Symmetry | Geometry | Group theory
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent notation for the symmetry group of an object X is G = Sym(X). For an object in a metric space, its symmetries form a subgroup of the isometry group of the ambient space. This article mainly considers symmetry groups in Euclidean geometry, but the concept may also be studied for more general types of geometric structure. (Wikipedia).
Group Theory II Symmetry Groups
Why are groups so popular? Well, in part it is because of their ability to characterise symmetries. This makes them a powerful tool in physics, where symmetry underlies our whole understanding of the fundamental forces. In this introduction to group theory, I explain the symmetry group of
From playlist Foundational Math
The Quaternion Symmetry Group – Vi Hart
From playlist G4G11 Videos
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
Visual Group Theory, Lecture 2.2: Dihedral groups
Cyclic groups describe the symmetry of objects that exhibit only rotational symmetry, like a pinwheel. Dihedral groups describe the symmetry of objects that exhibit rotational and reflective symmetry, like a regular n-gon. The corresponding dihedral group D_n has 2n elements: half are rota
From playlist Visual Group Theory
Simple groups, Lie groups, and the search for symmetry I | Math History | NJ Wildberger
During the 19th century, group theory shifted from its origins in number theory and the theory of equations to describing symmetry in geometry. In this video we talk about the history of the search for simple groups, the role of symmetry in tesselations, both Euclidean, spherical and hyper
From playlist MathHistory: A course in the History of Mathematics
Simple groups, Lie groups, and the search for symmetry II | Math History | NJ Wildberger
This is the second video in this lecture on simple groups, Lie groups and manifestations of symmetry. During the 19th century, the role of groups shifted from its origin in number theory and the theory of equations to its role in describing symmetry in geometry. In this video we talk abou
From playlist MathHistory: A course in the History of Mathematics
Abstract Algebra | The dihedral group
We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
In this video we construct a symmetric group from the set that contains the six permutations of a 3 element group under composition of mappings as our binary operation. The specifics topics in this video include: permutations, sets, groups, injective, surjective, bijective mappings, onto
From playlist Abstract algebra
http://www.teachastronomy.com/ A lot of fundamental concepts in physics are based on the idea of symmetry. Symmetry is familiar to us in an aesthetic sense. It often means things that have pleasing proportion, or look the same from every direction, or have a harmonious nature about them.
From playlist 23. The Big Bang, Inflation, and General Cosmology 2
This is lecture 1 of an online mathematics course on group theory. This lecture defines groups and gives a few examples of them.
From playlist Group theory
Mod-01 Lec-2 Symmetry in Perfect Solids
Condensed Matter Physics by Prof. G. Rangarajan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
From playlist NPTEL: Condensed Matter Physics - CosmoLearning.com Physics Course
Vortices and Generalised Symmetry by Mathew Bullimore
PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie
From playlist Vortex Moduli - 2023
Symmetry, Spaces and Undecidability
Oxford Mathematics Public Lectures: Martin Bridson - Symmetry, Spaces and Undecidability The understanding of the possible geometries in dimension 3 is one of the triumphs of 20th century mathematics. In this talk Martin Bridson explains why such an understanding is impossible in higher
From playlist Oxford Mathematics Public Lectures
Chemistry 107. Inorganic Chemistry. Lecture 02
UCI Chemistry: Inorganic Chemistry (Fall 2014) Lec 02. Inorganic Chemistry -- Symmetry and Point Groups View the complete course: http://ocw.uci.edu/courses/chem_107_inorganic_chemistry.html Instructor: Matthew D. Law License: Creative Commons CC-BY-SA Terms of Use: http://ocw.uci.edu/inf
From playlist Chem 107: Week 1
Chapter 7: Group actions, symmetric group and Cayley’s theorem | Essence of Group Theory
Group action can be thought of as a homomorphism to a symmetric group, so apart from orbit-stabiliser theorem, we can also use the isomorphism theorem to analyse any group action. It turns out that this correspondence between group action and homomorphism can be visualised rather easily. T
From playlist Essence of Group Theory
The Abel Prize announcement 2008 - John Thompson and Jacques Tits
0:00 Welcome by chair of the Mathematics group in The Norwegian Academy of Science and Letters, Tom Lyche 1:45 The Abel Prize announced by Ole Didrik Lærum, President of The Norwegian Academy of Science and Letters 2:41 Citation by Kristian Seip, Chair of the Abel committee 8:18 Professor
From playlist John Griggs Thompson
AMMI Course "Geometric Deep Learning" - Lecture 3 (Geometric Priors I) - Taco Cohen
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July-August 2021 by Michael Bronstein (Imperial College/Twitter), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 3: Symmetries • Abstract group
From playlist AMMI Geometric Deep Learning Course - First Edition (2021)
AMMI 2022 Course "Geometric Deep Learning" - Lecture 3 (Geometric Priors I) - Taco Cohen
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July 2022 by Michael Bronstein (Oxford), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 3: Symmetries • Abstract groups • Symmetry groups • Gro
From playlist AMMI Geometric Deep Learning Course - Second Edition (2022)
Symmetry in Physics | Noether's theorem
▶ Topics ◀ Global / Local Symmetries, Continuous / Discrete Symmetries ▶ Social Media ◀ [Instagram] @prettymuchvideo ▶ Music ◀ TheFatRat - Fly Away feat. Anjulie https://open.spotify.com/track/1DfFHyrenAJbqsLcpRiOD9 If you want to help us get rid of ads on YouTube, you can support us on
From playlist Symmetry