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> Calculus Made Easy

Thompson wrote the original edition a century ago. It is now Public Domain.

http://www.gutenberg.org/ebooks/33283

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:

http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/d...

> linear algebra

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.




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