7 ms·

Abstract Algebra: The Definition of a Group [video]

74 points by espeed 11y ago

1971genocide 11y ago
The videos are good but something is just off ( uncanny valley ?) about the way the person presents. It seems really fake :(
- iraphael 11y ago
  I wouldn't place it in the uncanny valley. It just sounds highly scripted and acted.
  - throwaway999888 11y ago
    Another comment mentioned that she's an actress.
- presidentender 11y ago
  The presenter is an actress. It's effectively a monologue.
- jaywunder 11y ago
  I saw the same thing... it was like she was trying to give sexy looks while also teaching me math. Rather distracting. Did you also notice that?
  - espeed 11y ago
    I suspect that's the point -- evoking a motivating and memory-enhancing dopamine shot -- a la the Van Wilder tutors.
    - jaywunder 11y ago
      Oh huh... I don't know if I like that, but if it works then I guess it works
    - throwaway999888 11y ago
      Sounds like bogus. Being primed for math and being primed for sex feels like two completely different modes to me.
      - espeed 11y ago
        Thinking about sex primes the brain for analytical thinking: http://tedxtalks.ted.com/video/Mathematics-and-sex-Clio-Cressw http://tedxtalks.ted.com/video/Mathematics-and-sex-Clio-Cres...
        cbd1984 11y ago
        Too bad that's TEDx, and not a real TED talk.
- angdis 11y ago
  I think the videos serve as an introduction to some basic concepts intended to bring some clarity for further in-depth study. The video is much like the "front matter" to a chapter in a book. Of course, the _REAL_ learning work starts when the student suffers through countless problems and proofs. This is no replacement for that. One doesn't learn math by passively watching videos or listening to lectures. That's the way it is and that is the way it will always be. This just provides a clear 30,000 foot view of the topic, a little motivation and background and, yes, some eye candy (and that's OK too).
darkxanthos 11y ago
Anything that can help make this subject more approachable is alright in my book. In my experience, the hardest part of Abstract Algebra isn't the abstract part of it. It's the lack of examples and clarity around how different named concepts behave. The proofs aren't terrible even except for the fact that they require a familiarity with number theory that many (at least I myself) don't have. I love the subject though. Really interesting.
- gh02t 11y ago
  For me, it has always been the terminology. The basic theorems are relatively easy to understand... once you can remember the vast number of algebra-specific definitions. The field also has a proclivity for umm "colorful" choices of names. It's not unlike say Haskell, which IMO is pretty straightforward once you have a feel for all the terminology.
  - goalieca 11y ago
    Like this from wikipedia on Monoid? Suppose that S is a set and • is some binary operation S × S → S, then S with • is a monoid if it satisfies the following two axioms: Associativity For all a, b and c in S, the equation (a • b) • c = a • (b • c) holds. Identity element There exists an element e in S such that for every element a in S, the equations e • a = a • e = a hold. In other words, a monoid is a semigroup with an identity element. It can also be thought of as a magma with associativity and identity. The identity element of a monoid is unique.[1] A monoid in which each element has an inverse is a group.
    - cmrx64 11y ago
      It seems to me that the definition presented there is relatively free of jargon, except the "in other words" section which links it to other (linked) structures.
      - gh02t 11y ago
        > except the "in other words" section which links it to other (linked) structures. That's what I was getting at. I took a few classes in AA and its sibling topology, including at graduate level. Most of the time was spent defining things, because there's so many terms with very specific definitions. Only after maybe 2/3rds of a course do you really start getting into deeper material. In my brain, reading definitions was always a process like: read through, substitute definitions for jargon terms, read through, substitute... iterate until you hit a fixed point. That's standard for math, but AA is particularly well known for its colorful choice of names. Some people enjoy it, but I was always more attracted to the analysis-family areas of math. I've always found the other name for category theory amusing though: https://en.wikipedia.org/wiki/Abstract_nonsense https://en.wikipedia.org/wiki/Abstract_nonsense
espeed 11y ago
Socratica was started by two Caltech grads: Michael Harrison (ex-Googler) and Kimberly Hatch Harrison (http://www.socratica.com/about.html http://www.socratica.com/about.html). The actress in the video is Liliana Castro (https://en.wikipedia.org/wiki/Liliana_Castro https://en.wikipedia.org/wiki/Liliana_Castro).
swagaholic 11y ago
The teacher in this vid is so hot. Does anyone have more of her? Does she do hardcore?
scionaura 11y ago
For some reason this reminds me of Twin Peaks. I was expecting a surreal, supernatural twist midway through.
uptownfunk 11y ago
I've probably taken too many courses on this and related topics during my undergrad, going from basic group theory to category theory, representation theory, and algebraic geometry. For the uninitiated, a great first book is Fraleigh's text - very down-to-earth and conversational. When you're done with that you can read Dummit/Foote and for those with serious gumption, Lang's classic text. Have to say, it was my favorite subject - clean, elegant, and abstract.
wbhart 11y ago
These sorts of videos take a lot of time to prepare and someone has gone to some trouble here. Abstract Algebra is a massive subject though, with thorough treatments running into the many hundreds of pages. So it's too much to expect to get to grips with the subject from a few short videos such as these. Recently I've been watching Benedict Gross' Abstract Algebra lectures, to see if I can learn anything about how he presents material (he's a famous number theorist and known for his expository style). http://wayback.archive-it.org/3671/20150528171650/https://www.extension.harvard.edu/open-learning-initiative/abstract-algebra http://wayback.archive-it.org/3671/20150528171650/https://ww... One neat trick there is that groups are introduced via symmetric groups and via orthogonal groups, which allows a lot of geometric (visual) intuition, in a subject which is otherwise just symbolic (by definition). What amazes me quite a lot is the total dearth of video lectures on commutative algebra online. This is taught in many undergrad courses, and there are plenty of written lecture notes online, but almost nothing when it comes to video presentation. I think a lot of people who set out with the best intentions just give up when they find out how enormous the subject is, and how hard it is to keep errors out of presentations.
- rickhanlonii 11y ago
  I started thisismath.org as a naive college kid in 2011 because there weren't any good video lectures on advanced maths. I knew it was going to be difficult but I couldn't appreciate how much work would go into actually editing the videos at the quality that I wanted until I felt the true weight of the commitment. I was in over my head and after a few videos I confronted the reality that I didn't have the extra time to commit and I just trailed off. I still think there's an important need for advanced math video resources, and we should commend anyone who puts in the effort.
thingsgoby 11y ago
Isn't is a bit sexist that they use a good looking actress instead of one of the creators doing it herself? I wonder why that is
- drdeca 11y ago
  I don't know. Why would it be or not be? Or might it only "sort of but not exactly" be? I've heard of things being said that any individual instance wouldn't necessarily be sexist, but the fact that it is particularly common is. Is that a relevant idea? I am not sure. However, perhaps the question might not be best considered only in terms of sexism, but in terms of general views on attractiveness, and then relating that to sexism? But then again, that could also not apply. I don't know. I'm not really making any claims here. I figure that this probably isn't a particularly harmful thing in this instance, if it is at all, though it might be a useful thing as a starting point for thinking about a topic. But also, it could be useless for that also. I don't know.
Achshar 11y ago
To me it feels forced. Idk, maybe we can just feel it when the presenter is reading a script. This feels a little... unnatural. Some youtube commentor said she's an "expression queen". I tend to agree, though I don't think they meant it in a negative way whereas I do. I guess that would be the appeal for some people but I am not used to learning stuff in such an expressive way.
kaipakartik 11y ago
This was good fun to watch. I didn't know much about group theory before this.

74 points by espeed 11y ago

1971genocide 11y ago

The videos are good but something is just off ( uncanny valley ?) about the way the person presents. It seems really fake :(

iraphael 11y ago
I wouldn't place it in the uncanny valley. It just sounds highly scripted and acted.
- throwaway999888 11y ago
  Another comment mentioned that she's an actress.
presidentender 11y ago
The presenter is an actress. It's effectively a monologue.
jaywunder 11y ago
I saw the same thing... it was like she was trying to give sexy looks while also teaching me math. Rather distracting. Did you also notice that?
- espeed 11y ago
  I suspect that's the point -- evoking a motivating and memory-enhancing dopamine shot -- a la the Van Wilder tutors.
  - jaywunder 11y ago
    Oh huh... I don't know if I like that, but if it works then I guess it works
  - throwaway999888 11y ago
    Sounds like bogus. Being primed for math and being primed for sex feels like two completely different modes to me.
    - espeed 11y ago
      Thinking about sex primes the brain for analytical thinking: http://tedxtalks.ted.com/video/Mathematics-and-sex-Clio-Cressw http://tedxtalks.ted.com/video/Mathematics-and-sex-Clio-Cres...
      - cbd1984 11y ago
        Too bad that's TEDx, and not a real TED talk.
angdis 11y ago
I think the videos serve as an introduction to some basic concepts intended to bring some clarity for further in-depth study. The video is much like the "front matter" to a chapter in a book. Of course, the _REAL_ learning work starts when the student suffers through countless problems and proofs. This is no replacement for that. One doesn't learn math by passively watching videos or listening to lectures. That's the way it is and that is the way it will always be. This just provides a clear 30,000 foot view of the topic, a little motivation and background and, yes, some eye candy (and that's OK too).

darkxanthos 11y ago

Anything that can help make this subject more approachable is alright in my book. In my experience, the hardest part of Abstract Algebra isn't the abstract part of it. It's the lack of examples and clarity around how different named concepts behave. The proofs aren't terrible even except for the fact that they require a familiarity with number theory that many (at least I myself) don't have. I love the subject though. Really interesting.

gh02t 11y ago
For me, it has always been the terminology. The basic theorems are relatively easy to understand... once you can remember the vast number of algebra-specific definitions. The field also has a proclivity for umm "colorful" choices of names. It's not unlike say Haskell, which IMO is pretty straightforward once you have a feel for all the terminology.
- goalieca 11y ago
  Like this from wikipedia on Monoid? Suppose that S is a set and • is some binary operation S × S → S, then S with • is a monoid if it satisfies the following two axioms: Associativity For all a, b and c in S, the equation (a • b) • c = a • (b • c) holds. Identity element There exists an element e in S such that for every element a in S, the equations e • a = a • e = a hold. In other words, a monoid is a semigroup with an identity element. It can also be thought of as a magma with associativity and identity. The identity element of a monoid is unique.[1] A monoid in which each element has an inverse is a group.
  - cmrx64 11y ago
    It seems to me that the definition presented there is relatively free of jargon, except the "in other words" section which links it to other (linked) structures.
    - gh02t 11y ago
      > except the "in other words" section which links it to other (linked) structures. That's what I was getting at. I took a few classes in AA and its sibling topology, including at graduate level. Most of the time was spent defining things, because there's so many terms with very specific definitions. Only after maybe 2/3rds of a course do you really start getting into deeper material. In my brain, reading definitions was always a process like: read through, substitute definitions for jargon terms, read through, substitute... iterate until you hit a fixed point. That's standard for math, but AA is particularly well known for its colorful choice of names. Some people enjoy it, but I was always more attracted to the analysis-family areas of math. I've always found the other name for category theory amusing though: https://en.wikipedia.org/wiki/Abstract_nonsense https://en.wikipedia.org/wiki/Abstract_nonsense

espeed 11y ago

Socratica was started by two Caltech grads: Michael Harrison (ex-Googler) and Kimberly Hatch Harrison (http://www.socratica.com/about.html http://www.socratica.com/about.html). The actress in the video is Liliana Castro (https://en.wikipedia.org/wiki/Liliana_Castro https://en.wikipedia.org/wiki/Liliana_Castro).

swagaholic 11y ago

The teacher in this vid is so hot. Does anyone have more of her? Does she do hardcore?

scionaura 11y ago

For some reason this reminds me of Twin Peaks. I was expecting a surreal, supernatural twist midway through.

uptownfunk 11y ago

I've probably taken too many courses on this and related topics during my undergrad, going from basic group theory to category theory, representation theory, and algebraic geometry. For the uninitiated, a great first book is Fraleigh's text - very down-to-earth and conversational. When you're done with that you can read Dummit/Foote and for those with serious gumption, Lang's classic text. Have to say, it was my favorite subject - clean, elegant, and abstract.

wbhart 11y ago

These sorts of videos take a lot of time to prepare and someone has gone to some trouble here. Abstract Algebra is a massive subject though, with thorough treatments running into the many hundreds of pages. So it's too much to expect to get to grips with the subject from a few short videos such as these. Recently I've been watching Benedict Gross' Abstract Algebra lectures, to see if I can learn anything about how he presents material (he's a famous number theorist and known for his expository style). http://wayback.archive-it.org/3671/20150528171650/https://www.extension.harvard.edu/open-learning-initiative/abstract-algebra http://wayback.archive-it.org/3671/20150528171650/https://ww... One neat trick there is that groups are introduced via symmetric groups and via orthogonal groups, which allows a lot of geometric (visual) intuition, in a subject which is otherwise just symbolic (by definition). What amazes me quite a lot is the total dearth of video lectures on commutative algebra online. This is taught in many undergrad courses, and there are plenty of written lecture notes online, but almost nothing when it comes to video presentation. I think a lot of people who set out with the best intentions just give up when they find out how enormous the subject is, and how hard it is to keep errors out of presentations.

rickhanlonii 11y ago
I started thisismath.org as a naive college kid in 2011 because there weren't any good video lectures on advanced maths. I knew it was going to be difficult but I couldn't appreciate how much work would go into actually editing the videos at the quality that I wanted until I felt the true weight of the commitment. I was in over my head and after a few videos I confronted the reality that I didn't have the extra time to commit and I just trailed off. I still think there's an important need for advanced math video resources, and we should commend anyone who puts in the effort.

thingsgoby 11y ago

Isn't is a bit sexist that they use a good looking actress instead of one of the creators doing it herself? I wonder why that is

drdeca 11y ago
I don't know. Why would it be or not be? Or might it only "sort of but not exactly" be? I've heard of things being said that any individual instance wouldn't necessarily be sexist, but the fact that it is particularly common is. Is that a relevant idea? I am not sure. However, perhaps the question might not be best considered only in terms of sexism, but in terms of general views on attractiveness, and then relating that to sexism? But then again, that could also not apply. I don't know. I'm not really making any claims here. I figure that this probably isn't a particularly harmful thing in this instance, if it is at all, though it might be a useful thing as a starting point for thinking about a topic. But also, it could be useless for that also. I don't know.

Achshar 11y ago

To me it feels forced. Idk, maybe we can just feel it when the presenter is reading a script. This feels a little... unnatural. Some youtube commentor said she's an "expression queen". I tend to agree, though I don't think they meant it in a negative way whereas I do. I guess that would be the appeal for some people but I am not used to learning stuff in such an expressive way.

kaipakartik 11y ago

This was good fun to watch. I didn't know much about group theory before this.