Provides a concise and self-contained introduction to statistical inference for
beginning undergraduates
Includes over 50 solved exercises and examples, including using R
Key concepts and ideas are described in lucid terms without sacrificing
mathematical rigor
This book offers a modern and accessible introduction to Statistical Inference, the science of
inferring key information from data. Aimed at beginning undergraduate students in
mathematics, it presents the concepts underpinning frequentist statistical theory. Written in a
conversational and informal style, this concise text concentrates on ideas and concepts, with
key theorems stated and proved. Detailed worked examples are included and each chapter
ends with a set of exercises, with full solutions given at the back of the book. Examples using
R are provided throughout the book, with a brief guide to the software included. Topics covered
in the book include: sampling distributions, properties of estimators, confidence intervals,
hypothesis testing, ANOVA, and fitting a straight line to paired data. Based on the author窶冱
extensive teaching experience, the material of the book has been honed by student feedback
for over a decade. Assuming only some familiarity with elementary probability, this textbook
has been devised for a one semester first course in statistics.
Due 2020-05-13
1st ed. 2020, X, 166 p. 23
illus., 6 illus. in color.
Softcover
ISBN 978-3-030-39560-5
Product category : Undergraduate textbook
Series : Springer Undergraduate Mathematics Series
A Minicourse on L2-Betti Numbers in Group Theory
Makes recent developments on L -Betti numbers of groups and related 2
invariants easily accessible to advanced students and researchers
Explains the rich interplay between the residually finite approach and the
dynamical systems approach
Each chapter is complemented by a set of exercises, ranging from simple
checks to challenging problems
This book offers a concise introduction to ergodic methods in group homology, with a
particular focus on the computation of L2-Betti numbers. Group homology integrates group
actions into homological structure. Coefficients based on probability measure preserving actions
combine ergodic theory and homology. An example of such an interaction is provided by L2-
Betti numbers: these invariants can be understood in terms of group homology with
coefficients related to the group von Neumann algebra, via approximation by finite index
subgroups, or via dynamical systems. In this way, L2-Betti numbers lead to orbit/measure
equivalence invariants and measured group theory helps to compute L2-Betti numbers. Similar
methods apply also to compute the rank gradient/cost of groups as well as the simplicial
volume of manifolds. This book introduces L2-Betti numbers of groups at an elementary level
and then develops the ergodic point of view, emphasising the connection with approximation
phenomena for homological gradient invariants of groups and spaces. The text is an extended
version of the lecture notes for a minicourse at the MSRI summer graduate
school andom
and arithmetic structures in topology and thus accessible to the graduate
or advanced
undergraduate students. Many examples and exercises illustrate the material.
Due 2020-05-15
1st ed. 2020, IX, 114 p.
Softcover
ISBN 978-3-030-44219-4
Product category : Brief
Series : SpringerBriefs in Mathematics
Presents the methodology for constructing computer models of dynamic
systems using the Wolfram visual modeling environment
Supplements university courses in modeling and simulation of dynamic
systems
Is useful for students and professionals in the field interested in issues of
modeling dynamic systems
This book briefly discusses the main provisions of the theory of modeling. It also describes in
detail the methodology for constructing computer models of dynamic systems using the
Wolfram visual modeling environment, SystemModeler, and provides illustrative examples of
solving problems of mechanics and hydraulics. Intended for students and professionals in the
field, the book also serves as a supplement to university courses in modeling and simulation of
dynamic systems.
Due 2020-05-16
1st ed. 2020, XVII, 263 p.
281 illus., 271 illus. in color.
Softcover
ISBN 978-981-15-2802-6
Product category : Educational supplement
Provides a timely overview and presents state-of-the-art research on chimera
patterns
Examines the complex interplay between stochasticity, time delay and
network topology
Discusses methods for controlling spatio-temporal patterns by means of the
interplay of network structure, time delay and noise
This is the first book devoted to chimera states - peculiar partial synchronization patterns in
networks. Providing an overview of the state of the art in research on this topic, it explores how
these hybrid states, which are composed of spatially separated domains of synchronized and
desynchronized behavior, arise surprisingly in networks of identical units and symmetric
coupling topologies. The book not only describes various types of chimeras, but also discusses
the role of time delay, stochasticity, and network topology for these synchronizationdesynchronization
patterns. Moreover, it addresses the question of robustness and control of
chimera states, which have various applications in physics, biology, chemistry, and engineering.
This book is intended for researchers with a background in physics, applied mathematics, or
engineering. Of great interest to specialists working on related problems, it is also a valuable
resource for newcomers to the field and other scientists working on the control of spatiotemporal patterns.
1st ed. 2020, XI, 233 p. 136
illus., 131 illus. in color.
Hardcover
ISBN 978-3-030-21713-6
Product category : Monograph
Series : Understanding Complex Systems
Is the world's first volume that focuses on the surprising and mysterious
Ohkawa's theorem: the Bousfield classes form a set
Starts with Ohkawa's theorem, stated in the universal stable homotopy
category, and narrates an inspiring, extensive mathematical story
Contains experts・surveys including motivic and chromatic homotopy theories,
higher categorical applications, derived categories, and L methods of 2
algebraic geometry
This volume originated in the workshop held at Nagoya University, August
28-30, 2015,
focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the
stable homotopy category SH form a set. An inspiring, extensive mathematical story can be
narrated starting with Ohkawa's theorem, evolving naturally with a chain of motivational
questions: Ohkawa's theorem states that the Bousfield classes of the stable homotopy category
SH surprisingly forms a set, which is still very mysterious. Are there any toy models where
analogous Bousfield classes form a set with a clear meaning? The fundamental theorem of
Hopkins, Neeman, Thomason, and others states that the analogue of the Bousfield classes in
the derived category of quasi-coherent sheaves Dqc(X) form a set with a clear algebrogeometric
description. However, Hopkins was actually motivated not by Ohkawa's theorem but
by his own theorem with Smith in the triangulated subcategory SHc, consisting of compact
objects in SH. Nowthe following questions naturally occur: (1) Having theorems of Ohkawa and
Hopkins-Smith in SH, are there analogues for the Morel-Voevodsky A1-stable homotopy
category SH(k), which subsumes SH when kis a subfield of C?, (2) Was it not natural for
Hopkins to have considered Dqc(X)c instead of Dqc(X)? However, whereas there is a
conceptually simple algebro-geometrical interpretation Dqc(X)c = Dperf(X), it is its close relative
Dbcoh(X) that traditionally, ever since Oka and Cartan, has been intensively studied because of
its rich geometric and physical information.
Due 2020-05-16
1st ed. 2020, X, 435 p. 2 illus., 1 illus. in color.
Hardcover
ISBN 978-981-15-1587-3
Product category : Proceedings
Series : Springer Proceedings in Mathematics & Statistic
Provides accompanying, fully updated R code
Evaluates the ethical and political implications of the application of
algorithmic methods
Features a new chapter on deep learning
This textbook considers statistical learning applications when interest centers on the
conditional distribution of a response variable, given a set of predictors, and in the absence of
a credible model that can be specified before the data analysis begins. Consistent with modern
data analytics, it emphasizes that a proper statistical learning data analysis depends in an
integrated fashion on sound data collection, intelligent data management, appropriate statistical
procedures, and an accessible interpretation of results. The unifying theme is that supervised
learning properly can be seen as a form of regression analysis. Key concepts and procedures
are illustrated with a large number of real applications and their associated code in R, with an
eye toward practical implications.The growing integration of computer science and statistics is
well represented including the occasional, but salient, tensions that result. Throughout, there
are links to the big picture. The third edition considers significant advances in recent years,
among which are: the development of overarching, conceptual frameworks for statistical
learning; the impact of ig dataon statistical learning; the nature and
consequences of postmodel
selection statistical inference; deep learning in various forms; the special challenges to
statistical inference posed by statistical learning; the fundamental connections between data
collection and data analysis; interdisciplinary ethical and political issues surrounding the
application of algorithmic methods in a wide variety of fields, each linked to concerns about
transparency, fairness, and accuracy. This edition features new sections on accuracy,
transparency, and fairness, as well as a new chapter on deep learning. Precursors to deep
learning get an expanded treatment.
Due 2020-06-12
2020, VIII, 472 p. 37 illus.
Hardcover
ISBN 978-3-030-40188-7
Product category : Graduate/advanced undergraduate textbook
Series : Springer Texts in Statistics
First textbook offering a complete exposition of local and global class field
theory as well as arithmetic duality theorems
Provides the necessary background in Galois cohomology and homological
algebra
Includes an appendix on analytical methods
This graduate textbook offers an introduction to modern methods in number theory. It gives a
complete account of the main results of class field theory as well as the Poitou-Tate duality
theorems, considered crowning achievements of modern number theory. Assuming a first
graduate course in algebra and number theory, the book begins with an introduction to group
and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal
group laws, are covered next, followed by global class field theory and the description of
abelian extensions of global fields. The final part of the book gives an accessible yet complete
exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary
background in homological algebra and the analytic theory of Dirichlet L-series, including the
ebotarev density theorem. Based on several advanced courses given by the author, this
textbook has been written for graduate students. Including complete proofs and numerous
exercises, the book will also appeal to more experienced mathematicians, either as a text to
learn the subject or as a reference.
Due 2020-06-21
1st ed. 2020, XVI, 364 p.
Softcover
ISBN 978-3-030-43900-2
Product category : Graduate/advanced undergraduate textbook
Series : Universitext