From the reviews of the third edition: .,." It is unusual for a
reviewer to have the opportunity to review the first three editions
of a book - the first edition was published in 1998, the second in
2001 and the third in 2004. ... I was fortunate enough to obtain a
copy of the first edition while travelling in Europe in 1999 and I
spent many pleasant hours reading it carefully from cover to cover.
The style is inviting and it is very hard to stop part way through
a chapter. Indeed I have recommended the book to talented
undergraduates and to mathematically literate friends. All report
that they are captivated by the material and the new view of
mathematics it engenders. By now a number of reviews of the earlier
editions have appeared and I must simply agree that the book is a
pleasure to hold and to look at, it has striking photographs,
instructive pictures and beautiful drawings. The style is clear and
entertaining and the proofs are brilliant and memorable. ... David
Hunt, The Mathematical Gazette, Vol. 32, Issue 2, p. 127-128 "The
newest edition contains three completely new chapters. a ] The
approach is refreshingly straightforward, all the necessary results
from analysis being summarised in boxes, and a short appendix
discusses the importance of the zeta-function in number theory. a ]
this edition also contains additional material interpolated in the
original text, notably the Calkin-Wilf enumeration of the
rationals." (Gerry Leversha, The Mathematical Gazette, March, 2005)
"A lot of solid mathematics is packed into Proofs. Its thirty
chapters, divided into sections on Number Theory, Geometry,
Analysis a ] . Each chapter is largely independent; some
includenecessary background as an appendix. a ] The key to the
approachability of Proofs lies not so much in the accessibility of
its mathematics, however, as in the rewards it offers: elegant
proofs of interesting results, which dona (TM)t leave the reader
feeling cheated or disappointed." (Zentralblatt fA1/4r Didaktik de
Mathematik, July, 2004) From the reviews of the second edition:
.,." Thirty sections treat results drawn from number theory,
geometry (mainly combinatorial), analysis, combinatorics and graph
theory; these can be follwed by one versed in undergraduate
matheamtics including discrete topics. ... The authors have done a
fine job of arranging diverse material into a thematic progression.
... The presentation is clear and attractive with wide margins for
portraits, diagrams and sketches." E.J.Barbeau, Mathematical
Reviews, Issue 2000k " ... This is a wonderful book that can be
recommended to anybody who is in any way connected to mathematics.
Those who have ever experienced the beauty of mathematics will
experience the chill again. For those who have never experienced
that, this book is just the right one to start." Acta Scientiarum
Mathematicarum, 1999, Vol. 65, 769-770 .,." Inside PFTB (Proofs
from The Book) is indeed a glimpse of mathematical heaven, where
clever insights and beautiful ideas combine in astonishing and
glorious ways. There is vast wealth within its pages, one gem after
another. Some of the proofs are classics, but many are new and
brilliant proofs of classical results. ...Aigner and Ziegler do not
claim to have presented the definitive collection of great
mathematics. In their brief introduction they write: "We have no
definition orcharacterization of what constitutes a proof from THE
BOOK: all we offer is the examples that we have selected, hoping
that our readers will share our enthusiasm about brilliant ideas,
clever insights and wonderful observations." I do. ..." Notices of
the American Mathematical Society, August 1999 .,." This book is a
pleasure to hold and to look at: ample margins, nice photos,
instructive pictures, and beautiful drawings ... It is a pleasure
to read as well: the style is clear and entertaining, the level is
close to elementary, the necessary background is given separately,
and the proofs are brilliant. Moreover, the exposition makes them
transparent. ..." London Mathematical Society Newsletter, January
1999 .,." Clearly this second edition is dangerously suited to
infect the reader with the enthusiasm of the authors." J.Elstrodt
(MA1/4nster), Zentralblatt fA1/4r Mathematik 0978.00002
From the reviews of the third edition: , .." It is unusual for a
reviewer to have the opportunity to review the first three editions
of a book - the first edition was published in 1998, the second in
2001 and the third in 2004. ... I was fortunate enough to obtain a
copy of the first edition while travelling in Europe in 1999 and I
spent many pleasant hours reading it carefully from cover to cover.
The style is inviting and it is very hard to stop part way through
a chapter. Indeed I have recommended the book to talented
undergraduates and to mathematically literate friends. All report
that they are captivated by the material and the new view of
mathematics it engenders. By now a number of reviews of the earlier
editions have appeared and I must simply agree that the book is a
pleasure to hold and to look at, it has striking photographs,
instructive pictures and beautiful drawings. The style is clear and
entertaining and the proofs are brilliant and memorable. ... David
Hunt, The Mathematical Gazette, Vol. 32, Issue 2, p. 127-128 "The
newest edition contains three completely new chapters. ??? The
approach is refreshingly straightforward, all the necessary results
from analysis being summarised in boxes, and a short appendix
discusses the importance of the zeta-function in number theory. ???
this edition also contains additional material interpolated in the
original text, notably the Calkin-Wilf enumeration of the
rationals." (Gerry Leversha, The Mathematical Gazette, March, 2005)
"A lot of solid mathematics is packed into Proofs. Its thirty
chapters, divided intosections on Number Theory, Geometry, Analysis
??? . Each chapter is largely independent; some include necessary
background as an appendix. ??? The key to the approachability of
Proofs lies not so much in the accessibility of its mathematics,
however, as in the rewards it offers: elegant proofs of interesting
results, which don???t leave the reader feeling cheated or
disappointed." (Zentralblatt f??r Didaktik de Mathematik, July,
2004) From the reviews of the second edition: , .." Thirty sections
treat results drawn from number theory, geometry (mainly
combinatorial), analysis, combinatorics and graph theory; these can
be follwed by one versed in undergraduate matheamtics including
discrete topics. ... The authors have done a fine job of arranging
diverse material into a thematic progression. ... The presentation
is clear and attractive with wide margins for portraits, diagrams
and sketches." E.J.Barbeau, Mathematical Reviews, Issue 2000k " ...
This is a wonderful book that can be recommended to anybody who is
in any way connected to mathematics. Those who have ever
experienced the beauty of mathematics will experience the chill
again. For those who have never experienced that, this book is just
the right one to start." Acta Scientiarum Mathematicarum, 1999,
Vol. 65, 769-770 , .." Inside PFTB (Proofs from The Book) is indeed
a glimpse of mathematical heaven, where clever insights and
beautiful ideas combine in astonishing and glorious ways. There is
vast wealth within itspages, one gem after another. Some of the
proofs are classics, but many are new and brilliant proofs of
classical results. ...Aigner and Ziegler do not claim to have
presented the definitive collection of great mathematics. In their
brief introduction they write: "We have no definition or
characterization of what constitutes a proof from THE BOOK: all we
offer is the examples that we have selected, hoping that our
readers will share our enthusiasm about brilliant ideas, clever
insights and wonderful observations." I do. ..." Notices of the
American Mathematical Society, August 1999, .." This book is a
pleasure to hold and to look at: ample margins, nice photos,
instructive pictures, and beautiful drawings ... It is a pleasure
to read as well: the style is clear and entertaining, the level is
close to elementary, the necessary background is given separately,
and the proofs are brilliant. Moreover, the exposition makes them
transparent. ..." London Mathematical Society Newsletter, January
1999 , .." Clearly this second edition is dangerously suited to
infect the reader with the enthusiasm of the authors." J.Elstrodt
(M??nster), Zentralblatt f??r Mathematik 0978.00002
From the reviews of the third edition: ..." It is unusual for a
reviewer to have the opportunity to review the first three editions
of a book - the first edition was published in 1998, the second in
2001 and the third in 2004. ... I was fortunate enough to obtain a
copy of the first edition while travelling in Europe in 1999 and I
spent many pleasant hours reading it carefully from cover to cover.
The style is inviting and it is very hard to stop part way through
a chapter. Indeed I have recommended the book to talented
undergraduates and to mathematically literate friends. All report
that they are captivated by the material and the new view of
mathematics it engenders. By now a number of reviews of the earlier
editions have appeared and I must simply agree that the book is a
pleasure to hold and to look at, it has striking photographs,
instructive pictures and beautiful drawings. The style is clear and
entertaining and the proofs are brilliant and memorable. ... David
Hunt, The Mathematical Gazette, Vol. 32, Issue 2, p. 127-128"The
newest edition contains three completely new chapters. The approach
is refreshingly straightforward, all the necessary results from
analysis being summarised in boxes, and a short appendix discusses
the importance of the zeta-function in number theory. this edition
also contains additional material interpolated in the original
text, notably the Calkin-Wilf enumeration of the rationals." (Gerry
Leversha, The Mathematical Gazette, March, 2005)"A lot of solid
mathematics is packed into Proofs. Its thirty chapters, divided
into sections on Number Theory, Geometry, Analysis . Each chapter
is largely independent; some include necessary backgroundas an
appendix. The key to the approachability of Proofs lies not so much
in the accessibility of its mathematics, however, as in the rewards
it offers: elegant proofs of interesting results, which dont leave
the reader feeling cheated or disappointed." (Zentralblatt fr
Didaktik de Mathematik, July, 2004)From the reviews of the second
edition: ..." Thirty sections treat results drawn from number
theory, geometry (mainly combinatorial), analysis, combinatorics
and graph theory; these can be follwed by one versed in
undergraduate matheamtics including discrete topics. ... The
authors have done a fine job of arranging diverse material into a
thematic progression. ... The presentation is clear and attractive
with wide margins for portraits, diagrams and
sketches."E.J.Barbeau, Mathematical Reviews, Issue 2000k " ... This
is a wonderful book that can be recommended to anybody who is in
any way connected to mathematics. Those who have ever experienced
the beauty of mathematics will experience the chill again. For
those who have never experienced that, this book is just the right
one to start." Acta Scientiarum Mathematicarum, 1999, Vol. 65,
769-770 ..." Inside PFTB (Proofs from The Book) is indeed a glimpse
of mathematical heaven, where clever insights and beautiful ideas
combine in astonishing and glorious ways. There is vast wealth
within its pages, one gem after another. Some of the proofs are
classics, but many are new and brilliant proofs of classical
results. ...Aigner and Ziegler do not claim to have presented the
definitive collection of great mathematics. In their brief
introduction they write: "We have no definition or characterization
of whatconstitutes a proof from THE BOOK: all we offer is the
examples that we have selected, hoping that our readers will share
our enthusiasm about brilliant ideas, clever insights and wonderful
observations." I do. ..." Notices of the American Mathematical
Society, August 1999 ..." This book is a pleasure to hold and to
look at: ample margins, nice photos, instructive pictures, and
beautiful drawings ... It is a pleasure to read as well: the style
is clear and entertaining, the level is close to elementary, the
necessary background is given separately, and the proofs are
brilliant. Moreover, the exposition makes them transparent. ..."
London Mathematical Society Newsletter, January 1999..." Clearly
this second edition is dangerously suited to infect the reader with
the enthusiasm of the authors." J.Elstrodt (Mnster), Zentralblatt
fr Mathematik 0978.00002
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