I agree with earlier comments, it depends on what area you are studying.
If you plan on studying numerical analysis or other areas that require computation, then YES, you will definitely need a very sturdy and reliable computer. As an undergrad I invested in a Lenovo laptop to handle heavy computations for courses and research, it has lasted four years.
If you just need a laptop for everyday use, using LaTeX to type papers or assignments, etc. then I don't think a heavy duty laptop is that important. A MacBook would probably be fine...but I wonder if a MacBook can handle the occasional Mathematica? MacBook Airs definitely won't be able to.
You will also have access to computers in grad school, you may have one in your office or have a computer lab. I never take my laptop with me anymore, I just email assignments to myself and print off what I need. So in that case you may just need a "normal" laptop or even a desktop to keep at your home/apartment/dorm.