Description:

The only  way  to learn mathematics  is  to do mathematics. That tenet  is  the

foundation  of  the do-it-yourself, Socratic, or Texas method, the method in

which the teacher plays the role  of  an omniscient but largely uncommuni-

cative referee between the learner and the facts. Although that method  is

usually and perhaps necessarily oral, this book tries to use the same method

to  give  a written exposition  of  certain topics in Hilbert space theory.

The right way to read mathematics  is  first to read the definitions  of  the

concepts and the statements  of  the theorems, and then, putting the book

aside, to try to discover the appropriate proofs.  If  the theorems are not

trivial, the attempt might fail, but it  is  likely to  be  instructive just the same.

To the passive reader a routine computation and a miracle  of  ingenuity

come with equal ease, and later, when  he  must depend on himself,  he  will

find that they went as easily as they came. The active reader, who has found

out what does not work,  is  in  a much better position to understand the reason

for the success  of  the author's method, and, later, to  find  answers that are

not in books.

This book was written for the active reader. The first part consists  of

problems, frequently preceded  by  definitions and motivation, and some-

times followed  by  corollaries and historical remarks. Most  of  the problems

are statements to  be  proved, but some are questions (is it?, what is?), and

some are challenges (construct, determine). The second part, a very short

one, consists  of  hints. A hint  is  a word,  or  a paragraph, usually intended

to help the reader  find  a solution. The hint itself  is  not necessarily a con-

densed solution  of  the problem;  it  may just point to what I regard as the

heart  of  the matter. Sometimes a problem contains a trap, and the hint may

serve to chide the reader for rushing  in  too recklessly. The third part, the

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A Hilbert Space Problem Book PDF

392 Pages·1982·27.9649 MB·other
by  Paul R. Halmos
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About A Hilbert Space Problem Book

<p>The only&nbsp; way&nbsp; to learn mathematics&nbsp; is&nbsp; to do mathematics. That tenet&nbsp; is&nbsp; the</p><p>foundation&nbsp; of&nbsp; the do-it-yourself, Socratic, or Texas method, the method in</p><p>which the teacher plays the role&nbsp; of&nbsp; an omniscient but largely uncommuni-</p><p>cative referee between the learner and the facts. Although that method&nbsp; is</p><p>usually and perhaps necessarily oral, this book tries to use the same method</p><p>to&nbsp; give&nbsp; a written exposition&nbsp; of&nbsp; certain topics in Hilbert space theory.</p><p>The right way to read mathematics&nbsp; is&nbsp; first to read the definitions&nbsp; of&nbsp; the</p><p>concepts and the statements&nbsp; of&nbsp; the theorems, and then, putting the book</p><p>aside, to try to discover the appropriate proofs.&nbsp; If&nbsp; the theorems are not</p><p>trivial, the attempt might fail, but it&nbsp; is&nbsp; likely to&nbsp; be&nbsp; instructive just the same.</p><p>To the passive reader a routine computation and a miracle&nbsp; of&nbsp; ingenuity</p><p>come with equal ease, and later, when&nbsp; he&nbsp; must depend on himself,&nbsp; he&nbsp; will</p><p>find that they went as easily as they came. The active reader, who has found</p><p>out what does not work,&nbsp; is&nbsp; in&nbsp; a much better position to understand the reason</p><p>for the success&nbsp; of&nbsp; the author's method, and, later, to&nbsp; find&nbsp; answers that are</p><p>not in books.</p><p>This book was written for the active reader. The first part consists&nbsp; of</p><p>problems, frequently preceded&nbsp; by&nbsp; definitions and motivation, and some-</p><p>times followed&nbsp; by&nbsp; corollaries and historical remarks. Most&nbsp; of&nbsp; the problems</p><p>are statements to&nbsp; be&nbsp; proved, but some are questions (is it?, what is?), and</p><p>some are challenges (construct, determine). The second part, a very short</p><p>one, consists&nbsp; of&nbsp; hints. A hint&nbsp; is&nbsp; a word,&nbsp; or&nbsp; a paragraph, usually intended</p><p>to help the reader&nbsp; find&nbsp; a solution. The hint itself&nbsp; is&nbsp; not necessarily a con-</p><p>densed solution&nbsp; of&nbsp; the problem;&nbsp; it&nbsp; may just point to what I regard as the</p><p>heart&nbsp; of&nbsp; the matter. Sometimes a problem contains a trap, and the hint may</p><p>serve to chide the reader for rushing&nbsp; in&nbsp; too recklessly. The third part, the</p>

Detailed Information

Author:Paul R. Halmos
Publication Year:1982
ISBN:1468493329
Pages:392
Language:other
File Size:27.9649
Format:PDF
Price:FREE
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