Mathematics encompasses two worlds: the continuous and the discrete. At times they seem impossibly different, yet they live together like a happily married couple, yin and yang, magically fitting to make a harmonious whole. Continuous math is called analysis. It focuses on rates of change, curves, surfaces, volumes, transformations, and the lovely patterns they engender. Discrete math is algebra --- and extends far beyond the solving of equations for X that high-school "algebra" students wrestle with. Higher algebra investigates the relationships among points, integers (counting-numbers), symbols, and sets of objects.
Analysis feels like space, flowing across the universe without bounds, smooth, calm, peaceful. Algebra feels gritty, rough, with pits and walls, jumps and sharp corners. Yet the two are united by some of the deepest results of modern mathematics.
Wednesday, December 15, 1999 at 06:22:05 (EST) = Datetag19991215