Series: Modern Birkhauser Classics
Originally published as a monograph
1st ed. 1984. 4th printing, 2007, XXII, 376 p., 18 illus.,
Softcover
ISBN-10: 0-8176-4565-9
ISBN-13: 978-0-8176-4565-6
About this book
Number Theory or arithmetic, as some prefer to call it, is the
oldest, purest, liveliest, most elementary yet sophisticated
field of mathematics. It is no coincidence that the fundamental
science of numbers has come to be known as the "Queen of
Mathematics." Indeed some of the most complex conventions of
the mathematical mind have evolved from the study of basic
problems of number theory.
Andre Weil, one of the outstanding contributors to number theory,
has written an historical exposition of this subject; his study
examines texts that span roughly thirty-six centuries of
arithmetical work ? from an Old Babylonian tablet, datable to the
time of Hammurapi to Legendrefs Essai sur la Theorie des
Nombres (1798). Motivated by a desire to present the substance of
his field to the educated reader, Weil employs an historical
approach in the analysis of problems and evolving methods of
number theory and their significance within mathematics. In the
course of his study Weil accompanies the reader into the
workshops of four major authors of modern number theory (Fermat,
Euler, Lagrange and Legendre) and there he conducts a detailed
and critical examination of their work. Enriched by a broad
coverage of intellectual history, Number Theory represents a
major contribution to the understanding of our cultural heritage
Table of contents
Preface.- Table of illustrations.- Abbreviations, basic
references and notations.- Protohistory.- Fermat and his
Correspondents.- Euler.- An Age of Transition: Lagrange and
Legendre.- Additional bibliography and references.- Index nominum.-
Index rerum.
Series: Progress in Mathematics , Vol. 260
2007, Approx. 445 p., Hardcover
ISBN-10: 3-7643-8283-X
ISBN-13: 978-3-7643-8283-4
About this book
This volume comprises lecture notes, survey and research articles
originating from the CIMPA Summer School Arithmetic and Geometry
around Hypergeometric Functions held at Galatasaray University,
Istanbul during June 13-25, 2005. A wide range of topics related
to hypergeometric functions is covered, thus giving a broad
perspective of the state of the art in the field.
Written for:
Graduates, postgraduates and researchers
Keywords:
K3 surface
hyperbolic geometry
hypergeometric function
moduli space
Table of contents
Preface.- Contributions by D. Allcock, F. Beukers, J.A. Carlson,
I.V. Dolgachev, A. Dzambic, R.-P. Holzapfel, A.N. Kochubei, S.
Kondo, E. Looijenga, K. Matsumoto, T. Riedel, H. Shiga, J.
Stienstra, D. Toledo, A.M. Uludag, J. Wolfart, M. Yoshida.-
Problem Session.
Series: Operator Theory: Advances and Applications , Vol. 174
2007, Approx. 270 p., Hardcover
ISBN-10: 3-7643-8134-5
ISBN-13: 978-3-7643-8134-9
About this book
This volume contains lectures delivered by the participants of
the International Conference Operator Theory and its Applications
in Mathematical Physics (OTAMP 2004), held at the Mathematical
Research and Conference Center in Bedlewo near Poznan, Poland.
The idea behind these lectures was to present interesting
ramifications of operator methods in current research of
mathematical physics. The main topics are functional models of
non-selfadjoint operators, spectral properties of Dirac and
Jacobi matrices, Dirichlet-to-Neumann techniques, Lyapunov
exponents methods, and inverse spectral problems for quantum
graphs.
Table of contents
Introduction.- Contributions by P.A. Cohujari, M. Combescure, P.
Exner, R.L. Frank, T. Ichinose, A.V. Kiselev, S. Kondej, J.
Michor, A.B. Mikhailova, M. Nowaczyk, B.S. Pavlov, V.I. Ryzhii, V.
Ryzhof, H. Schulz-Baldes, R.G. Shterenberg, L.O. Silva, S.
Simonov, G. Teschl, A. Tikhonov.
*
Series: Operator Theory: Advances and Applications , Vol. 175
2007, Approx. 255 p., Hardcover
ISBN-10: 3-7643-8269-4
ISBN-13: 978-3-7643-8269-8
About this book
This volume contains contributions written by participants of the
4th Workshop on Operator Theory in Krein Spaces and Applications,
which was held at the TU Berlin, Germany, December 17 to 19, 2004.
The workshop covered topics from spectral, perturbation and
extension theory of linear operators and relations in inner
product spaces, including spectral analysis of differential
operators, the theory of generalized Nevanlinna functions and
related classes of functions, spectral theory of matrix
polynomials, and problems from scattering theory.
Table of contents
Preface.- Contributions by T.Ya. Azizov, J. Behrndt, V. Derkach,
A. Fleige, K.-H. Forster, S. Hassi, P. Jonas, M. Kaltenback, I.
Karabash, A. Kostenko, H. Langer, A. Luger, C. Mehl, B. Nagy, H.
Neidhardt, V. Pivovarchik, J. Rehberg, L. Rodman, A. Sandovici, L.I.
Soukhotcheva, H. de Snoo, C. Trunk, H. Winkler, H. Woracek
Series: Progress in Mathematics , Vol. 259
2007, Approx. 230 p., Hardcover
ISBN-10: 3-7643-8132-9
ISBN-13: 978-3-7643-8132-5
About this book
This book gives an up-to-date account of progress on Pansu's
celebrated 1982 problem on the sub-Riemannian isoperimetric
profile of the Heisenberg group, while simultaneously serving as
an introduction to the general field of sub-Riemannian geometric
analysis in this restricted context. The focus is on developing
the methods and tools of sub-Riemannian differential geometry,
nonsmooth analysis, and geometric measure theory suitable for
attacks on Pansu's problem and other questions in the sub-Riemannian
calculus of variations.
Written for:
Graduate students and researchers in Analysis, Geometry, and
Mathematical Physics
Keywords:
Cauchy-Riemann manifold
Sobolev space
contact geometry
evolution equations
geometric measure theory
immersions
minimal surface
quasiconformal mapping
sub-Riemannian geometry
Table of contents
Preface.- 1. The Isoperimetric Problem.- 2. The Heisenberg Group.-
3. Horizontal Geometry of Submanifolds.- 4. Geometric Measure
Theory.- 5. The Isoperimetric Inequality.- 6. The Isoperimetric
Profile of the Heisenberg Group.- 7. Sharp Constants for Other
Geometric Inequalities.- Bibliography.- Index.
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