Analysis
So, why is such a thing as calculus taught when they could just teach analysis, and it would be so much more interesting?
So, why is such a thing as calculus taught when they could just teach analysis, and it would be so much more interesting?
That is a very good question. Unfortunately, over the last few decades, math has been taught in an increasing linear fashion. First you take algebra, then geometry, then algebra II, and so on. It's too bad that they don't offer options to students who wish to have a broad math experience. You really only get to learn some good stuff like number theory by actually having some computational major in college. Statistics is really the only math class outside the linear program. I agree that analysis should be taught to those who wish to learn it.
Good question. Unfortanately, the math curriculum has been "converging" towards a "linear model." Schools offer few options to students wishing for a broader math experience. Fascinating classes such as number theory contine to be relegated from the standard courseload to specialty majors like mathematics. However, AP Statistics is a countercurrent example that's offered to high schoolers yearning for more applied math. Hopefully, this trend of streamlining courses will reverse, no longer limiting the options of the next generation.
Analysis is awesome; it makes academic life so much fuller.