Basic abstract algebra, pt.6

[TSharF]

But if you choose b = a / 2, doesn't that imply that b is a rational number? Please explain what is going on :s

[patmenow]

@TSharF well, i think since 'a' is in 2Z then it must be even, thus 'b' will still be an integer.

[Tfirzli]

VeritySeeker, thanks so much for putting all this work into these videos. I am a math and physics major, and am teaching myself group theory out of interest, and I must say, these videos are doing a great job. Hopefully they will help when I actually take abstract. Just wanted to say my thanks

[VeritySeeker]

@Tfirzli Thanks, mate. Good luck on your studies!

[cmonington]

Very helpful! Is isomorphic the same thing as saying that the groups are congruent or no? Am I mixing up definitions?

[VeritySeeker]

@cmonington Congruent is something different. In my world congruence is about elements, while isomorphisms are about structures. But if course - we might talk about the same things. It all amounts to definitions, and that is the beauty. :)

[LINGFERNANDO]

VeritySeeker, you are much better than my professor. Thank you very much.

[tharinduuuu]

thx

[danielkim116]

love it, thank you

[NotJames1]

Really helpful. cheers

[magestaff567]

Thank you so much for making these videos. They are such a great learning tool! This is the clearest introduction to group theory I have come across.

[oryxfreeride]

@pyrofreakingmaniac I dunno I can't stand group theory. It seems so damn pointless to me and I don't know where its going. Maybe one day i'll see some applications of it, but for now its definitions of lots of things so we can understand more definitions of other things which we learn the week after. Seems my profs wouldn't dare tell us why on earth some area of math is actually useful.

[VeritySeeker]

Not all math is useful - yet. Much have no applications yet. But history shows us that it will have. Group theory, however, have many, many applications. I can mention: Error-correction (your CD player, satellite communication and satellite TV, mobile phones, and in any electronic communication), cryptography (communication with your bank when you use your visa card and paying your bills on the internet), physics, chemistry (symmetry in molecules, symmetry in particles string theory...)

[MrStinkyhindu]

Just a suggestion.

Since you defined f(a)=2a means a is in Z and 2a = b is in 2Z

For surjectivity you are changing the definition.

[Chaos7703]

You might not say "we regard them as the SAME group." It deemphasizes the fact that they're NOT the same group, but DO have identical algebraic structures. Sweet work dude, you're a pimp in the world of algebra!! 8D

[ldelossant]

The series of videos you presented about Abstract Algebra are really good. You should keep doing them especially in the most difficult part of group theory such as subgroups operations.

[peterpan795]

woo.. getting more exciting

[MathMikie]

thanks for making these videos they have really helped me to understand abstract algebra better