Represents a wide range of research trends in the area of commutative and
noncommutative ring theory and their modules, with an emphasis on the
interaction between quite different viewpoints and techniques
Shows that how diverse types of algebraic structures and contexts (rings,
modules, semigroups, categories) may be treated with overlapping and
reinforcing approaches
Is an excellent resource for scholars in the fields represented, as well as
graduate students seeking an entryway into current research in algebra
Occasioned by the international conference "Rings and Factorizations" held in February 2018 at
University of Graz, Austria, this volume represents a wide range of research trends in the
theory of commutative and non-commutative rings and their modules, including multiplicative
ideal theory, Dedekind and Krull rings and their generalizations, rings of integer valuedpolynomials,
topological aspects of ring theory, factorization theory in rings and semigroups
and direct-sum decompositions of modules. The volume will be of interest to researchers
seeking to extend or utilize work in these areas as well as graduate students wishing to find
entryways into active areas of current research in algebra. A novel aspect of the volume is an
emphasis on how diverse types of algebraic structures and contexts (rings, modules,
semigroups, categories) may be treated with overlapping and reinforcing approaches.
Due 2020-06-24
1st ed. 2020, X, 310 p. 6 illus.
Hardcover
ISBN 978-3-030-43415-1
Product category : Proceedings
Series : Springer Proceedings in Mathematics & Statistics
Offers readers a ehands onf introduction to Diophantine geometry
Progresses from introductory to advanced topics using the language of classical geometry
Assumes only modest prerequisites in abstract algebra and number theory
Contains numerous exercises throughout
This English translation of Daniel Corayfs original French textbook Notes de geometrie et df
arithmetique introduces students to Diophantine geometry. It engages the reader with concrete
and interesting problems using the language of classical geometry, setting aside all but the
most essential ideas from algebraic geometry and commutative algebra. Readers are invited to
discover rational points on varieties through an appealing ehands onf approach that offers a
pathway toward active research in arithmetic geometry. Along the way, the reader encounters
the state of the art on solving certain classes of polynomial equations with beautiful geometric
realizations, and travels a unique ascent towards variations on the Hasse Principle. Highlighting
the importance of Diophantus of Alexandria as a precursor to the study of arithmetic over the
rational numbers, this textbook introduces basic notions with an emphasis on Hilbertfs
Nullstellensatz over an arbitrary field. A digression on Euclidian rings is followed by a thorough
study of the arithmetic theory of cubic surfaces. Subsequent chapters are devoted to p-adic
fields, the Hasse principle, and the subtle notion of Diophantine dimension of fields. All
chapters contain exercises, with hints or complete solutions. Notes on Geometry and Arithmetic
will appeal to a wide readership, ranging from graduate students through to researchers.
Assuming only a basic background in abstract algebra and number theory, the text uses
Diophantine questions to motivate readers seeking an accessible pathway into arithmetic
geometry.
Due 2020-06-25
1st ed. 2020, X, 190 p. 19 illus., 2 illus. in color.
Softcover
ISBN 978-3-030-43780-0
Product category : Graduate/advanced undergraduate textbook
Series : Universitext
Presents a survey of state of the art aspects of applied Bayesian data science
Presents real-world case studies in applied Bayesian data science in the fields of health and ecology
Introduces new methodologies
Presenting a range of substantive applied problems within Bayesian Statistics along with their
Bayesian solutions, this book arises from a research program at CIRM in France in the second
semester of 2018, which supported Kerrie Mengersen as a visiting Jean-Morlet Chair and Pierre
Pudlo as the local Research Professor. The field of Bayesian statistics has exploded over the
past thirty years and is now an established field of research in mathematical statistics and
computer science, a key component of data science, and an underpinning methodology in
many domains of science, business and social science. Moreover, while remaining naturally
entwined, the three arms of Bayesian statistics, namely modelling, computation and inference,
have grown into independent research fields. While the research arms of Bayesian statistics
continue to grow in many directions, they are harnessed when attention turns to solving
substantive applied problems. Each such problem set has its own challenges and hence draws
from the suite of research a bespoke solution. The book will be useful for both theoretical and
applied statisticians, as well as practitioners, to inspect these solutions in the context of the
problems, in order to draw further understanding, awareness and inspiration.
Due 2020-06-29
1st ed. 2020, X, 475 p. 107 illus., 90 illus. in color.
Softcover
ISBN 978-3-030-42552-4
Product category : Contributed volume
Series : Lecture Notes in Mathematics
Useful text for second-semester graduate student learning Algebraic Topology
Useful for students or researchers at any level as a preface to Quillen's three landmark papers
As a historical or sociological point, these informal notes provide a glimpse of Quillen's magnificent mind
These are notes from a graduate student course on algebraic topology and K-theorygiven by
Daniel Quillen at the Massachusetts Institute of Technology during 1979-1980.He had just
received the Fields Medal for his work on these topics among others and was funny and
playful with a confident humility from the start. These are not meant to be polished lecture
notes, rather, things are presented as did Quillen reflected in the hand-written notes, resisting
any temptation to change or add notation, details or elaborations. Indeed, the text is faithful to
Quillen's own exposition, even respecting the {\sl board-like presentation} of formulae,
diagrams and proofs, omitting numbering theorems in favor of names and so on. This is meant
to be Quillen on Quillen as it happened forty years ago, an informal text for a second-semester
graduate student on topology, category theory and K-theory, a potential preface to studying
Quillen's own landmark papers and an informal glimpse of his great mind. The intellectual
pace of the lectures, namely fast and lively, is Quillen himself, and part of the point here is to
capture some of this intimacy. To be sure, much has happened since then from this categorical
perspective started by Grothendieck, and Misha Kapranov has contributed an Afterword in order
to make it more useful to current students
Due 2020-06-16
1st ed. 2020, Approx. 215 p.
Softcover
ISBN 978-3-030-43995-8
Product category : Monograph
Series : History of Mathematics Subseries
Suitable for an undergraduate applied algebra course
Covers a wide range of applications of algebra and number theory to
information handling, such as encryption and error-correcting codes
Uses the free GAP software to illustrate the main concepts
Includes numerous worked examples and exercises
Modern societies are awash with data that needs to be manipulated in many different ways:
encrypted, compressed, shared between users in a prescribed manner, protected from
unauthorised access, and transmitted over unreliable channels. All of these operations are
based on algebra and number theory and can only be properly understood with a good
knowledge of these fields. This textbook provides the mathematical tools and applies them to
study key aspects of data transmission such as encryption and compression. Designed for an
undergraduate lecture course, this textbook provides all of the background in arithmetic,
polynomials, groups, fields, and elliptic curves that is required to understand real-life
applications such as cryptography, secret sharing, error-correcting, fingerprinting, and
compression of information. It explains in detail how these applications really work. The book
uses the free GAP computational package, allowing the reader to develop intuition about
computationally hard problems and giving insights into how computational complexity can be
used to protect the integrity of data. The first undergraduate textbook to cover such a wide
range of applications, including some recent developments, this second edition has been
thoroughly revised with the addition of new topics and exercises. Based on a one semester
lecture course given to third year undergraduates, it is primarily intended for use as a textbook,
while numerous worked examples and solved exercises also make it suitable for self-study
Due 2020-06-22
2020, XI, 285 p. 7 illus., 1 illus. in color.
Softcover
ISBN 978-3-030-44073-2
Product category : Undergraduate textbook
Series : Springer Undergraduate Mathematics Series
Contains a complete account of the theta invariants
Presents the author's theory of infinite Hermitian vector bundles over arithmetic curves
Provides many interesting original insights and ties to other theories
This book presents the most up-to-date and sophisticated account of the theory of Euclidean
lattices and sequences of Euclidean lattices, in the framework of Arakelov geometry, where
Euclidean/Hermitian lattices are considered as vector bundles over arithmetic curves. It
contains a complete description of the theta invariants which give rise to a closer parallel with
the geometric case. The author then unfolds his theory of infinite Hermitian vector bundles
over arithmetic curves and their theta invariants, which provides a conceptual framework to
deal with the sequences of lattices occurring in many diophantine constructions. The book
contains many interesting original insights and ties to other theories. It is written with extreme
care, with a clear and pleasant style, and never sacrifices accessibility to sophistication.
Due 2020-10-11
1st ed. 2020, Approx. 300 p.
Hardcover
ISBN 978-3-030-44328-3
Product category : Monograph
Series : Progress in Mathematics
Simplifies the approach to birational properties of connections, based on a
formal analysis of singularities at infinity
Features a discussion on the stability of properties of connections based on
higher direct images under a smooth morphism, only using basic tools of
coherent cohomology
Presents a unified approach to GAGA-type theorems in De Rham cohomology
covering both complex and $p$-adic analytifications
This is the revised second edition of the well-received book by the first two authors. It offers a
systematic treatment of the theory of vector bundles with integrable connection on smooth
algebraic varieties over a field of characteristic 0. Special attention is paid to singularities along
divisors at infinity, and to the corresponding distinction between regular and irregular
singularities. The topic is first discussed in detail in dimension 1, with a wealth of examples,
and then in higher dimension using the method of restriction to transversal curves. The
authors develop a new approach to classical algebraic/analytic comparison theorems in De
Rham cohomology, and provide a unified discussion of the complex and the p-adic situations
while avoiding the resolution of singularities. They conclude with a proof of a conjecture by
Baldassarri to the effect that algebraic and p-adic analytic De Rham cohomologies coincide,
under an arithmetic condition on exponents. As used in this text, the term gDe Rham
cohomologyh refers to the hypercohomology of the De Rham complex of a connection with
respect to a smooth morphism of algebraic varieties, equipped with the Gauss-Manin
connection. This simplified approach suffices to establish the stability of crucial properties of
connections based on higher direct images.
Due 2020-08-21
2nd ed. 2021, XIV, 241 p.
Hardcover
ISBN 978-3-030-39718-0
Product category : Monograph
Series : Progress in Mathematics