Hindry, M., Universite de Paris, France
Silverman, J.H., Brown University, Providence, RI, USA
Diophantine Geometry
An Introduction
2000. Approx. 520 pp. 8 figs.
0-387-98975-7
This an introduction to diophantine geometry
at the advanced graduate
level. The book contains a proof of the
Mordell conjecture which will make it quite
attractive to graduate
students and professional mathematicians.
In the part of the book, the reader will
find numerous exercises.
Contents: The Geometry of Curves and Abelian Varieties.-
Height Functions.- Rational Points on Abelian
Varieties.- Diophantine Approximation and
Integral Points on Curves.-
Rational Points on Curves of Genus
Greater Than 2.- Further Results and Open
Problems.
Series: Graduate Texts in Mathematics.VOL. 201
Book category: Graduate Textbook
Publication language: English
Publication date: April 2000
Stahl, A., University of Bonn, Germany
Physics with Tau Leptons
2000. VIII, 316 pp. 236 figs.
3-540-66267-7
The book reviews the current status of tau
physics. It addresses the properties
of the tau lepton and summarizes
results achieved with tau leptons in the
fields of precision tests of the
Standard Model, investigations of the
strong interaction and many searches for
new physics beyond the scope of
the Standard Model.
Keywords: tau-lepton, heavy flavours, weak
and strong interactions, Standard
Model
Series: Springer Tracts in Modern Physics.VOL.
160
Fields: Nuclear Physics and Elementary Particle
Physics
Written for: Experimental
and theoretical physicists working in tau-Physics
Book category: Monograph
Publication language: English
Hedenmalm, H., University of Lund, Sweden
Korenblum, B., State University of New York at Albany, NY,
USA
Zhu, K., State University of New York at Albany, NY,
USA
Theory of Bergman Spaces
2000. Approx. 280 pp. 2 figs.
0-387-98791-6
Preliminary Text. Do not use. 15 years ago
the function theory and operator
theory connected with the Hardy
spaces was well understood (zeros; factorization;
interpolation; invariant
subspaces; Toeplitz and Hankel
operators, etc.). None of the techniques
that led to all the information
about Hardy spaces worked on their close
relatives the Bergman spaces. Most mathematicians
who worked in the intersection
of function theory and operator
theory thought that progress on the Bergman
spaces was unlikely. Now the
situation has completely changed.
Today there are rich theories describing
the Bergman spaces and their operators.
Research interest and research
activity in the area has been high for several
years. A book is badly needed
on Bergman spaces and the three
authors are the right people to write it.
Contents: The Bergman Spaces.- The Berezin Transform.-
A^p-Inner Functions.- Zero Sets for Bergman
Spaces.- Invariant Subspaces.- Interpolation
and Sampling.- Cyclic Vectors.
Series: Graduate Texts in Mathematics.VOL. 199
Fields: Complex Analysis; Functional Analysis,Operator
Theory
Written for: Mathematicians
and students
Book category: Graduate
Textbook
Publication language: English
Publication date: May 2000
Hartshorne, R., University of California, Berkeley, CA, USA
Geometry: Euclid and Beyond
2000. Approx. 350 pp. 513 figs.
0-387-98650-2
This book offers a unique opportunity to
understand the essence of one
of the great thinkers of western
civilization. A guided reading of Euclid's
Elements leads to a critical
discussion and rigorous modern treatment
of Euclid's geometry and its more recent
descendants. Also included are
complete proofs, introduction of
coordinates, the theory of area, geometrical
constructions and finite field
extensions, history of the parallel
postulate, the various non-Euclidean geometries,
and the regular and semi-regular
polyhedra. The text is
intended for junior-senior level mathematics
majors. Robin Hartshorne is
a professor of mathematics at the
University of California, Berkeley and is
the author of Foundations of
Projective Geometry (Benjamin, 1967) and
Algebraic Geometry (Springer, 1977).
Contents: Euclid's Geometry.- Hilbert's Axioms.-
Geometry over Fields.- Segment Arithmetic.-
Area.-
Construction Problems and Field Extensions.-
Non-Euclidean Geometry.- Polyhedra.
Series: Undergraduate Texts in Mathematics.
Fields: Axiomatic, Affine, Euclidean, Projective,
Analytic Geometry
Written for: Undergraduate
math students, math teachers
Book category: Undergraduate
Textbook
Publication language: English
Publication date: June 2000
Serre, J.-P., College de France, Paris, France
Local Algebra - Multiplicities
2000. XIII, 119 pp.
3-540-66641-9
This is an English translation of the now
classic "Algebre Locale - Multiplicites"
originally published by Springer
as LNM 11, in several editions since 1965.
It gives a short account of
the main theorems of commutative algebra,
with emphasis on modules, homological methods
and intersection multiplicities
("Tor-formula"). Many
modifications to the original French text
have been made by the author
for this English edition: They make the
text easier to read, without changing its
intended informal character".
Keywords: commutative algebra, Tor-formula, intersection
multiplicity
Contents: Prime Ideals and Localization.- Tools.-
Dimension Theory.- Homological Dimension
and Depth.-
Multiplicities.
Series: Springer Monographs in Mathematics.
Fields: Algebra
Written for: Researchers
and graduate students in algebra and algebraic
geometry
Book category: Monograph
Publication language: English
Publication date: June 2000
Osborne, M.S., University of Washington, Seattle, WA, USA
Basic Homological Algebra
2000. Approx. 365 pp.
0-387-98934-X
Preliminary text. Do not use. This book is
intended for one-quarter or one semester-courses
in homological
algebra. The aim is to cover Ext and Tor
early and without distraction.
It includes several further topics, which
can be pursued independently of each other.
Many of these, such as Lazard's
theorem, long exact sequences in
Abelian categories with no cheating, or the
relation between Krull dimension
and global dimension, are hard to
find elsewhere. The intended audience is
second or third year graduate
students in algebra, algebraic topology,
or
any other field that uses homological algebra.
Contents: Categories.- Modules.- Ext and Tor.- Dimension
Theory.- Change of Rings.- Derived Functors.-
Abstract Homological Algebra.- Colimits and
Tor.- Odds and Ends.
Series: Graduate Texts in Mathematics.VOL. 196
Fields: Category Theory, Homological Algebra, Algebraic
K-Theory
Written for: Graduate math
students, mathematicians
Book category: Graduate
Textbook
Publication language: English
Publication date: June 2000
Robert, A., University of Neuchatel, Switzerland
A Course in p-adic Analysis
2000. Approx. 400 pp. 27 figs.
0-387-98669-3
Preliminary Text. Do not use. Kurt Hensel
(1861-1941) discovered the p-adic
numbers around the turn of the
century. These exotic numbers (or so they
appeared at first) are now well-established
in the mathematical world
and used more and more by physicists as well.
This book offers a self-contained
presentation of basic p-adic
analysis. The author is especially interested
in the analytical topics
in this field. Some of the features which
are
not treated in other introductory p-adic
analysis texts are topological
models of p-adic spaces inside Euclidean
space, a construction of spherically complete
fields, a p-adic mean value
theorem and some consequences, a
special case of Hazewinkel's functional equation
lemma, a remainder formula
for the Mahler expansion, and most
importantly a treatment of analytic elements.
Contents: P-adic numbers.- Finite extensions of the
field of p-adic numbers.- Constructions of
universal p-adic
Fields.- Continuous functions.- Calculus.- Analytic
functions and elements.- Special functions.-
Congruences.
Series: Graduate Texts in Mathematics.VOL. 198
Fields: Number Theory
Written for: Graduate math
students, mathematicians
Book category: Graduate
Textbook
Publication language: English
Publication date: June 2000