Re: coming to know the world
I'm not sure I really know what you're asking, but I can recommend some courses. Aside from Calculus, these are the three that shaped my world view the most:
Game Theory
Mathematical(Calculus-Based) Statistics I
Quantum Mechanics
You need calculus, linear algebra and a lot of physics(strictly for Quantum Mechanics) if you want to take those courses. My Game Theory class was offered through the Mathematics department, but it looks like MIT OpenCourseWare offers one through the Econ department.
Another good class in this line that I didn't take, but wish I had was Chaotic and Dynamical Systems.
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