Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure. This can occur in many ways; for example, if X is a set with no additional structure, a symmetry is a bijective map from the set to itself, giving rise to permutation groups. If the object X is a set of points in the plane with its metric structure or any other metric space, a symmetry is a bijection of the set to itself which preserves the distance between each pair of points (i.e., an isometry). In general, every kind of structure in mathematics will have its own kind of symmetry, many of which are listed in the given points mentioned above. (Wikipedia).
Symmetry in Physics | Noether's theorem
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From playlist Symmetry
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
The science of symmetry - Colm Kelleher
View full lesson: http://ed.ted.com/lessons/the-science-of-symmetry-colm-kelleher When you hear the word symmetry, you might think generally of triangles, butterflies, or even ballerinas. But defined scientifically, symmetry is "a transformation that leaves an object unchanged." Huh? Colm
From playlist New TED-Ed Originals
This video was produced by Nina Qiu of Year 10 (2015).
From playlist Random
Pre-Calculus - The symmetry of functions
This video covers the symmetry that might be present in the graph of a function. A visual approach is taken so that you can see if the symmetry is over an axis, or if its with respect to the origin. Watch for the special names that we give to certain symmetries like "even" and "odd." Fo
From playlist Pre-Calculus
Symmetries show up everywhere in physics. But what is a symmetry? While the symmetries of shapes can be interesting, a lot of times, we are more interested in symmetries of space or symmetries of spacetime. To describe these, we need to build "invariants" which give a mathematical represen
From playlist Relativity
The Predictive Power Of Symmetry
From a bee’s hexagonal honeycomb to the elliptical paths of planets, symmetry has long been recognized as a vital quality of nature. Einstein saw symmetry hidden in the fabric of space and time. The brilliant Emmy Noether proved that symmetry is the mathematical flower of deeply rooted phy
From playlist Science Shorts and Explainers
Richard Feynman - The Character of Physical Law - Part4 Symmetry in Physical Law (full version)
Richard Feynman The Character of Physical Law Part4 Symmetry in Physical Law full version
From playlist Feynman's Lectures
Elementary Introduction to the Langlands Program, by Edward Frenkel (Part 1) [2015]
"Do we discover mathematics or do we invent it?" One of the most fascinating and important developments in mathematics in the last 50 years is the Langlands Program, a collection of ideas that provides a grand unification of many areas of mathematics. In September 2015, Edward Frenkel g
From playlist Number Theory
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
Mysteries of Math and the Langlands Program - Episode 1
The first in a series of 4 lectures by Edward Frenkel filmed at MSRI, Berkeley and broadcast on the Japanese TV channel NHK in the Fall of 2015 in the "Luminous Classroom" series. The lectures went from elementary topics such as Pythagoras theorem, prime numbers and symmetries to Fermat's
From playlist Mysteries of Math and the Langlands Program (4 episodes broadcast on the Japanese TV channel NHK)
Finding Moonshine: A Mathematician's journey through symmetry
Professor Marcus du Sautoy, University of Oxford Filmed at The Royal Society, London on Thu 21 Feb 2008 6.30pm-7.30pm For more information visit http://royalsociety.org/events/2008/finding-moonshine
From playlist Latest talks and lectures
WSU Master Class: Mathematics, The Language of Nature with Edward Frenkel Course
Join mathematician Edward Frenkel as he discusses how the elegant mathematical formulation of symmetry has been used throughout math and physics and could, through the Langlands program, give rise to a grand unified theory of mathematics. This lecture was recorded on May 31, 2014, at the
From playlist WSU Master Classes
WSU Master Class: Mathematics, The Language of Nature with Edward Frenkel Course
Join mathematician Edward Frenkel as he discusses how the elegant mathematical formulation of symmetry has been used throughout math and physics and could, through the Langlands program, give rise to a grand unified theory of mathematics. This lecture was recorded on May 31, 2014, at the
From playlist WSU Master Class
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
Beyond Beauty: The Predictive Power of Symmetry
From a bee’s hexagonal honeycomb to the elliptical paths of planets, symmetry has long been recognized as a vital quality of nature. Einstein saw symmetry hidden in the fabric of space and time. The brilliant Emmy Noether proved that symmetry is the mathematical flower of deeply rooted phy
From playlist Explore the World Science Festival
What is a Group (Intuitively) - Group Theory 001
Here we begin to explore the mathematical objects that describe symmetry - Groups, and look at one particular example: the group of symmetries of a square 0:00 - Intro 0:25 - What is a group? 0:49 - Simple mathematical object example 1:49 - Symmetries 3:09 - A group is 3:20 - The group of
From playlist Summer of Math Exposition Youtube Videos
How Does Beauty Color the Cosmos? | Episode 303 | Closer To Truth
What do scientists mean when they call the laws and regularities of nature "beautiful"? On the largest supra-cosmic scales, and on the smallest sub-atomic scales, why do scientists use "beauty" to assess their theories? Featuring interviews with Peter Atkins, Roger Penrose, Stephon Alexand
From playlist Closer To Truth | Season 3
Symmetry Introduction: x-axis, y-axis, the origin
This video produces symmetry about the x-axis, y-axis, and origin. It explains how to visually determine if a graph has symmetry and how to determine symmetry algebraically. Complete Library: http://mathispower4u.com Search by Topic: http://mathispower4u.wordpress.com
From playlist Graphing Functions (Algebra 1)