I'm not sure what your computational background is but if you're not familiar with the basics like sequence alignment I suggest you check out a book. I'd recommend An Introduction to Bioinformatics Algorithms by Neil C. Jones (http://www.amazon.com/Introduction-Bioinformatics-Algorithms...). In addition to describing the algorithmic techniques, it gives synopses of current research issues and big names in the field. There are also hundreds of sample problems - some of which are active research problems - and no answer key (because often these types of problems don't have clear "best" answers). It's kind of like being taught how to swim by being thrown in a lake. If you survive, you're better off for it.
Also, before approaching professors it helps to have read and understand their description of their research interests and maybe have read a few of their recent papers. This will give you an idea of whether they're doing something that you might be interested in or not.
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