1st ed. 2018, X, 444 p. 33
illus., 1 illus. in color.
Hardcover
ISBN 978-981-13-1773-6
Series
Sources and Studies in the History of Mathematics and Physical Sciences
Highlights the exceptionally fruitful periods of the millennia-long history of
the mathematical tradition of India
Discusses about the period of the construction of the now-universal system of
decimal numeration and of a framework for planar geometry
Reviews about about the classical period inaugurated by Aryabhata’s
invention of trigonometry and the principles of discrete calculus
Talks about the phase of Madhava, which produced a rigorous infinitesimal
calculus of such functions
This book identifies three of the exceptionally fruitful periods of the millennia-long history of
the mathematical tradition of India: the very beginning of that tradition in the construction of
the now-universal system of decimal numeration and of a framework for planar geometry; a
classical period inaugurated by Aryabhata’s invention of trigonometry and his enunciation of
the principles of discrete calculus as applied to trigonometric functions; and a final phase that
produced, in the work of Madhava, a rigorous infinitesimal calculus of such functions. The main
highlight of this book is a detailed examination of these critical phases and their
interconnectedness, primarily in mathematical terms but also in relation to their intellectual,
cultural and historical contexts. Recent decades have seen a renewal of interest in this history,
as manifested in the publication of an increasing number of critical editions and translations of
texts, as well as in an informed analytic interpretation of their content by the scholarly
community. The result has been the emergence of a more accurate and balanced view of the
subject, and the book has attempted to take an account of these nascent insights. As part of
an endeavour to promote the new awareness, a special attention has been given to the
presentation of proofs of all significant propositions in modern terminology and notation, either
directly transcribed from the original texts or by collecting together material from several texts.
Series
Mathematiques et Applications
1re d. 2018, XXXI, 511 p.
Printed book
Softcover
ISBN 978-3-319-93724-3
Cet ouvrage presente les types d'arbres les plus utilises en informatique, sous les angles
algorithmique et mathematique. Pour chaque type, nous donnons les algorithmes courants
associes et des exemples d'utilisation, directe ou en modelisation, puis nous etudions leurs
performances d'un point de vue mathematique. Nos outils sont les mathematiques discretes,
les probabilites et la combinatoire analytique, presentes ici simultanement. Le public vise est
d'abord celui des etudiants de niveau master scientifique ou en derniere annee d’ecole d’
ingenieurs avec un cursus prealable en informatique ou en mathematiques, ou ceux visant une
double competence en mathematiques et informatique ; ainsi que toute personne dotee d’un
bagage scientifique ≪ minimal ≫ et amenee a utiliser des structures arborescentes liees a des
algorithmes, qui souhaiterait avoir une meilleure connaissance de ces structures et une idee
des performances des algorithmes associes sans se plonger dans les travaux originaux.
This book presents a wide range of tree structures, from both a computer science and a
mathematical point of view. For each of these structures we give the algorithms that allow us
to visit or update the structure, and discuss their potential uses, either directly (for storing
data) or in modelling a variety of situations. We present a mathematical approach to their
performances; this is done by the systematic and parallel use of tools from discrete
mathematics, probability and analytic combinatorics. The book is intended for graduate
students in mathematics or computer science (or both) and in engineering schools. It is also
suitable for anyone with a basic level of scientific knowledge who may have to use tree
structures and related algorithms, and who wishes to get a rigorous knowledge of their
performance without going back to the original, often specialized, results.
Softcover
Scalar Linear Systems and Affine Algebraic Geometry
Series: Modern Birkhauser Classics
Provides a clear presentation of the core ideas in the algebra-geometric
treatment of scalar linear system theory with an applied flavor
Makes the basic ideas of algebraic geometry accessible to engineers and
applied scientists
Introduces the four representations of a scalar linear system and establishes
the major results of a similar theory for multivariable systems
"An introduction to the ideas of algebraic geometry in the motivated context of system theory."
Thus the author describes his textbook that has been specifically written to serve the needs of
students of systems and control. Without sacrificing mathematical care, the author makes the
basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis
is on constructive methods and clarity rather than abstraction. The student will find here a
clear presentation with an applied flavor, of the core ideas in the algebra-geometric treatment
of scalar linear system theory. The author introduces the four representations of a scalar linear
system and establishes the major results of a similar theory for multivariable systems
appearing in a succeeding volume (Part II: Multivariable Linear Systems and Projective
Algebraic Geometry). Prerequisites are the basics of linear algebra, some simple notions from
topology and the elementary properties of groups, rings, and fields, and a basic course in
linear systems. Exercises are an integral part of the treatment and are used where relevant in
the main body of the text. The present, softcover reprint is designed to make this classic
textbook available to a wider audience. "This book is a concise development of affine algebraic
geometry together with very explicit links to the applications...[and] should address a wide
community of readers, among pure and applied mathematicians." Monatshefte fur Mathematik
1st ed. 2018, X, 284 p. 51
illus., 15 illus. in color.
Hardcover
ISBN 978-3-319-97684-6
Favorite Conjectures and Open Problems - 2
Describes the origin and history behind conjectures and problems in graph
theory
Provides various methods to solving research problems in the field
Provides strong pedagogical content for graduate students and a reference to
researchers in the field
Includes an annotated glossary of nearly 300 parameters and 600 references
This second volume in a two-volume series provides an extensive collection of conjectures and
open problems in graph theory. It is designed for both graduate students and established
researchers in discrete mathematics who are searching for research ideas and references. Each
chapter provides more than a simple collection of results on a particular topic; it captures the
reader’s interest with techniques that worked and failed in attempting to solve particular
conjectures. The history and origins of specific conjectures and the methods of researching
them are also included throughout this volume. Students and researchers can discover how
the conjectures have evolved and the various approaches that have been used in an attempt to
solve them. An annotated glossary of nearly 300 graph theory parameters, 70 conjectures, and
over 600 references is also included in this volume. This glossary provides an understanding of
parameters beyond their definitions and enables readers to discover new ideas and new
definitions in graph theory. The editors were inspired to create this series of volumes by the
popular and well-attended special sessions entitled “My Favorite Graph Theory Conjectures,”
which they organized at past AMS meetings. These sessions were held at the winter AMS/MAA
Joint Meeting in Boston, January 2012, the SIAM Conference on Discrete Mathematics in
Halifax in June 2012, as well as the winter AMS/MAA Joint Meeting in Baltimore in January
2014, at which many of the best-known graph theorists spoke. In an effort to aid in the
creation and dissemination of conjectures and open problems, which is crucial to the growth
and development of this field, the editors invited these speakers, as well as other experts in
graph theory, to contribute to this series.
1st ed. 2018, XV, 555 p. 43
illus., 14 illus. in color.
Hardcover
ISBN 978-3-319-96826-1
Algebra, and Related Topics
Festschrift for Antonio Campillo on the Occasion of his 65th Birthday
Brings together recent, original research and survey articles by leading
experts in several fields
Honors the distinguished and prolific mathematician, Antonio Campillo
Papers are grouped into five categories: Singularities, Algebraic Geometry,
Commutative Algebra, Algebraic Codes and Other Topics
This volume brings together recent, original research and survey articles by leading experts in
several fields that include singularity theory, algebraic geometry and commutative algebra. The
motivation for this collection comes from the wide-ranging research of the distinguished
mathematician, Antonio Campillo, in these and related fields. Besides his influence in the
mathematical community stemming from his research, Campillo has also endeavored to
promote mathematics and mathematicians' networking everywhere, especially in Spain, Latin
America and Europe. Because of his impressive achievements throughout his career, we
dedicate this book to Campillo in honor of his 65th birthday. Researchers and students from
the world-wide, and in particular Latin American and European, communities in singularities,
algebraic geometry, commutative algebra, coding theory, and other fields covered in the
volume, will have interest in this book.