In answer to the second question, no. I know more math than most of the people I know, and I felt like I was making a little progress with advanced calculus and I am finally starting to understand taylor series after watching the khan academy videos about it, but I feel like what I know is a vanishingly small fraction of what there is to know and that I'm probably wrong about everything I think I know.

To the first question: I want to study to go on jeopardy, I want to write a spanish textbook and/or app or something, I want to learn more languages, I want to become a better engineer. The only thing I can imagine ever wanting to do with math is teaching crappy math to other people who are never going to do anything with it.

I can certainly say that I know more math than most of the people that I know, and I am finally starting to understand Taylor Series. What I have learned so far has made me aware of how much more there is to know, and how my existing knowledge can always be improved. I hope to apply my mathematical knowledge to future pursuits including using the software I learned about in the math software class to help me write a Spanish textbook. Although it's not directly related to math, the critical thinking skills involved in math will help with analyzing linguistic data.

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