Written for undergraduate students and beginners
More than 300 exercises, most with hints or solutions
Teaches the use of open source mathematical software in number theory
There are numbers of all kinds: rational, real, complex, p-adic, and more. The p-adic numbers
are not as well known as the others, but they play a fundamental role in number theory and in
other parts of mathematics, capturing information related to a chosen prime number p. They
also allow us to use methods from calculus and analysis to obtain results in algebra and
number theory. This book is an elementary introduction to p-adic numbers. Most other books
on the subject are written for more advanced students; this book provides an entryway to the
subject for students with an undergraduate mathematics education. Readers who want to have
an idea of and appreciation for the subject will probably find what they need in this book.
Readers on the way to becoming experts can begin here before moving on to more advanced
texts. This third edition has been thoroughly revised to correct mistakes, make the exposition
clearer, and call attention to significant aspects that are usually reserved for advanced books.
The most important addition is the integration of mathematical software for computations with
p-adic numbers and functions. A final chapter includes a selection of problems for further
exploration. From the reviews of the first and second editions: "Perhaps the most suitable text
for beginners" - The Mathematical Gazette "This text perfectly fulfills what it proposes" -
Mathematical Reviews "An extraordinarily nice manner to introduce the uninitiated to the
subject" - Mededelingen van het wiskundig genootschap "If I had to recommend one book on
the subject to a student ? or even to a fully grown mathematician ...? it would still be this
book" - MAA Reviews
Due 2020-07-22
3rd ed. 2020, VI, 373 p. 19 illus.
Softcover
ISBN 978-3-030-47294-8
Product category : Graduate/advanced undergraduate textbook
Mathematics : Number Theory
Series : Universitext
Provides a self-contained introduction to discrete harmonic analysis
Builds an advanced theory from scratch that can be applied to signal processing
Includes about 150 exercises, with solutions
This book provides an introduction to discrete harmonic analysis (DHA) with a view towards
applications to digital signal processing. In a nutshell, DHA is used to determine the timefrequency
structure of a digitized signal, providing a representation of the signal as a sum of
spectral components that can then be analyzed. The main methods of DHA are discrete Fourier
transform and other discrete orthogonal transforms such as the Walsh and Haar transforms.
Fast algorithms are used to process signals in real time, while additional options are provided
by spline harmonic analysis. These topics are carefully covered in the book. With only modest
prerequisites, some of which are recalled at the beginning, a profound mathematical theory is
built almost from scratch. The 150 exercises included form an integral part of the text. Based
decades of teaching experience, this book provides a basis for lecture courses starting at the
upper undergraduate level, and will also prove a valuable resource for mathematicians and
engineers interested in digital signal processing.
Due 2020-08-08
1st ed. 2020, XV, 247 p. 15 illus.
Softcover
ISBN 978-3-030-47047-0
Product category : Graduate/advanced undergraduate textbook
Mathematics : Computational Mathematics and Numerical Analysis
Series : Lecture Notes in Applied and Numerical Harmonic Analysis
Translation of Selected Papers and Discussion
Features translations by an award-winning translator of Henri Poincare
Recounts the discovery of radioactivity and the characterization of its components
An insightful reanalysis of data from 1902 concerning high-speed electrons
Offers a clear comparison of contributions by M. Abraham, H. A. Lorentz and
H. Poincare to a theory of electrons
Produced by an award-winning translator of Henri Poincare, this book contains translationsof
several seminal articles by Poincare and discusses the experimental and theoretical
investigations of electrons that form their context. In the 1950s, a dispute ignited about the
origin of the theory of special relativity and thrust considerable notoriety on a paper written by
Henri Poincare in 1905. Accordingly, Part I presents the relevant translations of Poincare’s
work showing that radiation carries momentumand the covariance of the equations of
electrodynamics, the continuity equation for charge,and the spacetime interval. Part II then
discusses investigations by Thomson,Becquerel, and Kaufmann of electrons in diverse contexts;
contributions of Abraham,Lorentz and Poincare to a theory of electrons that includes Lorentz
transformations andexplains the dependence of mass on velocity; and finally, Poincare’s
exploration of the relativityprinciple, electron stability, and gravitation while rejecting absolute
motion (ether) andan electromagnetic origin of mass. Part III contains the 1904 article by H.
A. Lorentzpresenting his transformations. This book will be a fascinating read to graduate-level
students, physicists, and sciencehistorians who are interested in the development of
electrodynamics and the classical,relativistic theory of electrons at the beginning of the 20th
century.
Due 2020-08-12
1st ed. 2020, VIII, 216 p. 7
illus., 4 illus. in color.
Hardcover
ISBN 978-3-030-48038-7
Product category : Monograph
Physics : Classical Electrodynamics
Introduces the concepts of causal inference in experiments and observational
studies using elementary mathematics
Presents many examples and with reference to implementation in R
Discusses design sensitivity in detail for the first time in book form
Features new to this edition include: a new R package DOS2, four new
chapters about the analysis of counterclaims (Chapter 7), the choice of
statistic for sensitivity analyses (Chapter 19), evidence factors (Chapter 20),
and the construction of several comparison groups (Chapter 21)
This second edition ofDesign of Observational Studiesis both an introduction to statistical
inference in observational studies and a detailed discussion of the principles that guide the
design of observational studies. An observational study is an empiric investigation of effects
caused by treatments when randomized experimentation is unethical or infeasible.
Observational studies are common in most fields that study the effects of treatments on
people, including medicine, economics, epidemiology, education, psychology, political science
and sociology. The quality and strength of evidence provided by an observational study is
determined largely by its design. Design of Observational Studiesis organized into five parts.
Chapters 2, 3, and 5 of Part I cover concisely many of the ideas discussed in Rosenbaum’
sObservational Studies(also published by Springer) but in a less technical fashion. Part II
discusses the practical aspects of using propensity scores and other tools to create a matched
comparison that balances many covariates, and includes an updated chapter on matching in R.
In Part III, the concept of design sensitivity is used to appraise the relative ability of competing
designs to distinguish treatment effects from biases due to unmeasured covariates. Part IV is
new to this edition; it discusses evidence factors and the computerized construction of more
than one comparison group.
Due 2020-08-21
2nd ed. 2020, XXVII, 545 p.34 illus.
Hardcover
ISBN 978-3-030-46404-2
Product category : Monograph
Statistics : Statistical Theory and Methods, 2nd ed.
Series : Springer Series in Statistics
Parametric Inference and Process Control
Serves as introductory textbook on the analysis of time series data for
students majoring in statistics and related fields
Includes numerous real-world data examples as well as R codes for implementation
Discusses times series data, from basic theories to real-world applications
This book provides statistical methodologies for time series data, focusing on copula-based
Markov chain models for serially correlated time series. It also includes data examples from
economics, engineering, finance, sport and other disciplines to illustrate the methods presented.
An accessible textbook for students in the fields of economics, management, mathematics,
statistics, and related fields wanting to gain insights into the statistical analysis of time series
data using copulas, the book also features stand-alone chapters to appeal to researchers. As
the subtitle suggests, the book highlights parametric models based on normal distribution,
tdistribution, normal mixture distribution, Poisson distribution, and others. Presenting likelihoodbased
methods as the main statistical tools for fitting the models, the book details the
development of computing techniques to find the maximum likelihood estimator. It also
addresses statistical process control, as well as Bayesian and regression methods. Lastly, to
help readers analyze their data, it provides computer codes (R codes) for most of the statistical
methods.
Due 2020-08-25
1st ed. 2020, XVI, 131 p. 26 illus., 9 illus. in color. With
online files/update.
Softcover
ISBN 978-981-15-4997-7
Product category : Brief
Statistics : Statistics for Business, Management, Economics, Finance, Insurance
Series : JSS Research Series in Statistics
One of the first books to give strong non-trivial bounds on the transversal number for linear hypergraphs
Provides the reader with state-of-the-art on transversals in linear uniform hypergraphs
Familiarizes the student with the subject, the research techniques, and the major accomplishments
in the field including photographs of several researchers who made important contributions to the subject
May lead to further study of those problems which have not been solved
completely, and may also inspire the readers to raise new questions and research directions
This book gives the state-of-the-art on transversals in linear uniform hypergraphs. The notion
of transversal is fundamental to hypergraph theory and has been studied extensively. Very few
articles have discussed bounds on the transversal number for linear hypergraphs, even though
these bounds are integral components in many applications. This book is one of the first to
give strong non-trivial bounds on the transversal number for linear hypergraphs. The
discussion may lead to further study of those problems which have not been solved
completely, and may also inspire the readers to raise new questions and research directions.
The book is written with two readerships in mind. The first is the graduate student who may
wish to work on open problems in the area or is interested in exploring the field of
transversals inhypergraphs. This exposition will go far to familiarize the student with the
subject, the research techniques,and the major accomplishments in the field. Thephotographs
includedallow the reader to associate faces withseveral researchers who made important
discoveries and contributions to the subject. The second audience is the established researcher
in hypergraph theory who will benefit from having easy access to knownresults and latest
developments in the field of transversals in linear hypergraphs.
Due 2020-08-23
1st ed. 2020, XV, 229 p. 43 illus., 23 illus. in color.
Hardcover
ISBN 978-3-030-46558-2
Product category : Monograph
Mathematics : Graph Theory
Series : Developments in Mathematics
Provides a general framework which will facilitate the further study of
nonlocal reaction-diffusion systems
Addresses the existence of (non-regular) mild solutions, strong solutions, and
the global regularity problem
Establishes clear connections between fractional in time and classical parabolic problems
This book provides a unified analysis and scheme for the existence and uniqueness of strong
and mild solutions to certain fractional kinetic equations. This class of equations is
characterized by the presence of a nonlinear time-dependent source, generally of arbitrary
growth in the unknown function, a time derivative in the sense of Caputo and the presence of
a large class of diffusion operators. The global regularity problem is then treated separately
and the analysis is extended to some systems of fractional kinetic equations, including
preypredator models of Volterra?Lotka type and chemical reactions models, all of them possibly
containing some fractional kinetics. Besides classical examples involving the Laplace operator,
subject to standard (namely, Dirichlet, Neumann, Robin, dynamic/Wentzell and Steklov)
boundary conditions, the framework also includes non-standard diffusion operators of
"fractional" type, subject to appropriate boundary conditions. This book is aimed at graduate
students and researchers in mathematics, physics, mathematical engineering and mathematical
biology, whose research involves partial differential equations.
Due 2020-08-21
1st ed. 2020, XII, 184 p.
Softcover
ISBN 978-3-030-45042-7
Product category : Graduate/advanced undergraduate textbook
Mathematics : Partial Differential Equations
Series : Mathematiques et Applications