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The Essentials

First you will need to download the JDK Package from sun. You can find that here , along with a great tutorial from Sun. One problem is that the JDK is pretty big to download from home. Some people go to the bookstore and buy a book with CD included.
Next you will need an IDE (Integrated Development Enviroment). Let me recommend JCreator, which is free!
Also you will need some graphics capabilities to plot out your results. I guess there are some good java packages out there...it depends on your specific needs! If you are doing image processing, java can easily do that. Another approach to consider is Gnuplot. This is a free, full-featured scientific plotting program that will give you most of what you want. The problem with this approach is that it will require you to export your data from your Java program, then plot it in Gnuplot. But once you figure out how to do this, its no problemo.

Some useful java webpages


Java for scientists and engineers

Lately I've got started learning java. It's not that hard, especially if you are familiar with C++.
My particular interest is scientific and engineering programming. Why did I choose Java, instead of Fortran, or C++?
No reason actually! Some people say that you should learn several languages. But I can say that Java is a great choice for engineering programming.
Let me briefly comment regarding a program called MATLAB, which is widely used by engineers. MATLAB is given out pretty much free to university professors and grad students. But if you want to use it once you get out of the university, it will cost you about $1900. Now I can understand that they need to make their money. On the other hand, I think its a pretty cheesy game to play. So if you are a student and have the opportunity to use MATLAB, maybe you should think twice. Learning Java or C++ may be harder...but on the other hand, getting Java is free!
I'll also comment on another program Mathematica. This program was priced at only $1300, which is getting close to reasonable. Mathematica does have a lot of nice features. Now I'm not an expert in Mathematica, but I did take a careful look at it. I found that Mathematica doesn't really support procedural programming. For some crazy reason, you have to write your whole program in one line. They call it a new paradigm. I call it "not what I want". It may be what you want, though. Who knows?
By the way, here are some useful commands in linux.