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Simply Science
Франция
Добавлен 21 окт 2022
A channel dedicated to simple explanations of basic science. Mathematics and physics are made accessible to the layman, the beginning apprentice or the eternal student. If you have suggestions for topics, feel free to pass them on, e.g. in the comments sections.
Inégalités: Comprendre les Règles de Calcul
On raisonne pour comprendre les règles de calcul pour les inégalités ou les inéquations.
Просмотров: 62
Видео
Puissances: Comprendre les Règles de Calcul
Просмотров 312 месяца назад
On définit les puissances d'un nombre. A partir de la définition, nous dérivons simplement les règles de calcul qui deviennent facile à retenir.
The Wallpaper Groups
Просмотров 222 месяца назад
We discuss all the possible symmetries of wallpaper patterns. The classifications is based on the possible crystallographic lattices and their extra discrete symmetries. We discuss the seventeen groups using illustrative examples. Errata: the centred rectangular example should be properly glide reflected and the point groups could also be of the type Z3, Z4 or Z6.
The Crystallographic Lattices
Просмотров 32 месяца назад
We discuss the possible shapes of two-dimensional crystallographic lattices and render the classification comprehensible through the analysis of vector length inequalities. This is a preparation for understanding the crystallographic groups in two dimensions, namely, the wallpaper groups.
The Crystallographic Angles
Просмотров 163 месяца назад
We review a crystallographic restriction theorem which determines the orders of possible rotation symmetries that are members of the point group of a crystallographic symmetry group of a pattern in space. The theorem is elementary yet of crucial importance in crystallography.
Frieze Groups
Просмотров 263 месяца назад
We discuss the seven symmetry groups of friezes. These are simple examples of crystallographic groups. They are the symmetries of a pattern in two-dimensional space with a one-dimensional translation subgroup. We list all seven groups, draw patterns with these symmetries and explain why the seven groups suffice.
One-dimensional Crystallography
Просмотров 13 месяца назад
We discuss the space groups or crystallographic groups in one dimension. These are the symmetry patterns of one-dimensional crystals. It is a very much simplified version of the classification of crystallographic groups in three-dimensional euclidean space. We go through the classification of the groups as well as the patterns of which they are. the symmetries. In one dimension, the whole proce...
Euler's Totient Function and Möbius Inversion
Просмотров 583 месяца назад
We discuss properties of the Euler's totient function and how it interfaces with Dirichlet convolution and the Möbius function. The totient function equals the convolution of the identical function with the Möbius function, as proven by Gauss.
Dirichlet Convolution and Möbius Inversion
Просмотров 293 месяца назад
We define Dirichlet convolution of arithmetic functions and use a property of the Möbius function to prove the Möbius inversion formula relating a sum of functions evaluated at divisors of a natural number.
The Möbius Function
Просмотров 2024 месяца назад
We define the Möbius function and prove its main property in three different manners. Namely, the sum of the Möbius function evaluated over the divisors of a number greater than one is equal to zero. We prove this using its definition, its multiplicativity as well as its relation to primitive roots of unity.
The Jordan-Hölder Theorem for Finite Groups
Просмотров 204 месяца назад
We prove the Jordan-Hölder theorem for finite groups. It says that finite groups can be consecutively constructed from simple composition factors and that these simple composition factors are unique (up to permutation). The proof uses the second and third isomorphism theorems for groups.
The Third Isomorpism Theorem for Groups
Просмотров 24 месяца назад
We prove the third isomorphism theorem for groups which says that one can simplify quotients of groups as one can fractions. The theorem is a consequence of the first isomorphism theorem.
Le Coefficient Directeur, la Tangente et un Exercice
Просмотров 94 месяца назад
On décrit la relation entre le coefficient directeur et la tangente. On se demande quel est le coefficient directeur d'une droite perpendiculaire à une droite avec un coefficient directeur donné.
The Second Isomorphism Theorem for Groups
Просмотров 165 месяцев назад
The second isomorphism theorem for groups relates quotients of groups related to a subgroup and a normal subgroup of a group. The product divided by the normal subgroup is isomorphic to the subgroup divided by the intersection. It is a consequence of the first isomorphism theorem and the second theorem in a row of three.
The First Isomorphism Theorem for Groups
Просмотров 115 месяцев назад
We state and prove the first isomorphism theorem for groups. Given a homomorphism between groups, the quotient of the source group by the kernel naturally equals the image.
The Hom and Ext Functors in the BGG Category O
Просмотров 125 месяцев назад
The Hom and Ext Functors in the BGG Category O
The First Structural Properties of the BGG Category O
Просмотров 176 месяцев назад
The First Structural Properties of the BGG Category O
Résoudre une Équation Quadratique par Symétrie
Просмотров 186 месяцев назад
Résoudre une Équation Quadratique par Symétrie
Center, Characters and Linked Weights
Просмотров 156 месяцев назад
Center, Characters and Linked Weights
Fonctions Affines et Géometrie Eucildienne
Просмотров 166 месяцев назад
Fonctions Affines et Géometrie Eucildienne
Finite Dimensional and Verma Modules of sl(2,C)
Просмотров 397 месяцев назад
Finite Dimensional and Verma Modules of sl(2,C)
Highest Weight Modules Of Semisimple Lie Algebras
Просмотров 437 месяцев назад
Highest Weight Modules Of Semisimple Lie Algebras
An Introduction to the BGG Category O
Просмотров 438 месяцев назад
An Introduction to the BGG Category O
La Tangente et le Calcul Littéral: un Exercise Royal
Просмотров 218 месяцев назад
La Tangente et le Calcul Littéral: un Exercise Royal
Choisir Avec Répétition (Combinatoire)
Просмотров 28 месяцев назад
Choisir Avec Répétition (Combinatoire)
At 5:38, do you mean lambda is not smaller than mu?
Morbius function: One of the functions of all time
Prof des grands maths
Can you provide a good reference for this
Unfortunately, there is no good reference for the exact content of the video. There are some standard references on the topic, including Alekseev, Faddeev and Shatashvili, ``Quantization of symplectic orbits of compact Lie groups by means of the functional integral,'' J. Geom. Phys. 5 (1988), 391-406 doi:10.1016/0393-0440(88)90031-9 and the book on the orbit method by Kirillov. These will neither contain this exact explanation nor are they strictly speaking the original references. Moreover, my point of view is slightly different. But, these are good entry points for further literature searches.
@@Simply_Science Also do you know of a good reference for phase space quantization ( don't confuse it for Dirac quantization ) ?
@@Slayer-bh7yd Good keywords to look for are Geometric Quantization (e.g. the book by Woodhouse) and Symplectic Quantization (e.g. references by Weinstein).
Any good reference for this
www.physics.rutgers.edu/~gmoore/695Fall2015/TopologicalFieldTheory.pdf by Greg Moore, or the book by Koch might be useful starting points depending on your background.
@@Simply_Science Thanks
Merci pour cette explication❤
Merci beaucoup pour cette explication❤
Black holes are based on a mathematical misconception. Most people don't know that Einstein said that singularities are not possible. In the 1939 journal "Annals of Mathematics" he wrote- "The essential result of this investigation is a clear understanding as to why the Schwarzchild singularities (Schwarzchild was the first to raise the issue of General Relativity predicting singularities) do not exist in physical reality. Although the theory given here treats only clusters (star clusters) whose particles move along circular paths it does seem to be subject to reasonable doubt that more general cases will have analogous results. The Schwarzchild singularities do not appear for the reason that matter cannot be concentrated arbitrarily. And this is due to the fact that otherwise the constituting particles would reach the velocity of light." He was referring to the phenomenon of dilation (sometimes called gamma or y) mass that is dilated is smeared through spacetime relative to an outside observer. "Time dilation" is one aspect of dilation. General Relativity does not predict singularities when you factor in dilation. What we see in modern astronomy has been known since 1925. This is when the existence of galaxies was confirmed. It was clear that there should be an astronomical quantity of light emanating from our own galactic center, but there isn't. The modern explanation for this is because gravitational forces there are so strong that not even light can escape, even though the mass of the photon is zero. The original and correct explanation is because the mass there is dilated relative to an Earthbound observer. In other words that mass is all around us. Television and movies popularized black holes starting in the 1960's.
Bravo 👍