I would say the top languages are Python and R. Many enterprises use SAS and/or SPSS. Java is often used in production settings or when dealing with Hadoop. Other less popular but still useful languages are: Julia, Octave/Matlab, and Perl.
Coursera, Udacity, and EdX all have great courses. Algorithms is not the starting place though. You first need to learn the basics of programming (functions, variables, looping,...).
I guess I should've been more clear. I've already been taught the fundamentals of a few languages (C++ and python mostly) in some first year classes. I'm just looking to take a few options to build on these without switching out of my math major.
Computing for Data Analysis from Coursera is just finishing up and it was good. It focused mainly on how to program in R. Data Analysis from Coursera is just getting started, and so far it looks excellent. It focuses on actually doing the analysis.
This is maybe not the answer you want to hear. Outside of academia, there are not a lot of places that will hire you to do pure math. Most companies need the math to be applied to some product/strategy for revenue purposes. If your math has no application, then why would a company pay you for it. That being said, fields such as data science and machine learning (both applied) are pretty hot right now.
A little further remark, I'm not actually opposed to applying math (or e.g. some kind of logical modeling), just to the "traditional" applied math subjects, i.e. numerical computing or statistics.
Somewhat related: Statistical Languages http://101.datascience.community/2014/07/07/statistical-prog...
Here is another list: http://101.datascience.community/2012/12/31/5-free-programmi...