Currently in the last year of my A.A in mathematics with an aim to transfer to a four year institution and earn an A.B in pure mathematics.
After completing my A.B I plan to go to graduate school to pursue dual Ph.Ds in pure mathematics; the reason I want to get two graduate degrees in the same subject is that I will be forced to pick a specialty and, well, I would rather not pick only one subfield.
I believe that I will most likely choose algebra as my first specialty however this is most emphatically not the algebra most of those of you reading this are likely to be familiar with from high school; I am actually referring to modern higher algebra. I have a very strong interest in those mathematical constructs that are the focus of algebra (i.e vector spaces, rings, groups, etc.) and an especially strong interest in multilinear algebra, which is concerned with exterior algebras and tensors.
I am not nearly so sure about the second specialty but I am leaning toward either analysis, which is basically a higher extension of calculus, mathematical logic, or one of the branches of differential geometry or differential topology such as symplectic geometry.
There's also a good chance that I'll end up getting an outlying degree in a language if the university I transfer to has one that is interesting enough.