The Hardy-Littlewood Circle Method is amazing. We’re learning about how to get asymptotic formulae for the Waring problem. It’s a shame that there is no (known) asymptotic bound or for the number of representations of n as the sum of two squares. That would tell us a lot about prime numbers (or at least those congruent to 1(mod 4)). We may also get to see the proof of Vinogradov’s Theorem (also known as the Weak Goldbach Conjecture, which is no longer a conjecture).
I wonder if it’s necessary to do differential calculus with lines. What happens if instead of fixing a point and moving another point closer, we fix a point and move two points on opposite sides closer to get a quadratic? Will that parabola have any interesting properties? I might play around with it some time.
Kevin makes me feel like a slacker. He’s taking nine classes, and I’m only taking seven at most depending on how taking is defined.