Very nice videos Patrick…Can you give a lecture on Real Analysis? from
Continuity to Integration???

supermanifold

(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.

patrickJMT

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

patrickJMT

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 : )

theboombody

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.

FatherAbyss

Towards the end when you’re distributing on both sides of the equal sign,
how do you know that the factors commute i.e. ab = ba?

SonOfNye

Between your videos, and my study habits I’ve had a real easy time in my
math major the last year or so. Thank you sir.

mrtamborineman10

why don’t you make more abstract algebra videos? i think its a very
interesting subject, I’m pretty bored of calculus

beatrixbelden

I REEEEEEALLY hope you make more abstract algebra videos. You’re videos
have gotten me through many math classes, but now I’m in modern algebra and
the videos are running out, eek! thanks for all you do.

1904home

hey thanks for posting this. learning a lot.

FallofDarkness55

thanks for this video. can you do tutorials on lie groups and topology?
thanks.

MyOverflow

I love this stuff. ðŸ™‚

Chi MInh

people with left hand are smart. think faster than right handed

Joshua Blevins

Please patrick. I watch your videos all the time putting up some videos on
abstract algebra would really help out a lot. I would even consider a
donation if they were really good. you really helpd get me through
differential equations and calc three.

patrickJMT

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

jayson060687

Teacher Patrick, I guess you forgot the binary operator in condtion 4
(inverse).

jamiepartap

For some reason I understand you so much better than most of my professors.
I have been looking at all the other videos and the little you have is of
great quality. Please, If you have the time, can you talk about permutation
groups and Isomorphism?

Harsha Tai

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 necessary?????plz help me with this

drewpasttenseofdraw

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

leeramdial

Omg you save my life in every one of my math courses please put more
abstract algebra up!

Tony f

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.ï»¿

karamjeet singh

what d we mean by closed ???ï»¿

Maryann Hibek

sir how to show that 3Z is a group?ï»¿

Vin Lee

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

antulioVery nice videos Patrick…Can you give a lecture on Real Analysis? from

Continuity to Integration???

supermanifold(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.

patrickJMTyep, i know it is redundant. it is redundant as people ofter forget to show

that part. so it is ‘built in’ redundancy

patrickJMTi 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 : )

theboombodyI 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.

FatherAbyssTowards the end when you’re distributing on both sides of the equal sign,

how do you know that the factors commute i.e. ab = ba?

SonOfNyeBetween your videos, and my study habits I’ve had a real easy time in my

math major the last year or so. Thank you sir.

mrtamborineman10why don’t you make more abstract algebra videos? i think its a very

interesting subject, I’m pretty bored of calculus

beatrixbeldenI REEEEEEALLY hope you make more abstract algebra videos. You’re videos

have gotten me through many math classes, but now I’m in modern algebra and

the videos are running out, eek! thanks for all you do.

1904homehey thanks for posting this. learning a lot.

FallofDarkness55thanks for this video. can you do tutorials on lie groups and topology?

thanks.

MyOverflowI love this stuff. ðŸ™‚

Chi MInhpeople with left hand are smart. think faster than right handed

Joshua BlevinsPlease patrick. I watch your videos all the time putting up some videos on

abstract algebra would really help out a lot. I would even consider a

donation if they were really good. you really helpd get me through

differential equations and calc three.

patrickJMT@loveangel1ish ha, i dont think it is gonna happen. they few i put up have

been barely viewed ðŸ˜‰ i have other stuff to work on first!

jayson060687Teacher Patrick, I guess you forgot the binary operator in condtion 4

(inverse).

jamiepartapFor some reason I understand you so much better than most of my professors.

I have been looking at all the other videos and the little you have is of

great quality. Please, If you have the time, can you talk about permutation

groups and Isomorphism?

Harsha Taia 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 necessary?????plz help me with this

drewpasttenseofdrawModern Algebra is basic. It requires the student to think mathematically,

which is something most students of mathematics are poor at.

leeramdialOmg you save my life in every one of my math courses please put more

abstract algebra up!

Tony fSo – 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.ï»¿

karamjeet singhwhat d we mean by closed ???ï»¿

Maryann Hibeksir how to show that 3Z is a group?ï»¿

Vin Leethis is mind boggling. you might as well explain it in Russian and i still

wouldnt understand itï»¿