Groups - Showing G is a group - Part 1

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i assume that if people are watching this vid, they have already seen the def of a group and know what a binary operation is.
basically, i was tutoring a girl in 11th grade that day (she is about to take a modern algebra class next semester at UT-Austin) and we did that problem that day.
i just put it up to see who would actually watch it more than anything : )

patrickjmt

@loveangel1ish ha, i dont think it is gonna happen. they few i put up have been barely viewed ;) i have other stuff to work on first!

patrickjmt

(i) is redundant: the operation * is indeed a function G x G --> G; in particular, it is well-defined, which implies that a*b is uniquely defined, for all a, b in G.

Also, in view of your example, if a nor b are equal to -1, then (a + 1)(b + 1) can't be zero (R is a field), hence

ab + a + b + 1 =/= 0, i.e. a*b =/= -1,

from which it follows that * is indeed an operation on G.

supermanifold

I think to show associativity you can just say that addition and multiplication are both associative, so a*b will be associative too.

shrimatkapoor

yep, i know it is redundant. it is redundant as people ofter forget to show that part. so it is 'built in' redundancy

patrickjmt

When you are teaching closure, you could give an example of a Set that contains elements under + that are only odd, and show how that does not fit the definition because if you add two odd numbers, you get an even number.

TheGameconomist

Holy shit! I need upper division help. I used to watch you for calculus and now I'm lost without you! Please continue these videos on modern algebra, and combinatorics if possible!

coolmisskitkat

this is mind boggling. you might as well explain it in Russian and i still wouldnt understand it

iluvbigbootie

hey thanks for posting this. learning a lot.

home

Modern Algebra is basic. It requires the student to think mathematically, which is something most students of mathematics are poor at.

drewpasttenseofdraw

What does it mean if the group is defined on
2Z = {2n | n is an element of Z}…?

roannaquiroga

@shortyife well, i could, but hardly anyone will watch. gonna go back and do the basics first : )

patrickjmt

I took real analysis, so I know a little about that, but I don't know anything about groups because they were in a class called algebraic structures, which I never took. Strange, isn't it? What are the applications for these darn group things for us to define them as they are? Anything extremely intuitive would help.

theboombody

a group definetly satisfy a closure law which is known as groupoid and also satisfy associative law called semigroup.but my question is for semigroup, groupoid is help me with this

harshatai

Is there any kind of example of a group (G, .) where o(a).o(b) is not equal to o(a.b) for all a, b belongs to G

kuddusali

So - I'm an "amateur math" person. Just started learning about groups. What is the connection with groups and symmetry? How does the requirements for (G.*) relate to symmetry - as is seen in nature. Thanks.

SpVad

Patrick how can I show that * is a valid operator for the set?

SiyabongaMkhwanazi

Patrick do you have any other video about Abstract Algebra

zaidamarneh

Thank you! Someone else thinks the * symbol is weird.

loquatrose

Please upload the video in the form of problem

kyrpangdkhar

Groups - Showing G is a group - Part 1

Groups - Showing G is a group - Part 1

Groups - Showing G is a group - Part 2

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