Mr. Fang's video demonstrates to us what a rigorous proof of your argument looks like. We can learn how to collect and verify evidence, how to make reasonable deductions, how to use logic and evidence to prove your points, and how to make a conclusion of your full process of reasoning.
姜萍说做梦都在解题。按照我学高数时的经验是我做梦都要把sigma的符号写对,不能写成二分之几几几,要不然的话再推五六步,自己都看不懂了,后患无穷。用MSWordEquation写sigma 还直观一点。用LaTeX,it is command line and sequential input typing. Without clear logic mind of sigma upper and bottom number 还真不行! 毕竟做梦的时候需要用数学符号作为一种思考的形象工具。