24 thoughts on “Groups

  1. antulio

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

  2. 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.

  3. patrickJMT

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

  4. 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 : )

  5. 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.

  6. 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?

  7. 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.

  8. mrtamborineman10

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

  9. 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.

  10. 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.

  11. 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!

  12. jayson060687

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

  13. 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?

  14. 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

  15. drewpasttenseofdraw

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

  16. 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.

  17. Vin Lee

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

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