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What is the best way to get into Engineering?

My son loves math and he is in the gifted program at school.  I am exposing him to electronics.  What subjects should someone study if they want to work in the Engineering field?  I know that some subjects like Math and English stay the same but the curriculum I took in computers looks different from when I started college till this day.

The good news is you can do

The good news is you can do almost any kind of electronics at home these days: as an example you can do your own FPGA development and hook it to math intensive design via Mathcad which has an interface to Altera.  (I.E. you write DSP in Mathcad and it download to Altera PGA)
In the old days a hardware design engineer, at least the good one, were multidisciplinary.  We could do analog, digital, sensors, ultrasonics, RF, PGA, tubes, etc etc   We comprise roughly half of the workforce as every device needed a piece of hardware and then the code.  There wasn't much of one without the other.  Now days there are millions of preexisting computer.  The down side was we needed a lab and test equipment that we ourselves could never have afforded. All of that has changed between scopes available off ebay, USB data loggers and $70 evaluation boards. 
Also what has changed is the availability of information.  I was self-taught long before the advent of the Internet and so had to rely on books and other smart people around me to pick up what they already knew.  I still have over 1000 books in the basement starting with ECL, OpAmps and PLL's on up.  Now days you can research any aspect you can think of, want to know the dimensions of a Yagi-Uda antenna, in less than a minute you will know, and right after that you will know the alternatives.  What a great time to be in the tech field!
So I would say that it is about what is of interest, there are so many subfields available now. For example Robotics, you could dive deep into a field that has software, hardware, ucontrollers, sensors, etc.  Erin Kennedy aka Robotgrrl has done exactly that.  You could get into the whole Make/Hacker thing or in my case I still like video.  (I once told a programmer that once you program video where you can see the output with your eyes, you will never go back to "dry" code.  He went on to work at Real Networks.)
If he is good at math the world is his oyster so to speak.  People with CS degrees and a math degree get an automatic pass to the front of the line.  My first hire ever was Dave Haynie best kwon for his Amiga stuff, he was a CS with a Math from Carnegie and was programming missiles for GE when I found him.
So I would ask, what part of technology excites him?  What floats his boat so to speak?

My Dad worked at G.E. at 32nd

My Dad worked at G.E. at 32nd and Walnut Street and he would never tell us what he did but he wasn't high up in the company but I gather that he assembled things.  He brought home at least two completely good soldering iron that someone threw away and showed me how to solder a few times.

My son likes to play video games on the Wii and the 3DS so I was showing him our Commodore 64 and he wanted to learn how to make video games so I told him he had to learn programming but the abilities of the Commodore 64 are not the same.  He wants to be a teacher and his grandfather taught at Drexil University so teaching isn't bad as long as it pays the bills and his grandfather also worked at Ratheon as an engineer before they sold it and changed the names. 

I see videos of other kids on the web soldering at five years old and I let my son attempt soldering but I haven't let him do any large projects because I'm still afraid of him hurting himself.  I let him watch me and he said that soldering takes a long time.

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