I was invited to give a guess lecture at a private high school to talk
something about mathematics. I am considering a topic about evolution
of the concept of limit. Besides taught math history classes once or
twice at college level, I am no expert in the math history area.
I was wondering if some one can help me out with a sketch of the
evolution of limit. My understanding was that it started, though not
explicitly, with perhaps the method of exhaustion in the Ancient Greek
time such as Euclid, and even in some ancient Chinese literature. It
was picked up by Fermat, Descartes in their calculation of certain
areas. Newton and Leibniz did make some attempt to explain it but not
quit satisfactory. Cauchy was the first one who came up with what is
similar to the epsilon-delta definition we are using today. Am I
generally on the mark? Assume all that was ok, I would still need a
little more than that to make a one-hour lecture.
Any suggestions? corrections?
Zhanbo Yang.