

Intro to Group Theory - profquail
http://ureddit.com/blog/2013/02/26/featured-class-intro-to-group-theory/

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lifebeyondfife
My AI doctorate used a lot of group theory. I use came up with the following
analogy for explaining what it is and what it's used for to fellow non-
mathematicians:

If you want to measure and describe the number of occurrences of something,
use an integer. If you want to measure and describe the amount of something,
use a rational number. If you want to measure and describe the symmetry of a
structure, use a group.

When programmatically dealing with objects that contain symmetry - e.g.
physical objects like a cube, a set of identical resources like a fleet of
lorries - having an understanding of group theory allows you another layer of
abstraction in your computation, potentially greatly reducing runtime or
memory consumption.

~~~
pfortuny
Groups are just the abstraction of "transformations of something", the usual
example being "symmetries" but it leaves out a bunch of other natural ideas
like translations, movements, etc.

Any teacher not mentioning "shape" when explaining group theory is either a
bad teacher or a bad teacher.

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paulrademacher
Group theory can be taught and appreciated without the geometric approach, but
instead as a pure abstract concept. Different textbooks reflect this: Herstein
is very abstract, Dummit and Foote uses probably more geometric examples, and
Fraleigh relies heavily on geometric cases. I've personally always preferred
the Herstein/abstract approach.

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pfortuny
Oh certainly: that is the way I studied and enjoyed it but a book is not a
teacher. I am not claiming books should always be "imagination" driven, on the
contrary. But teachers should.

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shocks
Mathematics student here, taken a few courses in abstract algebra. Group
theory is really interesting and I'd recommend all those intrigued to give it
a go.

Here is a great book about Abstract Algebra. It should be about right for this
course and it's free! :D <http://abstract.ups.edu/>

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tel
For anyone interested in another great way of looking into this field, take a
look at Aluffi's _Algebra Chapter 0_ [1].

[1]
[http://www.mimuw.edu.pl/~jarekw/pdf/Algebra0TextboookAluffi....](http://www.mimuw.edu.pl/~jarekw/pdf/Algebra0TextboookAluffi.pdf)

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anastas
Hello, I'm the UReddit admin and author of the linked post. I'm glad to see
appreciation here for Dr. Donley's class.

As we say in the article, we are trying to put together a better platform for
teachers to use when they want to teach with more freedom and with more rights
to their intellectual property rights than they might have when doing it
through a university, and so that they can have many parts of the teaching
process automated in order to be able to focus on actually playing the roles
of educators.

We're running a Kickstarter to help us get our prototype into beta, and we
appreciate any and all support.
<http://www.kickstarter.com/projects/1918344721/open-compass>

~~~
dmix
I haven't heard of UReddit before.

What's the pitch?

~~~
anastas
UReddit was a proof of concept based on which we founded the nonprofit. The
pitch is essentially that anyone that would like to teach should be free to do
so, so we made a place where people can do that. Now, Dr. Donley, who taught
the class the linked blog post is about, had been composing video lectures for
two years, but he did use the UReddit platform to run two classes and receive
more attention/recognition for his efforts and quality of execution. And now
we'd like to make a technologically sophisticated platform that automated the
busy work of teaching and is better suited to becoming a community.

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mikevm
I'm taking an Introductory Group Theory course right now.

Here are a few nice books I'm currently using:

[http://www.amazon.com/Introduction-Theory-Groups-Joseph-
Rotm...](http://www.amazon.com/Introduction-Theory-Groups-Joseph-
Rotman/dp/0387942858)

[http://www.amazon.com/Visual-Classroom-Resource-Materials-
Pr...](http://www.amazon.com/Visual-Classroom-Resource-Materials-
Problem/dp/088385757X)

[http://www.amazon.com/Groups-Their-Graphs-Mathematical-
Libra...](http://www.amazon.com/Groups-Their-Graphs-Mathematical-
Library/dp/088385614X) (available as eBook from
<http://www.maa.org/ebooks/nml/NML14.html>)

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betterunix
Group theory is a beautiful subject, as is the rest of abstract algebra. My
personal favorite result in mathematics is the Fundamental Theorem of Galois
Theory, which requires at least some understanding of group theory.

~~~
eru
And interesting enough, you can use the same machinery developed for those
problems to prove the impossibility of squaring the circle, or trisecting an
angle.

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jalayr
Looking forward to this. Group Theory has always evaded me.

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mrcactu5
I'm in math grad school, and I'm really surprised CS majors don't know this
stuff or find it useful. Probably this should be changed.

