Cayley's tree formula (after Andre Joyal)
This lecture gives Andre Joyal's combinatorial proof of Cayley's formula for the number n^(n-2) of labelled trees with n vertices.
From playlist Math talks
Cayley-Hamilton Theorem: General Case
Matrix Theory: We state and prove the Cayley-Hamilton Theorem over a general field F. That is, we show each square matrix with entries in F satisfies its characteristic polynomial. We consider the special cases of diagonal and companion matrices before giving the proof.
From playlist Matrix Theory
In this video I show you how to prove Cayley's theorem, which states that every group is isomorphic to a permutation group. This video is a bit long because I take the time to revisit all the concepts required in the proof. these include isomorphisms, injective, surjective, and bijective
From playlist Abstract algebra
This is a short, animated visual proof of Viviani's theorem, which states that the sum of the distances from any interior point to the sides of an equilateral triangle is equal to the length of the triangle's altitude. #math #geometry #mtbos #manim #animation #theorem #pww #proofwith
From playlist MathShorts
Graph Theory 37. Which Graphs are Trees
A proof that a graph of order n is a tree if and only if it is has no cycle and has n-1 edges. An introduction to Graph Theory by Dr. Sarada Herke. Related Videos: http://youtu.be/QFQlxtz7f6g - Graph Theory: 36. Definition of a Tree http://youtu.be/Yon2ndGQU5s - Graph Theory: 38. Three
From playlist Graph Theory part-7
Graph Theory: 36. Definition of a Tree
In this video I define a tree and a forest in graph theory. I discuss the difference between labelled trees and non-isomorphic trees. I also show why every tree must have at least two leaves. An introduction to Graph Theory by Dr. Sarada Herke. Related Videos: http://youtu.be/zxu0dL436gI
From playlist Graph Theory part-7
Natasha Dobrinen: Borel sets of Rado graphs are Ramsey
The Galvin-Prikry theorem states that Borel partitions of the Baire space are Ramsey. Thus, given any Borel subset $\chi$ of the Baire space and an infinite set $N$, there is an infinite subset $M$ of $N$ such that $\left [M \right ]^{\omega }$ is either contained in $\chi$ or disjoint fr
From playlist Combinatorics
Graph Theory: 38. Three ways to Identify Trees
A proof that a graph of order n is a tree if and only if it is connected and has n-1 edges. This, together with the previous video and the definition of a tree, gives three ways to determine if a graph is a tree. An introduction to Graph Theory by Dr. Sarada Herke. Related Videos: http:/
From playlist Graph Theory part-7
Session 3 - Becoming Caltech, 1910–1930: Presentations from the Archives - 7/9/2020
Session 3: Caltech's Early Architects (begins at 2:38) E. T. Bell and Mathematics Between the Wars, by special guest Judith R. Goodstein, University Archivist, Emeritus (begins at 14:07) Student Life and the Original Big T, Carved into a Mountain (begins at 31:51) Q&A (begins at 50:08) L
From playlist Becoming Caltech, 1910–1930: Presentations from the Archives
Session 4 - Becoming Caltech, 1910–1930: Presentations from the Archives - 7/23/2020
Session 4: From High Volts to High Energy Physics (begins at 1:41) The Life and Times of Mathematician Olga Taussky-Todd (begins at 16:15) Clubs and Sports (begins at 40:16) Q&A (begins at 1:00:12) Learn more about: - This series: https://www.library.caltech.edu/becoming-caltech-presenta
From playlist Becoming Caltech, 1910–1930: Presentations from the Archives
George Ellery Hale's Vision of the Humane Scientist: Has it Survived? - J. Sutherland - 9/29/2016
This lecture is part of a series - http://bit.ly/2cHFuOU - honoring the 50th anniversary of Caltech's Division of the Humanities and Social Sciences (HSS) - http://www.hss.caltech.edu/50th-anniversary John Sutherland is a British academic, newspaper columnist, and author of 18 books who h
From playlist Research & Science
Between the Archives and the Athenaeum: Caltech as Living History - D. Kevles - 1/28/2016
Recorded on Thursday, January 28, 2016 in Baxter Lecture Hall at Caltech.
From playlist Research & Science
Cayley-Hamilton Theorem Example 2
Matrix Theory: Let A be the 3x3 matrix A = [1 2 2 / 2 0 1 / 1 3 4] with entries in the field Z/5. We verify the Cayley-Hamilton Theorem for A and compute the inverse of I + A using a geometric power series.
From playlist Matrix Theory
Thomas Delzant - Holomorphic families of Riemann surfaces from the pov of asymptotic group theory
Thomas Delzant (Université de Strasbourg, France) Title: Holomorphic families of Riemann surfaces from the point of view of asymptotic group theory. We use standard methods of asymptotic group theory (asymptotic cones, limit groups), as well as recent results on the mapping class group t
From playlist T1-2014 : Random walks and asymptopic geometry of groups.
Episode 12: The Millikan Experiment - The Mechanical Universe
Episode 12. The Millikan Experiment: A dramatic recreation of Millikan's classic oil-drop experiment to determine the charge of a single electron. “The Mechanical Universe,” is a critically-acclaimed series of 52 thirty-minute videos covering the basic topics of an introductory university
From playlist The Mechanical Universe
Cayley-Hamilton Theorem: Example 1
Matrix Theory: We verify the Cayley-Hamilton Theorem for the real 3x3 matrix A = [ / / ]. Then we use CHT to find the inverse of A^2 + I.
From playlist Matrix Theory
Session 2 - Becoming Caltech, 1910–1930: Presentations from the Archives - 6/25/2020
Session 2: Chemistry Comes to Caltech (begins at 2:20) Women at Early Caltech (begins at 18:24) Paleontology and the Road Not Taken (begins at 35:28) Q&A (begins at 51:27) Learn more about: - This series: https://www.library.caltech.edu/becoming-caltech-presentations - The Caltech Archives
From playlist Becoming Caltech, 1910–1930: Presentations from the Archives
Millikan's oil drop experiment explained
This video covers the famous Millikan experiment, determining the charge of an electron. Done in collaboration with Simon Crook (Crooked Science) and Tom Gordon (University of Sydney) See www.physicshigh.com for all my videos and other resources. If you like this video, please press the L
From playlist Modern Physics
Intro to Tree Graphs | Trees in Graph Theory, Equivalent Definitions
What are trees in graph theory? Tree graphs are connected graphs with no cycles. We'll introduce them and some equivalent definitions, with of course examples of tree graphs in today's graph theory video lesson! Some equivalent definitions of tree graphs are as follows. A graph is a tree
From playlist Graph Theory
Session 6 - Becoming Caltech, 1910–1930: Presentations from the Archives - 8/20/2020
Session 6: - Caltech Takes to the Air (begins at 1:18) - The Cosmopolitan Club and Students of Color (begins at 18:20) - The Origins of the Athenaeum (begins at 39:56) - Q&A (begins at 56:15) Learn more about: - This series: https://www.library.caltech.edu/becoming-caltech-presentations
From playlist Becoming Caltech, 1910–1930: Presentations from the Archives