It is a good question, and I’ve been asked it quite a bit this semester. The answer I usually give is that the requirements worked out for my degree such that I have to take Calculus III. This is true, but my experiences this semester in this class has led me to something else.
The class started out rocky. The actual professor wasn’t there for the first 3 or 4 weeks of class, and during that time, we had 4 seperate teachers come in to cover basic Vector Calculus. I struggled for the first time in a math class. It had been 2 years since I took Calculus II, and I had heard that Calculus III is supposed to be the hardest undergraduate class someone can take. So I was very anxious about this venture. But now, with two weeks left in the semester, I couldn’t be happier with my choice. I have fallen in love with mathematics once again.
When you really understand an equation, there is something almost spiritual that happens. Others have described it as ‘reading the mind of god,’ but I don’t like that language. It doesn’t seem descriptive enough. It’s finding out something about reality completely with your mind, something that you know is true! You are literally discovering an ultimate truth with every step of the theorem.
Call me crazy but my two favorite math class periods in high school we when they actually showed the proof to two important concepts: the irrationality of square-root of two, and the derivation of the quadratic equation (x equals negative plus or minus the square root of b-squared minus four A C, all over 2 A.). It was one things to just be told these things, but for me, the more important question was, ‘How did we know them?’
This leads to something else, something that has drawn my interest lately, especially after reading ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences.’ I am a music major – how does this all fit together? Music may be the universal human language, but mathematics is the language of the Cosmos.