I am a high school science teacher and I am beginning to think that I should pursue a different career. I have a strong science and math background and a few people have told me that I would make a good engineer. I am not sure what type of engineer fits me best. Right now, I am considering computer engineering (either hardware or software) but I am not too smart at computers. However, I am a very logical thinker and have the ability to learn things easily and well. What do you suggest?
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Second the answer by Lee Kashka. Hardware and Software are highly intertwined but I'd definitely shoot for the MSEE (Masters or PhD in electrical engineering) if you're interested in product design in the hardware field. It will be far easier to jump into hardware with an EE degree than a Computer Science degree and EE graduates are highly accepted into Computer Science fields.
You may or may not know that hardware design is essentially software these days. Integrated Circuits are now designed and tested using "hardware descriptive languages" Verilog and VHDL which you could say is "like" software engineering although it certainly has its differences.
Typically software engineering leads into hardware engineering - as to say it would be practically un-feasable for a person to do hardware engineering without a professional level skill for software engineering.
I'd suggest doing some googling on embedded system design to get a clearer picture.
Note that Computer Engineers generally cover both hardware and software with some specialization at each university. The degree can be used for a variety of jobs. Probably your biggest challenge will be explaining to people that you don't just "build computers". If you aren't computer savvy, you might want to just grab an electronics book and a programming book and make sure it is something you want to learn. Your job opportunities will be endless, because when you are done with the degree you will be very smart on computers.
My dad once told me the only thing that realy matters about a job is that it makes you happy.