\newcommand{\falsepsilon}{\epsilon}

This is a polyhedron with cutaway faces, based on the snub dodecadodecahedron, which I posted here some time ago. In this version there is a single connected piece for each face, instead of multiple disconnected facets. I designed the model faces so that they avoid each other when assembled, with the holes making the interior of the model visible.

A new global report released Monday by the U.S. Geological Survey revealed that every place on earth currently has the wrong amount of water. “New satellite data confirms that every corner of the earth has the incorrect quantity of water,” the report read in part, noting that even though the total amount of water on the planet seemed to be about right, give or take a few hundred milliliters, the distribution of that water across the globe was “way off.”

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PBS: Language as Prejudice - Myth #6: Women Talk Too Much (via misandry-mermaid)

Every EVERY women’s studies class I’ve been in has had this problem and failed to address it. 

I've found that, pedagogically, the relationship between ring and field theory and classical algebra is much easier to illustrate, and that the relationship between rings and fields is much closer than either rings or fields to groups. It's just a lot easier to say that, as algebra studies polynomials, abstract algebra studies the various structures in which polynomials can be defined, and how they behave in those structures, but group theory really throws a wrench into the whole ordeal.

Like, I get that Galois theory is a whole thing, but that's like the exception that proves the rule. Galois theory is so great precisely because one doesn't expect fields and groups to be related.

I feel like group theory fits in far better with combinatorics and the like, both in ends and arguments. I admittedly don't have much experience with the two, so someone more informed could tell me this is ridiculous.

Even then, I feel like saying group theory is its own thing wouldn't be too far out there.

I suppose I am neglecting the fact that the notion of quotients in group and ring theory are remarkably similar (really the same thing), but it's not like the Galois groups and fundamental groups being manifestations of the same phenomenon means that field theory and topology should be considered the same subject (no matter what Grothendieck says).

I feel like, in the hypothetical event of a divorce, abstract algebra should keep abelian groups, but the only justification I can think of is that modules over a ring are still essentially ring theory.

I feel like, in the hypothetical event of a divorce, abstract algebra should keep abelian groups, but the only justification I can think of is that modules over a ring are still essentially ring theory.

Despite what I just said, I suppose that I am approaching this from a very algebro-geometric perspective, for a pair of reasons:

1. My justification using polynomials earlier

2. I wanted to say that there is no real analogue of 'group actions' in the context of ring theory, but I think a huge class of examples in noncommutative algebra are rings of operators on some space or object.

That second point makes me think that what I'm really getting at is the abelian/nonabelian divide in abstract algebra (which is also exemplified by my claim regarding abelian groups). Now, would I stand by saying that abelian algebra and nonabelian algebra shouldn't be considered the same subject? I don't know...

Your observation that group theory is a lot different from the study of rings and fields is an apt one. Though I'm not sure that necessarily disqualifies group theory from being abstract algebra. The whole game is essentially the same: we have some rules for some operations and we see what we can say about objects that satisfy these rules. The theories do end up having rather different flavours but they're both still algebra.

Also some places, ring theory is taught before group theory for precisely the reason that it's a generalisation of the usual algebra we do in secondary school. And then once you're comfortable with doing algebra with an abstract set of rules, you look at groups which aren't immediately as familiar.