Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
RNT1.4. Ideals and Quotient Rings
Ring Theory: We define ideals in rings as an analogue of normal subgroups in group theory. We give a correspondence between (two-sided) ideals and kernels of homomorphisms using quotient rings. We also state the First Isomorphism Theorem for Rings and give examples.
From playlist Abstract Algebra
Algebra Factoring Polynomials b1p2
Algebra Factoring Polynomials b1p2 GoToMath.com
From playlist Algebra Gotomath
Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.
From playlist Abstract algebra
Duality in projective geometry is a well-known phenomenon in any dimension. On the other hand, geometric triality deals with points and spaces of two different kinds in a sevendimensional projective space. It goes back to Study (1913) and Cartan (1925), and was soon realizedthat this pheno
From playlist Algebra
Tongmu He: Sen operators and Lie algebras arising from Galois representations over p-adic varieties
HYBRID EVENT Recorded during the meeting "Franco-Asian Summer School on Arithmetic Geometry in Luminy" the June 03, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Luca Recanzone Find this video and other talks given by worldwide mathematicia
From playlist Algebraic and Complex Geometry
Tongmu He - Sen operators and Lie algebras arising from Galois representations over p-adic varieties
Any finite-dimensional p-adic representation of the absolute Galois group of a p-adic local field with imperfect residue field is characterized by its arithmetic and geometric Sen operators defined by Sen-Brinon. We generalize their construction to the fundamental group of a p-adic affine
From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)
Linear Algebra: Given an orthonormal basis of R^n, we present a quick method for finding coefficients of linear combination in terms of the basis. We also give an analogue of Parseval's Identity, which relates these coefficients to the squared length of the vector.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
A p-adic monodromy theorem for de Rham local systems - Koji Shimizu
Joint IAS/Princeton University Number Theory Seminar Topic: A p-adic monodromy theorem for de Rham local systems Speaker: Koji Shimizu Affiliation: Member, School of Mathematics Date: February 27, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
End of the Samurai - The Imperial Army - Extra History - #4
Now that the Boshin War was over, the Meji Emperor could finally settle into the bloodless revolution and start modernizing Japan. Well... Maybe not so bloodless. It turns out that once in charge, the Emperor believed that the best way forward for the country was to embrace western ideas a
From playlist Extra History (ALL EPISODES)
Isomorphisms (Abstract Algebra)
An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism between two groups G and H, then they are equivalent and we say they are "isomorphic." The groups may look different from each other, but their group properties will be the same. Be sure to subscribe s
From playlist Abstract Algebra
Now that we have defined and understand quotient groups, we need to look at product groups. In this video I define the product of two groups as well as the group operation, proving that it is indeed a group.
From playlist Abstract algebra
OZI Rule & ϕ Meson | Particle Physics
In this video, we will explain the so-called OZI rule and why certain particle decays are suppressed because of it. References: Griffiths, "Introduction to Elementary Particles", Ch. 2.5 Wiki: OZI Rule: https://en.wikipedia.org/wiki/OZI_rule Wiki: phi meson: https://en.wikipedia.org/wi
From playlist Particle Physics
Richard Kerner - Geometry, Matter and Physics
We show how the fundamental statistical properties of quantum fields combined with the superposition principle lead to continuous symmetries including the $SL(2,\mathbb C)$ group and the internal symmetry groups $SU(2)$ and $SU(3)$. The exact colour symmetry is related to ternary $\mathbb
From playlist Combinatorics and Arithmetic for Physics: special days
Algebra Linear Equations part 2 b3p1
Algebra Linear Equations part 2 b3p1
From playlist Algebra Gotomath
Dynamics of non-spherical particles and chains by Samriddhi Sankar Ray
PROGRAM DYNAMICS OF COMPLEX SYSTEMS 2018 ORGANIZERS Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE: 16 June 2018 to 30 June 2018 VENUE: Ramanujan hall for Summer School held from 16 - 25 June, 2018; Madhava hall for W
From playlist Dynamics of Complex systems 2018
End of the Samurai - The Last Samurai - Extra History - #5
The chapter of history for the samurai is coming to a close. The Three Great Nobles of the restoration have fractured. Saigo Takamori returns to his land and vows not to get involved in politics but that in itself was a very strong political statement. And not a promise he could keep as di
From playlist Extra History (ALL EPISODES)
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
The Moth: The Randomness of Concentration Camps by Leonard Mlodinow
Leonard Mlodinow shares how learning about the heroism and hardship of his father, a Holocaust survivor, provided the eminent physicist and popular author with the strength to face just about anything in life. Scientists, writers, and artists take to the stage to tell stories about their
From playlist The Moth at the World Science Festival
Ring Theory: We define rings and give many examples. Items under consideration include commutativity and multiplicative inverses. Example include modular integers, square matrices, polynomial rings, quaternions, and adjoins of algebraic and transcendental numbers.
From playlist Abstract Algebra