Edit: I phrased this flippantly, but it's a serious question. My educational background is in Math, specifically Abstract Algebra. Would learning Haskell actually help me use those concepts for practical purposes?
There are "issues" with those structures in GHC, i.e. how the Functor/Applicative/Monoid hierarchy evolved in GHC (applicatives were discovered a little late)
http://stackoverflow.com/questions/7595023/why-is-this-decla...
http://stackoverflow.com/questions/5730270/alternative-imple...
But: (and this one of the beauties of Learn You a Haskell), learning the categories (functor, applicative, monoid through arrows, duality, groups etc), is a superb way to abstract the software analysis/development process and is one of the winning features of languages with good type systems (haskell, the *ML's incl F#, scala)
I'd encourage you to try Python. Its syntax is simple, natural, powerful, and very similar to mathematical notation (I'm thinking of list comprehensions). If you want to use Python for mathematics -- in the sense of an open-source replacement for Maple/Mathematica -- I recommend Sage [1].