Approximately speaking, first year undergraduate maths level is assumed, but no more. Most topics are elaborated on as required to teach the content.
You'll need to understand calculus, i.e. understand the principles behind derivatives and integrals. You certainly won't need to be proficient in manipulating them. A brief book, like Martin Gardner's updated edition of Calculus Made Easy, is the type of background that you need. A bit more specifically, having an intuition for vector calculus and partial differential equations is important.
Honestly, I can't think of anything else that you would necessarily need to know before starting, but to get the most out of it you WILL need to follow along with his working in pen-and-paper, and get used to rewatching, or looking up topics that you struggle with.
> Martin Gardner's updated edition of Calculus Made Easy
I've seen several (quite a few actually) books with this title on Amazon. Some of them written by Martin Gardner and Silvanus P. Thompson, others written by Thompson alone. Do you recommend a particular edition? (and what's the deal with the plethora of different editions?)
Gardner's revised edition adds introductory material, a problem set, and updates the language to keep it roughly in line with what is taught now. I can't speak to the differences between modern editions, but I have this one:
To be honest, all abstract algebra is tough on new-comers. Compared to undergraduate calculus, the "aha" moments have more pay-off, but usually take a lot more time. The significance and power of vector spaces is just not something that is easily learnt, other than by working through problems with pen-and-paper math, and while doing so, constantly asking yourself "why do mathematicians do things this way, rather than some other way?"
I bought a copy of Gilbert Strang's Linear Algebra And It's Applications when I was an undergrad, and still refer to it now. It's brilliant, but it's a traditional text book, and definitely not a "primer".
It's not the type of maths you would call "hard" (integral calculus can be infuriatingly "hard") but it's the type that takes time and work to understand. Once you understand vector spaces, QM is surprisingly straight-forward.
I haven't seen the updated version, but the one on gutenberg is gold. The old language is comical on its own: he cracks jokes and it is funny because of the jokes //and// because of the old language.
This book is so good, that gutenbeg volunteers took the time to typeset all the math in latex so the PDFs are very good for reading or printing out.
excerpt:
PROLOGUE.
Considering how many fools can calculate,
it is surprising that it should be thought
either a difficult or a tedious task for any
other fool to learn how to master the same tricks.
Some calculus-tricks are quite easy. Some are
enormously difficult. The fools who write the
textbooks of advanced mathematics—and they are
mostly clever fools—seldom take the trouble to
show you how easy the easy calculations are.
On the contrary, they seem to desire to impress
you with their tremendous cleverness by going about
it in the most difficult way.
Being myself a remarkably stupid fellow, I have had
to unteach myself the difficulties, and now beg to
present to my fellow fools the parts that are not hard.
Master these thoroughly, and the rest will follow.
What one fool can do, another can.
(despite being a math major in undergrad, I didn't really appreciate linear algebra until I saw it used in QM when in grad school... linear algebra is a very dry subject by itself, but incredibly useful when applied to various other fields).
