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Comment on What are some interesting areas of math to study beyond calculus?

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One thing I'd recommend is tying in the calculus you've learned with the language of differential forms. It really gives you a lot more power in visualizing what is going on (line integral-you aren't just projecting that dot product in the integral onto an "infinitesimally small element", it is a map that does something simple but profound), and also extends your reach with visualization.

Also, if you are interested in more sophisticated ways of capturing quantum physics, geometric algebra is really cool.

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