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Groups and Geometry

This class was created by Brainscape user Caleb Pleavin. Visit their profile to learn more about the creator.

By: Caleb Pleavin
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Decks in this class (12)

1) Groups and Symmetry
What is a binary operation,
What does it mean to be associative,
What is the identity and inverse ...
13  cards
2) Subgroups and Homomorphisms
What is the trivial subgroup,
What is a proper subgroup,
How does the identity element of ...
26  cards
3) Order and other Group Theory Properties
What is the order of a group,
What are the orders of the cyclic...,
What is the order of an element o...
19  cards
4) Cosets and Index
What is a coset,
Under what condition is a subgrou...,
When does a left coset of a subgr...
21  cards
5) Group Actions
What is a group action,
What is an orbit,
What is the relationship between ...
15  cards
6) Conjugacy
What is the conjugacy action of a...,
What are conjugacy classes and co...,
How do general properties of grou...
13  cards
7) Normal Subgroups and Factor Groups
What is a normal subgroup,
What characterises a normal subgr...,
What properties do all subgroups ...
17  cards
8) More on permutations
How can every permutation in sn b...,
What are even odd permutations,
What is the alternating group of ...
11  cards
9) Euclidean Space and Isometries
How should vectors be handled wit...,
How does changing the basis affec...,
What is the inner product of two ...
48  cards
10) Finite subgroups of isometries
What does it mean for two subgrou...,
How does averaging the orbit of a...,
What are the two types of subgrou...
5  cards
11) Wallpaper Patterns
What is a lattice,
What is the rank of a lattice,
What is the rank of
21  cards
12) The Riemann Sphere and Mobius Transformations
How are multiplication and transl...,
How is the map f z 1 z extended to,
What is the mobius transformation
29  cards

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Groups and Geometry

  • Class purpose General learning

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