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KloppOClock
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hi,

me lecture notes are a bit shite so i have no idea what any of this subsection means.

its about a brief introduction to groups (which theres a whole chapter on later).

it basically defines a group and its properties.
then it describes the general linear group, the special linear group and the symmetric group.

then it defines a polynomial in n variables, then the sgn function.


ive not a clue what any of it is tryna tell me. can you give us some resources thatll explain it cuz all the utube vids are absolute crap lol



also if you know any of these parts please explain it to me!
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RDKGames
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(Original post by KloppOClock)
hi,

me lecture notes are a bit shite so i have no idea what any of this subsection means.

its about a brief introduction to groups (which theres a whole chapter on later).

it basically defines a group and its properties.
then it describes the general linear group, the special linear group and the symmetric group.

then it defines a polynomial in n variables, then the sgn function.


ive not a clue what any of it is tryna tell me. can you give us some resources thatll explain it cuz all the utube vids are absolute crap lol



also if you know any of these parts please explain it to me!
Socratica’s youtube videos helped me get my head around these groups and other aspects of group theory, so try them. These are part of their Abstract Algebra playlist
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KloppOClock
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(Original post by RDKGames)
Socratica’s youtube videos helped me get my head around these groups and other aspects of group theory, so try them. These are part of their Abstract Algebra playlist
boss, think i got it now.

just dont get two things;
in my notes it defines the sign function as only being able to take -1 and 1 but not 0?
also dont get the cyclic function for symmetrical groups, mainly the part where its a product of transpositions and also "This gives a cycle (1 (1)σ (1)σσ (1)σ
r )" , where its just a **** ton of sigmas .
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RDKGames
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(Original post by KloppOClock)
boss, think i got it now.

just dont get two things;
in my notes it defines the sign function as only being able to take -1 and 1 but not 0?
also dont get the cyclic function for symmetrical groups, mainly the part where its a product of transpositions and also "This gives a cycle (1 (1)σ (1)σσ (1)σ
r )" , where its just a **** ton of sigmas .
Can you post a picture of how these appear in your notes?

The sgn function is precisely one that takes either 1 or -1 depending on the input. In the context of your theory, there won't be a case where you'd need to take sgn of something that is neither +ve or -ve, so it is sufficient to have \pm 1 only.
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Andrew97
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(Original post by KloppOClock)
boss, think i got it now.

just dont get two things;
in my notes it defines the sign function as only being able to take -1 and 1 but not 0?
also dont get the cyclic function for symmetrical groups, mainly the part where its a product of transpositions and also "This gives a cycle (1 (1)σ (1)σσ (1)σ
r )" , where its just a **** ton of sigmas .
Have you tired Lecture notes from other universities?
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