Focuses on algebraic aspects of supersymmetric gauge theories
Discusses geometrical and algebraic aspects of Nekrasov instanton calculus
and some interesting generalizations of those calculus
Consists of three parts, instanton calculus, quantum geometry, and quantum
algebra, with a lot of background information with clear technical exposition
This book pedagogically describes recent developments in gauge theory, in particular fourdimensiona
lN= 2 supersymmetric gauge theory, in relation to various fields in mathematics,
including algebraic geometry, geometric representation theory, vertex operator algebras. The
key concept is the instanton, which is a solution to the anti-self-dual Yang?Mills equation in
four dimensions. In the first part of the book, starting with the systematic description of the
instanton, how to integrate out the instanton moduli space is explained together with the
equivariant localization formula. It is then illustrated that this formalism is generalized to
various situations, including quiver and fractional quiver gauge theory, supergroup gauge
theory. The second part of the book is devoted to the algebraic geometric description of
supersymmetric gauge theory, known as the Seiberg?Witten theory, together with string
/Mtheory point of view. Based on its relation to integrable systems, how to quantize such a
geometric structure via the -deformation of gauge theory is addressed. The third part of the
book focuses on the quantum algebraic structure of supersymmetric gauge theory. After
introducing the free field realization of gauge theory, the underlying infinite dimensional
algebraic structure is discussed with emphasis on the connection with representation theory of
quiver, which leads to the notion of quiver W-algebra.
1st ed. 2021, XXIII, 285 p. 36 illus., 13 illus. in color.
Hardcover
ISBN 978-3-030-76189-9
Product category : Monograph
Series : Mathematical Physics Studies
Mathematics : Mathematical Physics
Balances theoretical and practical aspects with an implementation-oriented
approach
Guides readers through numerous hands-on tutorials to build practical skills
and algorithmic thinking
Supports three computer algebra systems with downloadable resources in
Mathematica, Maple, and Maxima
This textbook offers an algorithmic introduction to the field of computer algebra. A leading
expert in the field, the author guides readers through numerous hands-on tutorials designed to
build practical skills and algorithmic thinking. This implementation-oriented approach equips
readers with versatile tools that can be used to enhance studies in mathematical theory,
applications, or teaching. Presented using Mathematica code, the book is fully supported by
downloadable sessions in Mathematica, Maple, and Maxima. Opening with an introduction to
computer algebra systems and the basics of programming mathematical algorithms, the book
goes on to explore integer arithmetic. A chapter on modular arithmetic completes the numbertheoretic
foundations, which are then applied to coding theory and cryptography. From here,
the focus shifts to polynomial arithmetic and algebraic numbers, with modern algorithms
allowing the efficient factorization of polynomials. The final chapters offer extensions into more
advanced topics: simplification and normal forms, power series, summation formulas, and
integration. Computer Algebra is an indispensable resource for mathematics and computer
science students new to the field. Numerous examples illustrate algorithms and their
implementation throughout, with online support materials to encourage hands-on exploration.
Prerequisites are minimal, with only a knowledge of calculus and linear algebra assumed. In
addition to classroom use, the elementary approach and detailed index make this book an
ideal reference for algorithms in computer algebra.
Due 2021-08-25
1st ed. 2021, XII, 384 p. 27 illus., 26 illus. in color.
Hardcover
ISBN 978-3-030-78016-6
Product category : Undergraduate textbook
Series : Springer Undergraduate Texts in Mathematics and Technology
Mathematics : Algebra
Connects data science to the fields of sports management, sports marketing,
and related in an accessible and enjoyable way
Utilizes analytics to tackle the main questions that NBA fans debate,
providing empirical evidence for the answers
Provides useful insights for scouts, recruiters, and general managers in the
NBA who are looking to ground their work in data analytics
This book provides empirical evidence and statistical analyses to uncover answers to some of
the most debated questions in the NBA. The sports world lives and breathes off of debates on
who deserves an MVP award, and which athletes should be considered all-stars. This book
provides some statistics-backed perspectives to some of these debates that are specific to the
NBA. Was LeBron snubbed of an MVP in the 2010-2011 season? Why has the G.O.A.T. debate
turned into LeBron vs. Jordan….Did Kobe get overlooked? How come Klay Thompson didn’t get
All-NBA honors in the 2018-2019 season? This book explores these questions and many more
with empirical evidence. This book is invaluable for any undergraduate or masters level course
in sport analytics, sports marketing, or sports management. It will also be incredibly useful for
scouts, recruiters, and general managers in the NBA who would like to use analytics in their
work.
Due 2021-08-17
1st ed. 2021, VIII, 92 p. 4 illus.
Softcover
ISBN 978-3-030-79031-8
Product category : Brief
Series : SpringerBriefs in Statistics
Statistics : Statistics (general)
Introduces computation, spanning the key concepts and methods
Highly intuitive and accessible explanatory style
Firm grounding in logic and automata, with an approach using Haskell
Computation, itself a form of calculation, incorporates steps that include arithmetical
and nonarithmetical (logical) steps following a specific set of rules (an algorithm). This uniquely
accessible textbook introduces students using a very distinctive approach, quite rapidly leading
them into essential topics with sufficient depth, yet in a highly intuitive manner. From core
elements like sets, types, Venn diagrams and logic, to patterns of reasoning, calculus, recursion
and expression trees, the book spans the breadth of key concepts and methods that will
enable students to readily progress with their studies in Computer Science
Due 2021-11-01
1st ed. 2021, XIV, 366 p.
Softcover
ISBN 978-3-030-76907-9
Product category : Undergraduate textbook
Series : Undergraduate Topics in Computer Science
Computer Science : Theory of Computation
Key Concepts and Modern Results
Useful as supplementary reading in singularity courses and for independent
study
Blends fundamental concepts in foliations and singularity theory with modern
results on the topic
Includes relevant open questions to foster research in the field
This concise textbook gathers together key concepts and modern results on the theory of
holomorphic foliations with singularities, offering a compelling vision on how the notion of
foliation, usually linked to real functions and manifolds, can have an important role in the
holomorphic world, as shown by modern results from mathematicians as H. Cartan, K. Oka, T.
Nishino, and M. Suzuki. The text starts with a gentle presentation of the classical notion of
foliations, advancing to holomorphic foliations and then holomorphic foliations with
singularities. The theory behind reduction of singularities is described in detail, as well the
cases for dynamics of a local diffeomorphism and foliations on complex projective spaces. A
final chapter brings recent questions in the field, as holomorphic flows on Stein spaces and
transversely homogeneous holomorphic foliations, along with a list of open questions for
further study and research. Selected exercises at the end of each chapter help the reader to
grasp the theory. Graduate students in Mathematics with a special interest in the theory of
foliations will especially benefit from this book, which can be used as supplementary reading in
Singularity Theory courses, and as a resource for independent study on this vibrant field of
research.
Due 2021-08-23
1st ed. 2021, X, 210 p. 6 illus.
Hardcover
ISBN 978-3-030-76704-4
Product category : Graduate/advanced undergraduate textbook
Series : Latin American Mathematics Series
Mathematics : Algebraic Geometry
Brings carefully selected, challenging problems in mathematical analysis
Explores the standard topics of mathematical analysis in ways not seen in
regular textbooks
Offers original problems of mathematical analysis called gems, scattered
throughout the text, that stimulate the reader who enjoy creativity and
discovery in mathematics
Useful for students seeking to strengthen their skills in analysis, to prepare
for math contests, instructors and connoisseurs of ingenious computations
This book gathers together a novel collection of problems in mathematical analysis that are
challenging and worth studying.They cover most of the classical topics of a course in
mathematical analysis, and include challenges presented with an increasing level of difficulty.
Problems are designed to encourage creativity, and some of them were especially crafted to
lead to open problems which might be of interest for students seeking motivation to get a
start in research. The sets of problems are comprised in Part I. The exercises are arranged on
topics, many of them being preceded by supporting theory. Content starts with limits, series of
real numbers and power series, extending to derivatives and their applications, partial
derivatives and implicit functions. Difficult problems have been structured in parts, helping the
reader to find a solution. Challenges and open problems are scattered throughout the text,
being an invitation to discover new original methods for proving known results and establishing
new ones. The final two chapters offer ambitious readers splendid problems and two new
proofs of a famous quadratic series involving harmonic numbers.In Part II, the reader will find
solutions to the proposed exercises. Undergraduate students in mathematics, physics and
engineering, seeking to strengthen their skills in analysis, will most benefit from this work,
along with instructors involved in math contests, individuals who want to enrich and test their
knowledge in analysis, and anyone willing to explore the standard topics of mathematical
analysis in ways that aren’t commonly seen in regular textbooks.
Due 2021-08-17
1st ed. 2021, X, 480 p. 11 illus., 10 illus. in color.
Hardcover
ISBN 978-3-030-77138-6
Product category : Undergraduate textbook
Series : Problem Books in Mathematics
Mathematics : Analysis
Integrates multivariate data analysis with Riemannian geometry
Provides a unified treatment of several MDA techniques
Incorporates new tools and technology into current theory of MDA
Includes Manpot codes which can be directly used to solve a number of
problems or be used as templates to create new codes
This graduate-level textbook aims to give a unified presentation and solution of several
commonly used techniques for multivariate data analysis (MDA). Unlike similar texts, it treats
the MDA problems as optimization problems on matrix manifolds defined by the MDA model
parameters, allowing them to be solved using (free) optimization software Manopt. The book
includes numerous in-text examples as well as Manopt codes and software guides, which can
be applied directly or used as templates for solving similar and new problems. The first two
chapters provide an overview and essential background for studying MDA, giving basic
information and notations. Next, it considers several sets of matrices routinely used in MDA as
parameter spaces, along with their basic topological properties. A brief introduction to matrix
(Riemannian) manifolds and optimization methods on them with Manopt complete the MDA
prerequisite. The remaining chapters study individual MDA techniques in depth. The number of
exercises complement the main text with additional information and occasionally involve open
and/or challenging research questions. Suitable fields include computational statistics, data
analysis, data mining and data science, as well as theoretical computer science, machine
learning and optimization. It is assumed that the readers have some familiarity with MDA and
some experience with matrix analysis, computing, and optimization.
Due 2021-08-28
1st ed. 2021, XVIII, 452 p. 4 illus. in color.
Hardcover
ISBN 978-3-030-76973-4
Product category : Graduate/advanced undergraduate textbook
Series : Springer Series in the Data Sciences
Mathematics : Computational Mathematics and Numerical Analysis