Knapp, Anthony W.
Basic Algebra
Series: Cornerstones
2006, XXII, 717 p., 42 illus., Hardcover
ISBN-10: 0-8176-3248-4
ISBN-13: 978-0-8176-3248-9
About this textbook
Basic Algebra and Advanced Algebra systematically develop
concepts and tools in algebra that are vital to every
mathematician, whether pure or applied, aspiring or established.
Together, the two books give the reader a global view of algebra
and its role in mathematics as a whole.
Key topics and features of Basic Algebra:
・Linear algebra and group theory build on each other
continually
・Chapters on modern algebra treat groups, rings, fields, modules, and
Galois groups, with emphasis on methods of computation throughout
・Three prominent themes recur and blend together at times: the
analogy between integers and polynomials in one variable over a
field, the interplay between linear algebra and group theory, and
the relationship between number theory and geometry
・Many examples and hundreds of problems are included, along
with a separate 90-page section giving hints or complete solutions
for most of the problems
・The exposition proceeds from the particular to the general,
often providing examples well before a theory that incorporates
them; includes blocks of problems that introduce additional
topics and applications for further study
・Applications to science and engineering (e.g., the fast
Fourier transform, the theory of error-correcting codes, the use
of the Jordan canonical form in solving linear systems of
ordinary differential equations, and constructions of interest in
mathematical physics) appear in sequences of problems
Basic Algebra presents the subject matter in a forward-looking
way that takes into account its historical development. It is
suitable as a text in a two-semester advanced undergraduate or
first-year graduate sequence in algebra, possibly supplemented by
some material from Advanced Algebra at the graduate level. It
requires of the reader only familiarity with matrix algebra, an
understanding of the geometry and reduction of linear equations,
and an acquaintance with proofs.
Table of contents
Contents.- Preface.- Guide for the Reader.- Preliminaries about
the Integers, Polynomials, and Matrices.- Vector Spaces over Q,
R, and C.- Inner-Product Spaces.- Groups and Group Actions.-
Theory of a Single Linear Transformation.- Multilinear Algebra.-
Advanced Group Theory.- Commutative Rings and Their Modules.-
Fields and Galois Theory.- Modules over Noncommutative Rings.-
Appendix.- Index.
Bogachev, Vladimir I.
Measure Theory, 2 vols.
2006, XX, 1075 p., Hardcover
ISBN-10: 3-540-34513-2
ISBN-13: 978-3-540-34513-8
About this book
Measure theory is a classical area of mathematics born more than
two thousand years ago. Nowadays it continues intensive
development and has fruitful connections with most other fields
of mathematics as well as important applications in physics.
This book gives an exposition of the foundations of modern
measure theory and offers three levels of presentation: a
standard university graduate course, an advanced study containing
some complements to the basic course (the material of this level
corresponds to a variety of special courses), and, finally, more
specialized topics partly covered by more than 850 exercises.
Volume 1 (Chapters 1-5) is devoted to the classical theory of
measure and integral. Whereas the first volume presents the ideas
that go back mainly to Lebesgue, the second volume (Chapters 6-10)
is to a large extent the result of the later development up to
the recent years. The central subjects in Volume 2 are:
transformations of measures, conditional measures, and weak
convergence of measures. These three topics are closely
interwoven and form the heart of modern measure theory.
The organization of the book does not require systematic reading
from beginning to end; in particular, almost all sections in the
supplements are independent of each other and are directly linked
only to specific sections of the main part.
The target readership includes graduate students interested in
deeper knowledge of measure theory, instructors of courses in
measure and integration theory, and researchers in all fields of
mathematics. The book may serve as a source for many advanced
courses or as a reference.
Table of contents
Volume 1: Constructions and extensions of measures.- The Lebesgue
integral.- Operations on measures and functions.- The spaces L^p
and spaces of measures.- Connections between the integral and
derivative. Volume 2: Borel, Baire and Souslin sets.- Measures on
topological spaces.- Weak convergence of measures.-
Transformations of measures and isomorphisms.- Conditional
measures and conditional expectations.- Bibliographical and
Historical Comments.- References.- Author Index.- Subject Index.
Aletti, G.; Burger, M.; Micheletti, A.; Morale, D. (Eds.)
Math Everywhere
Deterministic and Stochastic Modelling in Biomedicine,
Economics and Industry
Dedicated to the 60th Birthday of Vincenzo Capasso
2006, XVIII, 343 p., 64 illus., 8 in colour, Hardcover
ISBN-10: 3-540-44445-9
ISBN-13: 978-3-540-44445-9
About this book
These proceedings are reporting on the conference ''Math
Everywhere", a successful event celebrating a leading
scientist, promoting ideas he pursued and sharing the open
atmosphere he is known for. The broad spectrum of contributions
to this volume illustrates that its title is correct. The areas
of the contributions are the following: Deterministic and
Stochastic Systems. Mathematical Problems in Biology, Medicine
and Ecology. Mathematical Problems in Industry and Economics.
Disciplinarity is basic for interdisciplinarity. This statement
seems to be trivial, however, everyone, not influenced by
fashionable trends and buzzwords entering more and more also
science, will find out that it is nontrivial at all in practice.
Competence in mathematics and the field of application are both
needed. The relevance of mathematical theory is getting more
obvious the more one faces the challenges of real life
applications. It is a well-known fact that mathematical modelling
of real problems very often leads to frontiers of mathematical
theory and requires new mathematical methods. This conference
combined competence in mathematical theory and methods with
competence in the fields of applications.
Table of contents
Louise Nyssen (Universite Montpellier, France), Editor
Physics and Number Theory
IRMA Lectures in Mathematics and Theoretical Physics Vol. 10
ISBN 978-3-03719-028-9
October 2006, 276 pages, softcover, 17.0 cm x 24.0 cm.
There is a rich and historical relationship between theoretical
physics and number theory. This volume presents a selection of
problems which are currently in full development and inspire a
lot of research going on. Each of the seven contributions starts
with an introductory survey which makes it possible even for non-specialists
to understand the results and to gain an idea of the great
variety of subjects and techniques used.
Topics covered are: phase locking in oscillating systems,
crystallography, Hopf algebras and renormalisation theory, Zeta-function
and random matrices, Kloosterman sums and the local Langlands
correspondence.
Intended for research mathematicians and theoretical physicists
as well as graduate students, this volume gives an overview of
recent developments in an exciting subject crossing several
disciplines
Table of contents
Autor(en): Sigmund, Karl / Dawson, John / Muhlberger, Kurt
Kurt Godel
Das Album - The Album
2006. 225 S. Mit 200 Abb.Mit einem Geleitwort von Hans Magnus Enzensberger
Geb.
ISBN: 978-3-8348-0173-9 - Sofort lieferbar
Godel fur Genieser - eine besonders anschauliche Einfuhrung in
sein Leben und Werk mit vielen Abbildungen
Time Magazine reihte ihn unter die hundert wichtigsten Personen
des zwanzigsten Jahrhunderts. Die Harvard University verlieh ihm
das Ehrendoktorat fur die Entdeckung "der bedeutsamsten
mathematischen Wahrheit des Jahrhunderts". Er gilt allgemein
als der groste Logiker seit Aristoteles. Sein Freund Einstein
ging, nach eigener Aussage, nur deshalb ans Institut, um Godel
auf dem Heimweg begleiten zu durfen. Und John von Neumann, einer
der Vater des Computers, schrieb: "Godel ist tatsachlich
absolut unersetzlich. Er ist der einzige Mathematiker, von dem
ich das zu behaupten wage."
Dieses Buch ist eine leichtverdauliche, einfache und anschauliche
Einfuhrung in Godels Leben und Werk, gedacht fur jene, die sich
fur die menschlichen und kulturellen Aspekte der Wissenschaft
interessieren. Ausgangspunkt des Buches waren die Vorbereitungen
zu einer Ausstellung uber Kurt Godel aus Anlass seines
hundertsten Geburtstags. Eine Ausstellung hat etwas von einem
Spaziergang an sich, und gerade das wollen wir bieten: einen
Spaziergang mit Godel. Albert Einstein genoss solche Spaziergange
sehr. Man kann also Godel geniesen.
Time Magazine ranked him among the hundred most important persons
of the twentieth century. Harvard University made him an honorary
doctor "for the discovery of the most significant
mathematical truth of the century". He is generally viewed
as the greatest logician since Aristotle. His friend Einstein
liked to say that he only went to the institute to have the
privilege of walking back home with Kurt Godel. And John von
Neumann, one of the fathers of the computer, wrote: "Indeed
Godel is absolutely irreplaceable. He is the only mathematician
about whom I dare make this assertion."
This book wants to give a simple, intuitive and easily digestible
introduction to Godel's life and work, meant for readers
interested in the human and cultural aspects of science. Its
starting point were the preparations for an exhibition on Kurt
Godel, on occasion of his hundredth
Giuseppe Della Sala, Alberto Saracco, Alexandru Simioniuc and Giuseppe Tomassini
Lectures on complex analysis and analytic geometry
This book is an introduction to the theory of holomorphic
functions of several complex variables. It is based on the
courses attended by the students of mathematics at Scuola Normale
Superiore of Pisa. Its treated subjects range from an advanced
undergraduate course to a Ph.D. level.
The book is largely divided into three parts. The first one,
perhaps the most curricular, deals with the domains of holomorphy
and their characterizations, through different notions of
convexity (holomorphic convexity, Leviconvexity and
pseudoconvexity) and the Cauchy-Riemann equation. The extension
of this matter to complex spaces, known as the Oka-Cartan theory,
is the content of the second part. This theory makes
systematically use of the local analytic geometry and of the
theory of sheaves and cohomology. The last part deals with the
interplay between the theory of topological algebras and the
theory of holomorphic functions. Some of the advanced results in
the field are overviewed, sometimes without detailed proofs, and
(still) open problems are discussed.
Giuseppe Della Sala, Alberto Saracco, Alexandru Simioniuc and Giuseppe
Tomassini, Lectures on complex analysis and analytic geometry. Pisa, Edizioni
della Normale 2006, ISBN 88-7642-199-8, pp. 447,