Struggling through Spivak

Question

My friend recommended that I try out Spivak. So I figured what the heck, its just a calculus book, can't be that hard...I was wrong.

I'm very slowly working through Chapter 1, not even on calculus yet. I don't think I've ever put this much mental energy into thinking! I enjoy it, a lot. I've never thought about math this way in my life.

But I'm a little worried that it's taking me such a time to get through "Basic Properties of Numbers," how am I going to get through the rest of the book? Will I understand it?

Or am I just overthinking it?

As you can see from my previous post my background is kind of shady, should I put Spivak on hold until I "fill the gaps" of my previous knowledge?

I also bought this book today. Should I work through that first? I have a very weak proof background

Answer 1

I suppose you're starting/halfway through calculus, but haven't done Real Analysis yet.

I first started with Spivak after taking one semester of calculus, and like you, enjoyed it tremendously, but couldn't keep up with the difficulty. Now that I've done a course in analysis, the book really feels a lot more accessible (I'd say * 'd exercises are at the same level as usual analysis workload, such as Abbott, and ** 's can be a bit more challenging).

Nonetheless, it's just a beautiful book, I can't get enough of it. I couldn't find better motivation for the completeness axiom anywhere else, and the exercises cover pretty much anything a starting mathematician would need to know in basic analysis/calculus (and a lot more, actually).

In general, I'd suggest you not to worry so much with your pace. Even though its difficult, you know you have all the knowledge required to read it, and mathematical maturity will come with time. Just enjoy the book and keep going back and forth between it and your regular textbooks. Eventually things will just click!