The Enjoyment of Math by Hans Rademacher download in iPad, ePub, pdf
Finally - this is a difficult book, though never an impossible one. But this is also true with music. No mention is made of differential or integral calculus. Finally, other books have discussed the foundations of mathematics with regard to their general philosophical validity. But by the same token, only very few are musically gifted in that they are able to compose music.
On the other hand, many books have been written on mathematical games and pastimes. This means that we must omit something that is quite essential in the nature of the mathematical edifice, the great and surprising cross-connections that permeate this edifice in all directions.
Fortunately, the difficulty is a function of the material, not its presentation, so it never feels unfair. In the case of a small work of music it may not only be the line of melody with which it opens that makes it beautiful.
This is not our intention here. For the most part, the problems are pretty awesome. If he does this, he will find no difficulty in grasping the essential ideas of each subject.
On the other hand, that wall very often limits the view of him who stays within. This book is intended to give samples of the diversified phenomena which comprise mathematics, of mathematics for its own sake, and of the intrinsic values which it possesses. What goes on behind that wall is, for the most part, a secret to the layman.
Otto Toeplitz Introduction Mathematics, because of its language and notation and its oddlooking special symbols, is closed off from the surrounding world as by a high wall. Presupposing only a minimal foundation of background knowledge and using nothing but deductive reasoning, this book presents varied and ingenious proofs of some fascinating results.
But besides the great works of music there are the smaller pieces which have something of true sublimity and whose spirit reveals itself to everyone. He thinks of dull uninspiring numbers, of a lifeless mechanism which functions according to laws of inescapable necessity. Your reaction to the above paragraph is a good indicator as to whether or not you'll enjoy this book. This book will definitely not change your mind. Only he who has listened attentively to the basic theme will fully perceive and understand this climax.
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