So I have the opportunity of instead of going for a PHD, to go for a Masters in Applied Math with a focus on the mathematical theory of communications. The math that is used seems really cool, information theory, cryptography, applied fourier analysis etc. And it straddles the area between applied math and electrical engineering, which is a type of engineering I would love to learn more about. The description of the degree lists possible places of employment as places such as Qualcomm, Bell Labs, Hewlett Packard, Texas Instruments, etc. So I'm wondering exactly what kind of work could I expect to be doing upon graduation? How math heavy will it be? Is telecom engineering what I'd be doing? And if so exactly what does that entail? What are the general starting salaries? Is it normal to come at this area from the applied math side rather than the electrical engineering side? And anything else you feel like imparting to me about the field would be great, thanks.