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Group Theory Lecture 03
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Delivered by: Jay Mehta.
In the last video, we saw that the set A(S), of bijective functions from a nonempty set S to itself, is a group under the operation of composition of functions. Here we investigate the cardinality of A(S) depending on |S| and so in particular S_n has n! elements. We observe that A(S) is abelian whenever |S|=1 or 2 and in general if S is finite we have A(S)=S_n which is non-abelian. We see in detail, the group S_3, of permutation on 3-symbols and how it is related to symmetries of an equilateral triangle.
These video lectures are of Group Theory course which I discuss with my M.Sc Semester-III students at our university. Just like PDF files of lecture notes are provided as additional reading material, these videos can be considered as additional watching material besides the regular online classes on google meet.
We follow the book Topics in Algebra by I. N. Herstein as the main text of our syllabus and so I stick to it more or less. I am not an expert in the subject and and these videos are not polished final lectures. What I presented here is a my loud thinking, the rough informal discussion like we have sometimes in the class. So you might see me thinking in the video, pausing and learning, and making mistakes (even Mathematical).
These videos are recorded to serve the following purposes:
-- students hesitated to ask again to repeat explanation of certain topics.
-- students can learn at their own convenience.
-- not losing link of the subject due to missed classes.
-- for revision of topic after the course is over.
-- not missing any online lectures due to poor internet connection at that time.
-- and other viewers might also get benefited.
--feedback received would help me improve.
The digital notes and whatever work I did in this video can be downloaded in the form of a pdf file from the following link:
Do share your feedback, suggestion, comments for improving the quality of lectures in future.
In the last video, we saw that the set A(S), of bijective functions from a nonempty set S to itself, is a group under the operation of composition of functions. Here we investigate the cardinality of A(S) depending on |S| and so in particular S_n has n! elements. We observe that A(S) is abelian whenever |S|=1 or 2 and in general if S is finite we have A(S)=S_n which is non-abelian. We see in detail, the group S_3, of permutation on 3-symbols and how it is related to symmetries of an equilateral triangle.
These video lectures are of Group Theory course which I discuss with my M.Sc Semester-III students at our university. Just like PDF files of lecture notes are provided as additional reading material, these videos can be considered as additional watching material besides the regular online classes on google meet.
We follow the book Topics in Algebra by I. N. Herstein as the main text of our syllabus and so I stick to it more or less. I am not an expert in the subject and and these videos are not polished final lectures. What I presented here is a my loud thinking, the rough informal discussion like we have sometimes in the class. So you might see me thinking in the video, pausing and learning, and making mistakes (even Mathematical).
These videos are recorded to serve the following purposes:
-- students hesitated to ask again to repeat explanation of certain topics.
-- students can learn at their own convenience.
-- not losing link of the subject due to missed classes.
-- for revision of topic after the course is over.
-- not missing any online lectures due to poor internet connection at that time.
-- and other viewers might also get benefited.
--feedback received would help me improve.
The digital notes and whatever work I did in this video can be downloaded in the form of a pdf file from the following link:
Do share your feedback, suggestion, comments for improving the quality of lectures in future.
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