Includes Greek texts with associated translation
Contains several appendices and rich indices
Is of interest to linguists and historians of ancient philosophy
The aim of this monograph is to describe Greek mathematics as a literary product, studying its
style from a logico-syntactic point of view and setting parallels with logical and grammatical
doctrines developed in antiquity. In this way, major philosophical themes such as the
expression of mathematical generality and the selection of criteria of validity for arguments can
be treated without anachronism. Thus, the book is of interest for both historians of ancient
philosophy and specialists in Ancient Greek, in addition to historians of mathematics. This
volume is divided into five parts, ordered in decreasing size of the linguistic units involved. The
first part describes the three stylistic codes of Greek mathematics; the second expounds in
detail the mechanism of "validation"; the third deals with the status of mathematical objects
and the problem of mathematical generality; the fourth analyzes the main features of the
"deductive machine," i.e. the suprasentential logical system dictated by the traditional division of
a mathematical proposition into enunciation, setting-out, construction, and proof; and the fifth
deals with the sentential logical system of a mathematical proposition, with special emphasis
on quantification, modalities, and connectors. A number of complementary appendices are
included as well
1st ed. 2021, XII, 396 p. 12 illus., 9 illus. in color.
Hardcover
ISBN 978-3-030-76958-1
Product category : Monograph
Series : Sources and Studies in the History of Mathematics and Physical Sciences
Mathematics : History of Mathematics
Notions, Equivalences, and Lyapunov-like Characterizations
Offers a unified presentation of stability results for dynamical systems using
Lyapunov-like characterizations
Provides derivation of strong/weak complete instability results for systems in
terms of Lyapunov-like and comparison functions
Discusses combined stability and avoidance problem for control systems from
the perspective of Lyapunov functions
Lyapunov methods have been and are still one of the main tools to analyze the stability
properties of dynamical systems.In this monograph, Lyapunov results characterizing the
stability and stability of the origin of differential inclusions are reviewed.To characterize
instability and destabilizability, Lyapunov-like functions, called Chetaev and control Chetaev
functions in the monograph, are introduced. Based on their definition and by mirroring existing
results on stability, analogue results for instability are derived. Moreover, by looking at the
dynamics of a differential inclusion in backward time, similarities and differences between
stability of the origin in forward time and instability in backward time, and vice versa, are
discussed.Similarly, the invariance of the stability and instability properties of the equilibria of
differential equations with respect to scaling are summarized.As a final result, ideas combining
control Lyapunov and control Chetaev functions to simultaneously guarantee stability, i.e.,
convergence, and instability, i.e., avoidance, are outlined. The work is addressed at researchers
working in control as well as graduate students in control engineering and applied
mathematics
Due 2021-08-21
1st ed. 2021, IX, 116 p. 16 illus., 15 illus. in color.
Softcover
ISBN 978-3-030-76316-9
Product category : Brief
Series : SpringerBriefs in Mathematics
Mathematics : Mathematics (general)
Research Directions in Number Theory
Contains articles in number theory in abroad sense such us arithmetic
geometry, algebraic and analytic number theory, and applications in
cryptography and coding theory
The content of this book should be of interest to graduate students and
researchers in number theory
Showcases the outcomes of collaborative efforts from the WIN-E3 conference
This volume includes articles spanning several research areas in number theory, such as
arithmetic geometry, algebraic number theory, analytic number theory, and applications in
cryptography and coding theory. Most of the articles are the results of collaborations started at
the 3rdedition of the Women in Numbers Europe (WINE) conference between senior and midlevel
faculty, junior faculty, postdocs, and graduate students. The contents of this book should
be of interest to graduate students and researchers in number theory.
Due 2021-08-25
1st ed. 2021, X, 190 p. 30 illus., 8 illus. in color.
Hardcover
ISBN 978-3-030-77699-2
Product category : Contributed volume
Series : Association for Women in Mathematics Series
Mathematics : Number Theory
Presents the effect of perturbations in terms of analytic functions instead of
in terms of the more classical asymptotic expansions
Shows a powerful tool for the analysis of nonlinear and non-variational
boundary value problems
Presents a step-by-step exposition from the theoretical foundations of the
Functional Analytic Approach to the implementation in challenging problems
Provides an effective tool in the analysis of specific perturbation problems
arising in continuum mechanics and material sciences
Introductory style is accessible to a wide readership
This book is devoted to the analysis of the basic boundary value problems for the Laplace
equation in singularly perturbed domains. The main purpose is to illustrate a method called
Functional Analytic Approach, to describe the dependence of the solutions upon a singular
perturbation parameter in terms of analytic functions. Here the focus is on domains with small
holes and the perturbation parameter is the size of the holes. The book is the first introduction
to the topic and covers the theoretical material and its applications to a series of problems that
range from simple illustrative examples to more involved research results. TheFunctional
Analytic Approach makes constant use ofthe integral representation method for the solutions
of boundary value problems, of Potential Theory, of the Theory of Analytic Functions both in
finite and infinite dimension, and of Nonlinear Functional Analysis. Designed to servevarious
purposes and readerships, the extensive introductory part spanning Chapters 1?7 can be used
as a reference textbook for graduate courses on classical Potential Theory and its applications
to boundary value problems.
Due 2021-09-02
1st ed. 2021, XVI, 668 p. 4 illus.
Hardcover
ISBN 978-3-030-76258-2
Product category : Monograph
Mathematics : Partial Differential Equations
The differential forms formalism is explained through the classical theorems
of integrations and applied to obtain topological invariants
Includes applications to the study of harmonic functions and to the
formulation of the Maxwellfs equations using differential forms
Avoiding complicated notation
This book is divided into two parts, the first one to study the theory of differentiable functions
between Banach spaces and the second to study the differential form formalism and to
address the Stokes' Theorem and its applications. Related to the first part, there is an
introduction to the content of Linear Bounded Operators in Banach Spaces with classic
examples of compact and Fredholm operators, this aiming to define the derivative of Frechet
and to give examples in Variational Calculus and to extend the results to Fredholm maps. The
Inverse Function Theorem is explained in full details to help the reader to understand the
proof details and its motivations. The inverse function theorem and applications make up this
first part. The text contains an elementary approach to Vector Fields and Flows, including the
Frobenius Theorem. The Differential Forms are introduced and applied to obtain the Stokes
Theorem and to define De Rham cohomology groups. As an application, the final chapter
contains an introduction to the Harmonic Functions and a geometric approach to Maxwell's
equations of electromagnetism.
Due 2021-08-07
1st ed. 2021, XIV, 364 p. 69 illus., 26 illus. in color.
Hardcover
ISBN 978-3-030-77833-0
Product category : Graduate/advanced undergraduate textbook
Mathematics : Global Analysis and Analysis on Manifolds
Features numerous contributions on Hilbert's axiomatic method
Authored by leading experts in the subject
Addressed to logicians, philosophers, physicists and computer scientists with
an interest in foundations
In this two-volume compilation of articles, leading researchers reevaluate the success of
Hilbert's axiomatic method, which not only laid the foundations for our understanding of
modern mathematics, but also found applications in physics, computer science and elsewhere.
The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a
meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of
Hilbert's return to his foundational studies, which ultimately resulted in the establishment of
proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used
the opportunity to bring Paul Bernays back to Gottingen as his main collaborator in
foundational studies in the years to come.The contributions are addressed to mathematical and
philosophical logicians, but also to philosophers of science as well as physicists and computer
scientists with an interest in foundations.
Due 2021-09-22
1st ed. 2021, XVI, 216 p. 5 illus., 3 illus. in color.
Hardcover
ISBN 978-3-030-77656-5
Product category : Contributed volume
Mathematics : Mathematical Logic and Foundations
Features research in a broad variety of problems in different areas of graph theory
Each chapter offers an introduction to a graph theory topic of current
research, aiming at clarity and high-quality exposition while emphasizing
recent advances and open problems
Presents concepts and ideas thoroughly and with details
Each chapter corresponds to research proposed and led by prominent
research experts in each field
The Workshop for Women in Graph Theory and Applications was held at the Institute for
Mathematics and Its Applications (University of Minnesota, Minneapolis) on August 19-23,
2019. During this five-day workshop, 42 participants performed collaborative research, in six
teams, each focused on open problems in different areas of graph theory and its applications.
The research work of each team was led by two experts in the corresponding area, who prior
to the workshop, carefully selected relevant and meaningful open problems that would yield
high-quality research and results of strong impact. As a result, all six teams have made
significant contributions to several open problems in their respective areas. The workshop led
to the creation of the Women in Graph Theory and Applications Research Collaboration
Network, which provided the framework to continue collaborating and to produce this volume.
This book contains six chapters, each of them on one of the different areas of research at the
Workshop for Women in Graph Theory and Applications, and written by participants of each
team.
Due 2021-08-16
1st ed. 2021, IV, 196 p. 47 illus.
Hardcover
ISBN 978-3-030-77982-5
Product category : Contributed volume
Series : Association for Women in Mathematics Series
Mathematics : Graph Theory