Quite simple really:
- Depends what you're programming.
- Yes, but most people don't get that far anyways.
- Definately yes.
Common rule: the higher level of abstraction, the less you need to know. Executable pseudo-code requires less knowledge to program effectively in than portable assembler. The more theoretical the work, the more a math background helps. And if you want to mathematically prove your code is correct, then you'll definately need at least an undergrad level of understanding.
Don't forget the old saying: biologists want to think they're chemists, chemists want to think they're physicists, and physicists want to think they're mathematicians. Personally I don't think computer scientists really exist, they're just script kiddies who are starting to learn math ;-)
The only advantage in making computers understand English is that it will prove once and for all that programmers can't write English. - Mike Taylor
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