Permutation Groups and Symmetric Groups | Abstract Algebra

We introduce permutation groups and symmetric groups. We cover some permutation notation, composition of permutations, composition of functions in general, and prove that the permutations of a set make a group (with certain details omitted). #abstractalgebra #grouptheory
We will see the Cayley table for the symmetric group S3, and look at some inverse permutations. We also cover the definition of a permutation, which is a bijection from a set to itself.
A proof that compositions of bijections are bijective in two parts:
• Proof: Composition of ...
• Proof: Composition of ...
Abstract Algebra Course: • Abstract Algebra
Abstract Algebra Exercises:
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[@Adecto]

In the first 3 minutes I understood everything better than after 4 hours of lectures and hours of watching other TH-cam videos. Thank you so much!!!

[@user-um5ep3ih3n]

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[@area51xi]

These are some of the best math videos on YT. Other math YT-ers should take note. Aside from good content: 1. high resolution, 2. good mic/clear audio, 3. clear annotations. Not sure why others can't just buy a good microphone and put it by their mouth rather than putting it across the room, in their waving hand, in the kitchen sink, not plugging it in, handing it to their crying baby....

[@WrathofMath]

Thanks so much! Though it took me nearly 6 years to be making the videos this high quality, it's all a learning process!

[@misterentername8869]

These are amazing explanations, clear and mentions everything! Thank you, this deserves more views.

[@WrathofMath]

Thank you, that's precisely what I've been trying to achieve with the Abstract Algebra videos. Lots more to come in the playlist: th-cam.com/play/PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN.html

[@namelessflower7]

Thank you! You made everything so easy to understand.

[@letsimage]

thank you a lot for this explanation, now this topic is much clear for me!

[@prianborah]

Hi, this is a fantastic video. Could you make a video on A4 discrete symmetry group and its character table and what its irreducible representations like 1,1',1'', and 3 means, and also its multiplication table??

[@DrMATHJO]

Thanks for this,🙏🙏

[@estherlevenson1835]

Thank you so much. I'd like to know more about the relationship between symmetry groups and permutation groups.

[@turefu8681]

Thanks a lot for this explanation. It helps me with a problem troubling for two days.

[@WrathofMath]

Glad to help! Check out my playlist if you're looking for more abstract algebra! th-cam.com/play/PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN.html

[@ParvejBiswas-qi4re]

Such a great math❤ explanation ❤

[@ma.lourdezs]

Hi! Can you explain the general associative law?

[@FMTanmayChopra]

Wonderful man, really clear explanations.

[@WrathofMath]

Thank you!

[@benallen9112]

alpha is its own inverse because it is a transposition. i.e., any 2 cycle is its own inverse. The cycle decomposition of alpha is (1 2)(3) = (1 2). Hence, (1 2) is its own inverse as is any other transposition. Hope this helps anyone else studying for their abstract algebra final!

[@bryanherrera9549]

Thank you!

[@WrathofMath]

You're welcome!

[@ismailadekunle1978]

Thanks so much for his video❤

[@WrathofMath]

Thanks for watching!

[@shwetabhsingh5437]

Lovely video, great conceptual clarity, this seems to be missing from a lot of physics lectures which involve group theory. Thanks.

[@WrathofMath]

You're very welcome!

[@Bertilsdotter1]

Very good explained... Big thanks

[@WrathofMath]

Glad to help - thanks for watching!

[@user-gz2el8gj7f]

Thank you amazing video.

[@WrathofMath]

Thank you!

[@jaydevdeshmukh3831]

In your table at the end of the video, Why does Beta and Beta lead to delta? Should it also not have identity there? Same goes with Delta and Delta which is giving Beta.

[@backiyalakshmi5990]

Thank you so much sir

[@WrathofMath]

Most welcome!

[@xibbit6322]

my teachers making us do fuunction composition from left to right because he prefers it but no one uses that... its so annoying and confusing :(

[@mzarinchang3744]

Thats so cool....I thought that if a=a^(-1) then a must be the identity.......but this example showed that its not neccessarily true.....

[@ismailadekunle1978]

Can you do a full tutorial on Groups 😢❤

[@WrathofMath]

Like this you mean? th-cam.com/video/dfCNJmT0-uI/w-d-xo.html&pp=ygUUd3JhdGggb2YgbWF0aCBncm91cHM%3D

[@ismailadekunle1978]

@@WrathofMath thanks so much

[@danielrosen4496]

Wondering if Set is infinite,

[@WrathofMath]

Which set? I'm not sure what your question is. If you're asking if there are infinite permutation groups, the answer is yes. For example, one permutation on the reals might swap the positives and negatives and keep 0 fixed.

[@MYTHBuSS]

Please Solve This Problem!! My Maths Teacher Asked me to Prove that For Area of Square =, 1/2 x d x d
Please help 😌🔥

[@quiteagezabylquimpoturnino1385]