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this is the advantage of the command line.
IDE's hide how the process of building a program actually works.
Using the command line teaches you a lot about that.

Of course it can be debatable if...

unfortunately you're leading him at the wrong track
the above errors have nothing to do with header files

A header file won't solve the linking problem
undefined reference is an error in the linking stage, not the compile stage.

What the compiler did in Sim's line is following:
gcc -c math.cpp -o...