The C Programming Language is the book you need on C, nothing compares to this book. One of the best written non-fiction books I know. Clear, with realistic examples, and a useful reference to the library. And it is surprisingly brief: This is not one of the huge tomes that use bulk for advertising. Programmers know that this is the most important book on C. Buy this book. I keep one copy at work and one at home.
The GNU Scientific Library has several useful routines for doing scientific calculations, with a bit of all the basics. With this library, transitioning from something simpler (such as Ox) need not be a pain. You can buy the Reference Manual from Amazon. In my opinion, a better choice than the Numerical Recipes, although there is nothing that compares to the book by Press et al. for a quick introduction to get-your-hands-dirty numerical methods.
Because nothing ever works the way that it should, it is useful to learn how to use GNU gdb, which will help you track down those pointers. I can’t claim to fully understand this wonderful programme, but I bought the official documentation as a book from GNU Press and this helped me get started.
Recently, I bought O’Reilly’s C in a Nutshell. This book contains a simple one-book reference to the language, the standard libraries, GCC, GDB and Make. This book cannot replace the other books here when it comes to learning to use the tools, but it is much easier to carry around.
The comp.lang.c FAQ will help you when the compiler spits out strange errors and refuse to compile your wonderful programme.
(This is an old page I wrote, still relevant.)