### Bad Habits?

#### by Carson Reynolds

In an effort to help check and expedite my work through Apostol’s Calculus, I’ve started monkeying around with Mathematica. After the inital syntactic-sugar shock I’m becoming somewhat pleased with it. Here’s an example of a mathematica function which takes another function as an argument and returns a list: html notebook.

It might seem a little funny that I’m reading a book on calculus. I started by trying to read a more formal text on Topology. This suggested that I have a background in” Rigorous Calculus” or Analysis. I then picked up Rudin’s Analysis book, which proved a little terse for my inital forays. Following that I asked Prof. Goroff for a recommendation. He suggested Apostol. It seems the treatments of calculus I had when I was an undergraduate was pretty far from being rigorous. This text is sort of a fusion between an analysis text and a calculus text. This means it works through calculus demanding that readers prove much of the material themselves.

So the question is, should I be old-school and do all of this work by hand or is it better to use something like mathematica to do the work. It seems that the answer is a little of both. If you rely too heavily on Mathematica you could end up with a shoddy understanding of the material. If you rely too heavily on doing all the work by hand then it takes forever. A balance must be struck it seems.

I am finishing a masters in math next semester. I will go back and learn some calc 2 and 3 stuff, and then hit up advanced calc, and then real analysis. I’m curious, is there a book for learning calc 2/3 and advanced calc? Is it Apostol? I have baby Rudin already, but perhaps I need to rethink where I should start. Any advice? Thanks