This page contains some advice for non-CS majors who are interested in programming or have some need for programming in their coursework or research. Note that this advice also applies to CS majors who are working on interdisciplinary projects.
The most popular (open-source) programming languages for science and mathematics are currently Python and R. Both are also popular currently because they are used a great deal in data science. There are a great many other languages which have been popular in the past or are still useful in particular situations. But if you are starting out fresh it is likely that Python or R would be your best bet for getting started. Another language/tool of note is GNU Octave, which is an open-source free alternative to MATLAB.
Mention Sage, QGIS, python.org tutorial, how to think like a computer scientist. Mention numpy/scipy
Mention Bioconductor, R information linked from GH 101 page, R for Data Science