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Symmetry is a classic study of symmetry in mathematics, the
sciences, nature, and art from one of the twentieth century's
greatest mathematicians. Hermann Weyl explores the concept of
symmetry beginning with the idea that it represents a harmony of
proportions, and gradually departs to examine its more abstract
varieties and manifestations--as bilateral, translatory,
rotational, ornamental, and crystallographic. Weyl investigates the
general abstract mathematical idea underlying all these special
forms, using a wealth of illustrations as support. Symmetry is a
work of seminal relevance that explores the great variety of
applications and importance of symmetry.
From the Preface: "The name of Hermann Weyl is enshrined in the
history of mathematics. A thinker of exceptional depth, and a
creator of ideas, Weyl possessed an intellect which ranged far and
wide over the realm of mathematics and beyond. His mind was sharp
and quick, his vision clear and penetrating. Whatever he touched he
adorned. His personality was suffused with humanity and compassion
and a keen aesthetic sensibility. Its fullness radiated charm. He
was young at heart to the end. By precept and example, he inspired
many mathematicians and influenced their lives. The force of his
ideas has affected the course of science. He ranks among the few
universalists of our time. This collection of papers is a tribute
to his genius. It is intended as a service to the mathematical
community....These papers will no doubt be a source of inspirations
to scholars through the ages." Volume IV comprises 46 articles
written between 1941 and 1953.
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Symmetry (Paperback)
Hermann Weyl
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R472
R389
Discovery Miles 3 890
Save R83 (18%)
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Ships in 10 - 15 working days
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Symmetry is a classic study of symmetry in mathematics, the
sciences, nature, and art from one of the twentieth century's
greatest mathematicians. Hermann Weyl explores the concept of
symmetry beginning with the idea that it represents a harmony of
proportions, and gradually departs to examine its more abstract
varieties and manifestations--as bilateral, translatory,
rotational, ornamental, and crystallographic. Weyl investigates the
general abstract mathematical idea underlying all these special
forms, using a wealth of illustrations as support. Symmetry is a
work of seminal relevance that explores the great variety of
applications and importance of symmetry.
In this, one of the first books to appear in English on the
theory of numbers, the eminent mathematician Hermann Weyl explores
fundamental concepts in arithmetic. The book begins with the
definitions and properties of algebraic fields, which are relied
upon throughout. The theory of divisibility is then discussed, from
an axiomatic viewpoint, rather than by the use of ideals. There
follows an introduction to "p"-adic numbers and their uses, which
are so important in modern number theory, and the book culminates
with an extensive examination of algebraic number fields.
Weyl's own modest hope, that the work "will be of some use," has
more than been fulfilled, for the book's clarity, succinctness, and
importance rank it as a masterpiece of mathematical exposition.
When mathematician Hermann Weyl decided to write a book on
philosophy, he faced what he referred to as "conflicts of
conscience"--the objective nature of science, he felt, did not mesh
easily with the incredulous, uncertain nature of philosophy. Yet
the two disciplines were already intertwined. In "Philosophy of
Mathematics and Natural Science," Weyl examines how advances in
philosophy were led by scientific discoveries--the more humankind
understood about the physical world, the more curious we became.
The book is divided into two parts, one on mathematics and the
other on the physical sciences. Drawing on work by Descartes,
Galileo, Hume, Kant, Leibniz, and Newton, Weyl provides readers
with a guide to understanding science through the lens of
philosophy. This is a book that no one but Weyl could have
written--and, indeed, no one has written anything quite like it
since.
This original anthology assembles eleven accessible essays by a
giant of modern mathematics. Hermann Weyl (1885-1955) made lasting
contributions to number theory as well as theoretical physics, and
he was associated with Princeton's Institute for Advanced Study,
the University of Gottingen, and ETH Zurich. Spanning the
1930s-50s, these articles offer insights into logic and relativity
theory in addition to reflections on the work of Weyl's mentor,
David Hilbert, and his friend Emmy Noether.
Subjects include "Topology and Abstract Algebra as Two Roads of
Mathematical Comprehension," "The Mathematical Way of Thinking,"
"Relativity Theory as a Stimulus in Mathematical Research," and
"Why is the World Four-Dimensional?" Historians of mathematics,
advanced undergraduates, and graduate students will appreciate
these writings, many of which have been long unavailable to
English-language readers.
In this renowned volume, Hermann Weyl discusses the symmetric,
full linear, orthogonal, and symplectic groups and determines their
different invariants and representations. Using basic concepts from
algebra, he examines the various properties of the groups. Analysis
and topology are used wherever appropriate. The book also covers
topics such as matrix algebras, semigroups, commutators, and
spinors, which are of great importance in understanding the
group-theoretic structure of quantum mechanics.
Hermann Weyl was among the greatest mathematicians of the
twentieth century. He made fundamental contributions to most
branches of mathematics, but he is best remembered as one of the
major developers of group theory, a powerful formal method for
analyzing abstract and physical systems in which symmetry is
present. In "The Classical Groups," his most important book, Weyl
provided a detailed introduction to the development of group
theory, and he did it in a way that motivated and entertained his
readers. Departing from most theoretical mathematics books of the
time, he introduced historical events and people as well as
theorems and proofs. One learned not only about the theory of
invariants but also when and where they were originated, and by
whom. He once said of his writing, "My work always tried to unite
the truth with the beautiful, but when I had to choose one or the
other, I usually chose the beautiful."
Weyl believed in the overall unity of mathematics and that it
should be integrated into other fields. He had serious interest in
modern physics, especially quantum mechanics, a field to which "The
Classical Groups" has proved important, as it has to quantum
chemistry and other fields. Among the five books Weyl published
with Princeton, "Algebraic Theory of Numbers" inaugurated the
"Annals of Mathematics Studies" book series, a crucial and enduring
foundation of Princeton's mathematics list and the most
distinguished book series in mathematics.
From the Preface: "The name of Hermann Weyl is enshrined in the
history of mathematics. A thinker of exceptional depth, and a
creator of ideas, Weyl possessed an intellect which ranged far and
wide over the realm of mathematics, and beyond. His mind was sharp
and quick, his vision clear and penetrating. Whatever he touched he
adorned. His personality was suffused with humanity and compassion,
and a keen aesthetic sensibility. Its fullness radiated charm. He
was young at heart to the end. By precept and example, he inspired
many mathematicians, and influenced their lives. The force of his
ideas has affected the course of science. He ranks among the few
universalists of our time. This collection of papers is a tribute
to his genius. It is intended as a service to the mathematical
community....These papers will no doubt be a source of inspirations
to scholars through the ages." Volume III comprises 52 articles
written between 1926 and 1940.
From the Preface: "The name of Hermann Weyl is enshrined in the
history of mathematics. A thinker of exceptional depth, and a
creator of ideas, Weyl possessed an intellect which ranged far and
wide over the realm of mathematics, and beyond. His mind was sharp
and quick, his vision clear and penetrating. Whatever he touched he
adorned. His personality was suffused with humanity and compassion,
and a keen aesthetic sensibility. Its fullness radiated charm. He
was young at heart to the end. By precept and example, he inspired
many mathematicians, and influenced their lives. The force of his
ideas has affected the course of science. He ranks among the few
universalists of our time. This collection of papers is a tribute
to his genius. It is intended as a service to the mathematical
community....These papers will no doubt be a source of inspirations
to scholars through the ages." Volume I comprises 29 articles
written between 1908 and 1917.
From the Preface: "The name of Hermann Weyl is enshrined in the
history of mathematics. A thinker of exceptional depth, and a
creator of ideas, Weyl possessed an intellect which ranged far and
wide over the realm of mathematics, and beyond. His mind was sharp
and quick, his vision clear and penetrating. Whatever he touched he
adorned. His personality was suffused with humanity and compassion,
and a keen aesthetic sensibility. Its fullness radiated charm. He
was young at heart to the end. By precept and example, he inspired
many mathematicians, and influenced their lives. The force of his
ideas has affected the course of science. He ranks among the few
universalists of our time. This collection of papers is a tribute
to his genius. It is intended as a service to the mathematical
community....These papers will no doubt be a source of inspirations
to scholars through the ages." Volume II comprises 38 articles
written between 1918 and 1926.
Dieser Text ist die Transkription einer Vorlesung zur
Funktionentheorie, die Hermann Weyl im Wintersemester 1910-11 an
der UniversitAt GAttingen gehalten hat, kurz vor der Entstehung
seines einflussreichen Buches A1/4ber Riemannsche FlAchen, das auf
der Fortsetzung dieser Vorlesung im Sommersemester 1911 beruht.
Weyl betont in dieser Vorlesung die kinematische Deutung
gebrochen-linearer Transformationen und die Beziehungen zwischen
konformen Abbildungen und StrAmungstheorie. HAhepunkt der Vorlesung
ist der Vergleich der Riemannschen und WeierstraAschen Behandlung
mehrdeutiger analytischer Funktionen durch Riemannsche FlAchen
beziehungsweise analytische Fortsetzung.
Aus dem Vorwort von Jurgen Ehlers zur 7. Auflage: "Die ...
Entwicklung der Physik macht verstandlich, warum ein so "altes"
Werk wie Raum, Zeit, Materie noch aktuell ist: Die
Riemann-Einsteinsche Raumzeitstruktur, die von Weyl so meisterhaft
beschrieben und aus ihren mathematischen und physikalischen Wurzeln
hervorwachsend dargestellt wird, ist immer noch die physikalisch
umfassendste und erfolgreichste Raumzeittheorie, die bisher
entwickelt und mit der Erfahrung konfrontiert wurde. (...) Als
erstes Lehrbuch der noch neuen Theorie setzt es sich grundlicher
als spatere Bucher mit den historischen Wurzeln und den sachlichen
Motiven auseinander, die zur Einfuhrung der damals neuen Begriffe
wie Zusammenhang und Krummung in die Physik gefuhrt haben. Zweitens
ist es von dem vielleicht letzten Universalisten geschrieben
worden, der alle wesentlichen Entwicklungen der Mathematik und
Physik seiner Zeit nicht nur uberblickte, sondern in wesentlichen
Teilen mitgestaltete. Das Studium dieses Werkes vermittelt nicht
nur die Grundzuge der beiden Relativitatstheorien, sondern zeigt
Zusammenhange mit anderen Ideen, nicht zuletzt auch der
Naturphilosophie auf.""
Ganz in Hermann Weyls bekannt klarer Darstellung geschrieben, gibt
dieser Beitrag einen Bericht uber die Entstehung der grundlegenden
Ideen, die der modernen Geometrie zugrunde liegen. Diese Schrift
spiegelt in einzigartiger Weise Weyls mathematische Personlichkeit
wider. Sie richtet sich an alle, die sich mit Fragen der
Topologiegruppentheorie, Differentialgeometrie und mathematischer
Physik beschaftigen. From the foreword of the editor K.
Chandrasekharan: "Written in Weyl's finest style, while he was
rising forty, the article is an authentic report on the genesis and
evolution of those fundamental ideas that underlie the modern
conception of geometry. Part I is on the continuum, and deals with
analysis situs, imbeddings, and coverings. Part II is on structure,
and deals with infinitesimal geometry in its many aspects, metric,
conformal, affine, and projective; with the question of
homogeneity, homogeneous spaces from the group-theoretical
standpoint, the role of the metric field theories in physics, and
the related problems of group theory. It is hoped that this article
will be of interest to all those concerned with the growth and
development of topology, group theory, differential geometry,
geometric function theory, and mathematical physics. It bears the
unmistakable imprint of Weyl's mathematical personality, and of his
remarkable capacity to capture and delineate the transmutation of
some of the nascent into the dominant ideas of the mathematics of
our time".
Das Studium von Hermann Weyls "Raum . Zeit . Materie" ist auch
heute noch lohnenswert. Als erste systematische Gesamtdarstellung
der speziellen und allgemeinen Relativitatstheorie einschliesslich
der zugehorigen Mathematik setzt es sich grundlich mit den
historischen Wurzeln auseinander. Die Betonung des Begriffs des
linearen Zusammenhangs unabhangig von der Metrik kommt der heutigen
Auffassung und den Verallgemeinerungen in den Eichtheorien
entgegen. Fur ein grundliches Verstandnis der modernen Eichtheorie
ist Weyls Buch immer noch eine wichtige Grundlage."
David Hilbert was one of the truly great mathematicians of his
time. His work and his inspiring scientific personality have
profoundly influenced the development of the mathematical sciences
up to the present time. His vision, his productive power and
independent originality as a mathematical thinker, his versatility
and breadth of interest made him a pioneer in many different
mathematical fields. He was a unique personality, profoundly
immersed in his work and totally dedicated to his science, a
teacher and leader of the very highest order, inspiring and most
generous, tireless and persistent in all of his efforts. To me, one
of the few survivors of Hilbert's inner circle, it always has
appeared most desirable that a biography should be published.
Considering, however, the enormous scientific scope of Hilbert's
work, it seemed to me humanly impossible that a single biographer
could do justice to all the as pects of Hilbert as a productive
scientist and to the impact of his radiant personality. Thus, when
I learned of Mrs. Reid's plan for the present book I was at first
skeptical whether somebody not thoroughly familiar with mathematics
could possibly write an acceptable book. Yet, when I saw the
manuscript my skepticism faded, and I became more and more
enthusiastic about the author's achievement. I trust that the book
will fascinate not only mathematicians but everybody who is
interested in the mystery of the origin of great scientists in our
society."
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