Lots of Maths, lots of basic aeronautical theory, lots of general Engineering, and a fair bit of labwork - about 50 hours of work per week for 3 or 4 years. Entry requirement is generally around 3 Bs, in Maths, Physics and another science / mathematical subject.
I've got an Aero-Eng degree and work in general aircraft design approvals and flight testing. Friends I graduated with are RAF Officers, an oil company executive, a couple of well paid programmers, a software developer for a flight simulator company, a project manager for a digital TV company, a project manager for the MoD, a missionary, and a few professional pilots.
Friends and colleages who graduated with the same degree from other places include test pilots, a senior stressman at Westlands, pretty much everybody in the CAA's Safety Regulation Group HQ at Gatwick, and lots of computer programmers / project managers.
So, in essence you can enter pretty much any technical or aeronautical field with an Aero Eng degree. If you want to be a technician / mechanic, you'd be better off with an apprenticeship. If you want to end up a full time pilot, opinions are divided as to whether an Aero degree, or straight into the self improver route is the best bet - but the degree will probably give you more options.
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