I had basically no programming experience (except for a one semester class I took in first year - Octave) when I started solving problems in computational physics (it was basic quantum mechanics), as part of my Honours year coursework. In the first week of learning how to code in FORTRAN, we did trivial things, like formatting text for printing, and compiling source code contained in one file. In the second week, we solved the 1D Schrodinger equation using a shooting method. By the fourth week, we were coding the Numerov-Cooley method, and it was a few weeks later (this was a half-semester course), after a few more assignments, that we were propagating a Gaussian wave packet. The math involved was a little tricky at first, but it was the programming which made life very difficult for the uninitiated.
It was about the fifth week when I learnt about options to see helpful error messages when compiling my programs! You mean you know which array reference is out of bounds, and you haven't been telling me? I was livid that this had not been considered important enough for the lecture slides.
Anyhow, enough about me, and my hopelessly inefficient 80 hour coding weeks which were required to ace that course... the point is that you don't want to go through what I went through, and you don't have to. Here are the lessons, in order of importance:
1) Don't bother with FORTRAN or C as your first language, if you're trying to solve mathematical problems. These languages (especially C) will only slow you down in reaching your short term goal of completing a scientific computing course. Instead, learn a language which is designed to help you write useful code faster (Python is ideal, but Octave and Matlab have their advantages too). With Python and the appropriate modules installed (mainly just numpy), you'll have no problems performing "simple" tasks like reading data files into arrays, sorting the data, and subjecting it to standard linear algebra operations. In FORTRAN, on the contrary, you're likely to give up trying to write your own parser for input files, or smash the keyboard after getting every one of the ten thousand arguments to a LAPACK routine incorrect. C is better to learn than FORTRAN, but in your case, it will only make writing numerical routines more frustrating, as well as looking much uglier in your text editor (C is a horrendously ugly language - at least FORTRAN code looks a bit like math on the page).
2) Ask for help early, regularly, and online. Don't allow simple, idiosyncratic tricks of the trade to waste all your free time. It's OK that you don't know that stuff; it's unintuitive.
3) If you can't debug the code in time, don't destroy it with hacks and arbitrary "bug fixes". Submit your concise pseudo code, along with the source code, and provide a clear writeup of the problems. Sometimes, only time and a clear head will help, while at other times (equally often when you're first learning) you just need the help of someone more experienced.
4) Get your math right before you start planning your code. Algorithms are understood on paper by humans, and then taught to computers via programming languages. If you get the algorithm wrong, you'll never be able to find the bug, because it doesn't actually exist (you just coded the wrong algorithm, correctly).
5) Forget about parallel computing, until you've "mastered" writing programs for one processor. Most computational scientists just lean on the expertise of colleagues here.
In summary: learn Python as quickly as possible, and try using numpy to solve linear algebra problems. Use of a language like Python will make your life a million times easier.