Analysis

As a computer scientist by trade, it is worth noting that I never was expected to go into analysis. In particular during undergrad it was spectacular if a CS major (exclusively) had taken a variation of three dimensional calculus. I find it peculiar as I have found that mathematics only becomes fun after you stop focusing on calculations. Returning to pure mathematics during my thesis and studying proof theory was incredibly entertaining. Thus, since my thesis I have been working my way through analysis in the hope of creating a personal intuition for an introduction to topology. What at first was a means to an end, has created a new respect for calculus in me. During calculus one is taught about limits in such restrictive and brief a format that its not common (at least in me) to think past that brief introduction. That is however, a great mistake. It is not obvious to me that before learning these $\epsilon$-$\delta$ definitions that one can quite comprehend a limit at all.