Due 2017-12-17
1st ed. 2017, XVIII, 277 p.
10 illus., 6 illus. in color.
Printed book
Softcover
ISBN 978-3-319-69427-6
Provides a self-contained introduction to the construction of integers,
rationals, reals, complex numbers and Hamilton's quaternions
Develops the basic prerequisites in group and ring theory as well as elementary number theory
Contains appendices to each chapter highlighting the ubiquity of the material
Includes more than 100 exercises with solutions
This textbook offers an invitation to modern algebra through number systems of increasing
complexity, beginning with the natural numbers and culminating with Hamilton's quaternions.
Along the way, the authors carefully develop the necessary concepts and methods from
abstract algebra: monoids, groups, rings, fields, and skew fields. Each chapter ends with an
appendix discussing related topics from algebra and number theory, including recent
developments reflecting the relevance of the material to current research. The present volume
is intended for undergraduate courses in abstract algebra or elementary number theory. The
inclusion of exercises with solutions also makes it suitable for self-study and accessible to
anyone with an interest in modern algebra and number theory.
Due 2018-02-05
1st ed. 2017, XVI, 404 p. 1
illus. in color.
Printed book
Hardcover
ISBN 978-3-319-71305-2
Series
Springer Monographs in Mathematics
Provides the homotopy theoretic foundations for surgery theory
Includes a self-contained account of the Hopf invariant in terms of Z_2-
equivariant homotopy
Covers applications of the Hopf invariant to surgery theory, in particular the
Double Point Theorem
Written by leading experts in the field, this monograph provides homotopy theoretic
foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a
modern framework, the authors carefully highlight how their results relate to (and generalize)
existing results in the literature. The central result of the book expresses algebraic surgery
theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory
which captures the double points of immersions. Many illustrative examples and applications of
the abstract results are included in the book, making it of wide interest to topologists. Serving
as a valuable reference, this work is aimed at graduate students and researchers interested in
understanding how the algebraic and geometric topology fit together in the surgery theory of
manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf
invariant, double points and surgery theory, with many results old and new.
Due 2018-03-29
1st ed. 2018, Approx. 150 p.
29 illus., 22 illus. in color.
Printed book
Softcover
ISBN 978-3-319-71427-1
Series
Lecture Notes in Mathematics
Perfectly suited for young researchers who want to become acquainted with
this important field and its open problems
Contains a very timely exposition of the state of the art on the subject, with
an eye to both classical and very recent developments
Exceptionally well written in a rigorous but also charming style
Presenting a selection of recent developments in geometrical problems inspired by the N-body
problem, these lecture notes offer a variety of approaches to study them, ranging from
variational to dynamical, while developing new insights, making geometrical and topological
detours, and providing historical references. A. Guillotfs notes aim to describe differential
equations in the complex domain, motivated by the evolution of N particles moving on the
plane subject to the influence of a magnetic field. Guillot studies such differential equations
using different geometric structures on complex curves (in the sense of W. Thurston) in order
to find isochronicity conditions. R. Montgomeryfs notes deal with a version of the planar
Newtonian three-body equation. Namely, he investigates the problem of whether every free
homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical
systems, and the McGehee blow-up. A novelty of the approach is the use of energy-balance in
order to motivate the McGehee transformation. A. Pedrozafs notes provide a brief introduction
to Lagrangian Floer homology and its relation to the solution of the Arnolfd conjecture on the
minimal number of non-degenerate fixed points of a Hamiltonian diffeomorphism.
Due 2018-05-13
1st ed. 2018, Approx. 130 p.
Printed book
Softcover
ISBN 978-3-319-71332-8
Series
Lecture Notes in Mathematics
No prerequisites required to fully understand an active research line
Full proofs of all the main results
Systematic study of spear operators for the first time in a book
This monograph is devoted to the study of spear operators, that is, bounded linear operators
$G$ between Banach spaces $X$ and $Y$ satisfying that for every other bounded linear
operator $T:X\longrightarrow Y$ there exists a modulus-one scalar $\omega$ such that $\|G
+ \omega\,T\|=1+ \|T\|$. This concept extends the properties of the identity operator in those
Banach spaces having numerical index one. Many examples among classical spaces are
provided, being one of them the Fourier transform on $L_1$. The relationships with the Radon-
Nikodym property, with Asplund spaces and with the duality, and some isometric and
isomorphic consequences are provided. Finally, Lipschitz operators satisfying the Lipschitz
version of the equation above are studied. The book could be of interest to young
researchers and specialists in functional analysis, in particular to those interested in Banach
spaces and their geometry. It is essentially self-contained and only basic knowledge of
functional analysis is needed.
Due 2018-07-14
1st ed. 2018, Approx. 300 p.
Printed book
Hardcover
ISBN 978-3-319-70823-2
Series
Trends in Mathematics
Collection of lecture notes, written by experts in the field of inverse problems
Contributions present a perspective on the current research trends on
selected research topics
Fosters the disciplinary and interdisciplinary in Numerical Analysis and
Mechanical Engineering
The Proceedings volume contains 16 contributions to the IMPA conference gNew Trends in
Parameter Identification for Mathematical Modelsh, Rio de Janeiro, Oct 30 ? Nov 3, 2017,
integrating the gChemnitz Symposium on Inverse Problems on Tourh. This conference is part
of the gThematic Program on Parameter Identification in Mathematical Modelsh organized at
IMPA in October and November 2017. One goal is to foster the scientific collaboration between
mathematicians and engineers from the Brazialian, European and Asian communities. Main
topics are iterative and variational regularization methods in Hilbert and Banach spaces for the
stable approximate solution of ill-posed inverse problems, novel methods for parameter
identification in partial differential equations, problems of tomography , solution of coupled
conduction-radiation problems at high temperatures, and the statistical solution of inverse
problems with applications in physics.