I've never had to use calculus. Ever.
On the other hand I HAVE had to use lots of algebra, matrix transformations and trigonometry. 3D graphics is FULL of translational mathematics but it's all good fun.
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I do not doubt your particular experience but it would depend on what your programmes are for. If the application involves a lot of heavy-going calculus then obviously you'd need to understand the subject of the calculation and the necessary calculus, and how to turn it into computer code.
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Do you need to take an aptitude test to become a computer programmer? No, you don't. Given sufficient time anyone can program a computer. But without the required aptitude, it will take longer to become proficient. No institution is going to give a highly sought-after position to someone who may not have the aptitude over someone who evidently does.
You'll need to acquire a programmer board and the application software. The programmer boards typically plug into your PC and you can write an application using the application software, then you can load the application into the microcontroller using the programmer board.
A compiler.
I would say MIT. Massachusetts institute of technology. Digipen hands down. It's run by Nintendo, offers all sorts of degrees in the gaming industry, provides internships with the best companies in the business. It's located in Washington state and people come from all over the world to attend it.
Yes. If you need a more specific or detailed answer then please edit your question to include more context.