
Abstract Algebra: The Definition of a Group [video] - espeed
https://www.youtube.com/watch?v=QudbrUcVPxk&list=PLi01XoE8jYoi3SgnnGorR_XOW3IcK-TP6
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wbhart
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://ww...](http://wayback.archive-
it.org/3671/20150528171650/https://www.extension.harvard.edu/open-learning-
initiative/abstract-algebra)

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
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.

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darkxanthos
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
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
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
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
> 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)

~~~
cmrx64
Fair enough! My biggest struggle taking AA was also remembering the
definitions of everything. There are so many things all tied together.

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espeed
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)).

------
1971genocide
The videos are good but something is just off ( uncanny valley ?) about the
way the person presents. It seems really fake :(

~~~
iraphael
I wouldn't place it in the uncanny valley. It just sounds highly scripted and
acted.

~~~
throwaway999888
Another comment mentioned that she's an actress.

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uptownfunk
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.

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

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thingsgoby
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
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.

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Achshar
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.

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

