Does anybody have a recommendation for a book covering all of mathematics. In other words, if all math books were to be burnt, and you were given a choice to preserve only one, which one would you choose?
Thats an impossible ask. General maths books don't have enough depth in the big topics. When I was an undergrad I found Mathematical Techniques by Jordan and Smith a really good basic book, but it doesn't have a lot on vector spaces, complex integration etc etc.
From mathematics I think, need + - / *, a little bit x^2=y, a little bit matrix (to understand some information 
), sin cos and maybe complex numbers if you want understand rotation, a little bit integrals and diferentials 
to understand what a hell it is . That's all, everything over things is dublation of this things. 
And maybe combinatorics if you want understand what it is NP-complete problems. 
Every over things with very unusual strange langue is:
), sin cos and maybe complex numbers if you want understand rotation, a little bit integrals and diferentials to understand what a hell it is . That's all, everything over things is dublation of this things. And maybe combinatorics if you want understand what it is NP-complete problems. Every over things with very unusual strange langue is:
QUOTE (DavidD+Nov 2 2007, 02:10 PM)
From mathematics I think, need + - / *, a little bit x^2=y, a little bit matrix (to understand some information ), sin cos and maybe complex numbers if you want understand rotation, a little bit integrals and diferentials to understand what a hell it is . That's all, everything over things is dublation of this things. And maybe combinatorics if you want understand what it is NP-complete problems.
This is a quantum physics forum, not an engineering forum.
I'm thinking along these lines:
Oxford User's Guide to Mathematics
), sin cos and maybe complex numbers if you want understand rotation, a little bit integrals and diferentials to understand what a hell it is . That's all, everything over things is dublation of this things. And maybe combinatorics if you want understand what it is NP-complete problems. This is a quantum physics forum, not an engineering forum.
I'm thinking along these lines:
Oxford User's Guide to Mathematics
No such book exists. Even if you could cut and paste together your own book of 10,000 pages long would it be enough. 'Introductions to....' do not cover enough material and anything which attempts to cover enough topics fails to cover them in enough depth to recover all the topic.
If the scenario was something like :
All of Man's mathematical knowledge, save this book, was going to be wiped out and you wanted to provide the next generation of 'mathematicians' with the best base from which to recover, as rigorously and exacty as possible, our current knowledge of mathematics, what would you pass onto them?
Then I'd go for something like Principia Mathematica by Russell and Whitehead. It shows how mathematical logic works, really works and while there are VAST tracks of mathematics it doesn't cover (doesn't even touch geometry), it would provide those who study it with the method of thinking which has served current mathematicians so well. Things like "Logic is everything" or "No result is assumed, everything is proven". Sure, it doesn't provide any information on things like field theory, geometry, more advanced topics like topology etc, but it's the more solid foundation you could give a generation of mathematicians. It'd take years before that group's geniuses develop enough for the rest to make use of it (ie if you gave it to me, I'd be utterly unable to use it, but give it to a bunch of Cambridge mathematicians and 20 years later they'd have developed something I could then work on) but it'd set up the intellectual inertia for our mathematics to be redeveloped.
Introduction books wouldn't cover the rigour needed and while would show plenty more topics, they wouldn't emphasis the essential mathematical concepts needed.
If the scenario was something like :
All of Man's mathematical knowledge, save this book, was going to be wiped out and you wanted to provide the next generation of 'mathematicians' with the best base from which to recover, as rigorously and exacty as possible, our current knowledge of mathematics, what would you pass onto them?
Then I'd go for something like Principia Mathematica by Russell and Whitehead. It shows how mathematical logic works, really works and while there are VAST tracks of mathematics it doesn't cover (doesn't even touch geometry), it would provide those who study it with the method of thinking which has served current mathematicians so well. Things like "Logic is everything" or "No result is assumed, everything is proven". Sure, it doesn't provide any information on things like field theory, geometry, more advanced topics like topology etc, but it's the more solid foundation you could give a generation of mathematicians. It'd take years before that group's geniuses develop enough for the rest to make use of it (ie if you gave it to me, I'd be utterly unable to use it, but give it to a bunch of Cambridge mathematicians and 20 years later they'd have developed something I could then work on) but it'd set up the intellectual inertia for our mathematics to be redeveloped.
Introduction books wouldn't cover the rigour needed and while would show plenty more topics, they wouldn't emphasis the essential mathematical concepts needed.
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