In mathematics, the conformal group of an inner product space is the group of transformations from the space to itself that preserve angles. More formally, it is the group of transformations that preserve the conformal geometry of the space. Several specific conformal groups are particularly important: * The conformal orthogonal group. If V is a vector space with a quadratic form Q, then the conformal orthogonal group CO(V, Q) is the group of linear transformations T of V for which there exists a scalar λ such that for all x in VFor a definite quadratic form, the conformal orthogonal group is equal to the orthogonal group times the group of dilations. * The conformal group of the sphere is generated by the inversions in circles. This group is also known as the Möbius group. * In Euclidean space En, n > 2, the conformal group is generated by inversions in hyperspheres. * In a pseudo-Euclidean space Ep,q, the conformal group is Conf(p, q) ≃ O(p + 1, q + 1) / Z2. All conformal groups are Lie groups. (Wikipedia).
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
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
Definition of a group Lesson 24
In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el
From playlist Abstract algebra
A group is (in a sense) the simplest structure in which we can do the familiar tasks associated with "algebra." First, in this video, we review the definition of a group.
From playlist Modern Algebra - Chapter 15 (groups)
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
What is a Group? | Abstract Algebra
Welcome to group theory! In today's lesson we'll be going over the definition of a group. We'll see the four group axioms in action with some examples, and some non-examples as well which violate the axioms and are thus not groups. In a fundamental way, groups are structures built from s
From playlist Abstract Algebra
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 idea of a quotient group follows easily from cosets and Lagrange's theorem. In this video, we start with a normal subgroup and develop the idea of a quotient group, by viewing each coset (together with the normal subgroup) as individual mathematical objects in a set. This set, under
From playlist Abstract algebra
Dihedral Group (Abstract Algebra)
The Dihedral Group is a classic finite group from abstract algebra. It is a non abelian groups (non commutative), and it is the group of symmetries of a regular polygon. This group is easy to work with computationally, and provides a great example of one connection between groups and geo
From playlist Abstract Algebra
The Simplifying Synthesis Ultimate Guide To Conformational Analysis
A chemistry lecture on the conformational analysis of organic compounds. Timestamps: Newman projections, nomenclature 0:42 Alkane Conformation 1:42 Allylic Strain 7:10 Cyclic Systems 11:14 Cyclohexane Substituent Effects: Heterocycles, Anomeric Effect 13.39 Fused Ring Systems: Conformati
From playlist Ultimate Guides
This organic chemistry video tutorial provides a basic introduction into newman projections. It explains how to draw the newman projections of ethane, butane, and 2,3-dimethylpentane. It explains how to draw the eclipsed and staggered conformations of ethane as well as the gauche and ant
From playlist New Organic Chemistry Playlist
Conformational analysis of butane | Organic chemistry | Khan Academy
How to analyze the staggered and eclipsed conformations of butane. Watch the next lesson: https://www.khanacademy.org/science/organic-chemistry/bond-line-structures-alkanes-cycloalkanes/conformations-alkanes-cycloalkanes/v/newman-projection-practice-1?utm_source=YT&utm_medium=Desc&utm_cam
From playlist Alkanes, cycloalkanes, and functional groups | Organic Chemistry | Khan Academy
Newman projection practice 1 | Organic chemistry | Khan Academy
How to use Newman projections to determine the most and least stable conformations of a compound. Watch the next lesson: https://www.khanacademy.org/science/organic-chemistry/bond-line-structures-alkanes-cycloalkanes/conformations-alkanes-cycloalkanes/v/newman-projection-practice-2?utm_so
From playlist Alkanes, cycloalkanes, and functional groups | Organic Chemistry | Khan Academy
Newman projection practice 2 | Organic chemistry | Khan Academy
How to determine the most and least stable conformations using Newman projections. Watch the next lesson: https://www.khanacademy.org/science/organic-chemistry/bond-line-structures-alkanes-cycloalkanes/conformations/v/chair-and-boat-shapes-for-cyclohexane?utm_source=YT&utm_medium=Desc&utm
From playlist Alkanes, cycloalkanes, and functional groups | Organic Chemistry | Khan Academy
Factors affecting conformity | Revision for A-Level Psychology
I want to help you achieve the grades you (and I) know you are capable of; these grades are the stepping stone to your future. Even if you don't want to study science or maths further, the grades you get now will open doors in the future. A-Level Maths Courses, FREE revision guide and wor
From playlist WJEC A-Level Psychology Playlist
Chair Conformation and Ring Flips
This organic chemistry video tutorial provides a basic introduction into drawing the chair conformation of cyclohexane and identifying the most stable conformation of Methylcyclohexane and 1-tert-butyl-4-methylcyclohexane. It also discusses how to perform a ring flip by adjusting the ap
From playlist New Organic Chemistry Playlist
Conformal Dynamics in Pseudo-Riemannian Geometry: a Question of A. Lichnerowicz - Charles Frances
Charles Frances Universite Paris-Sud 11; Member, School of Mathematics April 1, 2013 In the middle of the sixties, A. Lichnerowicz raised the following simple question: “Is the round sphere the only compact Riemannian manifold admitting a noncompact group of conformal transformations?” The
From playlist Mathematics
Conformational Analysis of Ethane and Butane - Newman Projections
Hooray for molecular models! Here we will examine the different conformations of ethane and butane, and discuss their relative energies. Also, Dave will show you how to draw Newman projections. Watch the whole Organic Chemistry playlist: http://bit.ly/ProfDaveOrgChem General Chemistry Tu
From playlist Organic Chemistry
Abstract Algebra 1.5 : Examples of Groups
In this video, I introduce many important examples of groups. This includes the group of (rigid) motions, orthogonal group, special orthogonal group, the dihedral groups, and the "finite cyclic group" Z/nZ (or Z_n). Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animatio
From playlist Abstract Algebra