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You are definitely more of a mathematician than I. After doing some physics, I have come to terms with the fact that expecting the kind of mathematical rigor you would see in mathematics text is not a practical thing to expect from physics texts at the undergraduate or early graduate level. I have been spoiled, you could say, because the physics book I have used more than any other (save for Kleppner) is Wald's "General Relativity" and this book is quite precise as far as proper mathematics is concerned so I have the bad habit of using it as a reference to gauge the level of mathematics of other first year graduate texts with.Bipolarity said:The thing about EE courses though is that a lot of stuff needs to be taken for granted. Often your textbooks will use results from math, but not prove them. A simple example is the fact that any piece-wise continuous function has a Fourier series which converges to it at points of continuity. This result from Fourier analysis is proven by mathematicians, but engineers don't care for the proof: they use it as an indispensable tool in signal processing though! If you really like math, you will take those courses alongside and it may or may not help you in signals. A lot of EE is also an "art" and there are not well-developed algorithmic ways of doing many things, which may annoy you if you are not at heart a mathematician, like I was.
BiP
Eventually I came to terms with the fact that not all physics book will be that mathematically rigorous but they can still be very rigorous and difficult as far as physics is concerned (and by physics texts I don't mean mathematical physics texts such as the ones published under the Cambridge Monograph series because these can be extremely mathematical, especially books on gauge theory). I'm sure EE is the same way, in which case I wouldn't have any grievances.