoy! Euler-Poisson-Darboux Equation: https://youtu.be/lIdrncWaZPY Partial Differential Equations playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCXfuXUAt9dT1Gjy_GK89OH Su

From playlist Partial Differential Equations

Lec 13 | MIT 18.085 Computational Science and Engineering I, Fall 2008

Lecture 13: Kirchhoff's Current Law License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008

24. Structure of set addition IV: proof of Freiman's theorem

MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX This lecture concludes the proof of Freiman's theorem on

From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

Euler's Formula for the Quaternions

In this video, we will derive Euler's formula using a quaternion power, instead of a complex power, which will allow us to calculate quaternion exponentials such as e^(i+j+k). If you like quaternions, this is a pretty neat formula and a simple generalization of Euler's formula for complex

From playlist Math

Observable events" and "typical trajectories" in...dynamical systems - Lai-Sang Young

Analysis Seminar Topic: Observable events" and "typical trajectories" in finite and infinite dimensional dynamical systems Speaker: Lai-Sang Young Affiliation: New York University; Distinguished Visiting Professor, School of Mathematics and Natural Sciences Date: February 24, 2020 For mo

From playlist Mathematics