2017, XXVII, 643 p. 209 illus., 178
illus. in color.
Softcover
ISBN 978-3-319-52400-9
Series: Springer Texts in Statistics
* Software-oriented approach*illustrating importance of software
for carrying out simulations when answers to questions cannot be
obtained analytically
* Examples and problems in R and Matlab, including code so students
can create simulations
* Introduction addresses “Why study probability*” by surveying
selected examples from recent journal articles and discussing classic
problems whose solutions are counterintuitive
* Preface details mathematical level and uses three sample course
syllabi to suggest what can be covered in courses of varying duration
* Three sample syllabi (covering a one-semester, one-quarter, or yearlong
course)
* Updated and re-worked exposition of Recommended Coverage for
instructors, detailing which courses should use the textbook and
how to utilize different sections for various objectives and time
constraints
* Extended and revised instructions and solutions to problem sets
* Adjusted axes, design, and labels*making tables more illuminating
* Overhaul of Section 7.7 on continuous-time Markov chains
* Supplementary materials include sample syllabi and updated
solutions manuals for both instructors and students
This updated and revised first-course textbook in applied probability provides a
contemporary and lively post-calculus introduction to the subject of probability.
The exposition reflects a desirable balance between fundamental theory and many
applications involving a broad range of real problem scenarios. It is intended to appeal
to a wide audience, including mathematics and statistics majors, prospective engineers
and scientists, and those business and social science majors interested in the quantitative
aspects of their disciplines.
The textbook contains enough material for a year-long course, though many instructors
will use it for a single term (one semester or one quarter). As such, three course syllabi
with expanded course outlines are now available for download on the book’s page on the
Springer website.
1st ed. 2017, XV, 509 p. 107 illus., 2 illus. in color.
Softcover
ISBN 978-3-319-55160-9
Series: Springer Undergraduate Mathematics Series
* Provides a well-structured introduction to the modeling process
using mathematical structures as ordering principle
* Contains a wealth of examples from applications in the natural and
engineering sciences
* The book starts with simple models based on linear algebra and
ends up with complex models involving nonlinear PDEs and free
boundaries
* Contains more than 150 exercises with increasing difficulty
* Of use both for undergraduate students as well as experienced
researchers which aim to learn about the modeling process
Mathematical models are the decisive tool to explain and predict phenomena in the
natural and engineering sciences. With this book readers will learn to derive mathematical
models which help to understand real world phenomena. At the same time a wealth of
important examples for the abstract concepts treated in the curriculum of mathematics
degrees are given. An essential feature of this book is that mathematical structures are
used as an ordering principle and not the fields of application.
Methods from linear algebra, analysis and the theory of ordinary and partial differential
equations are thoroughly introduced and applied in the modeling process. Examples
of applications in the fields electrical networks, chemical reaction dynamics,
population dynamics, fluid dynamics, elasticity theory and crystal growth are treated
comprehensively.
1st ed. 2017, XIV, 375 p. 64 illus., 1 illus. in color.
Softcover
ISBN 978-1-4471-7315-1
Series: Springer Undergraduate Mathematics Series
* Includes the theory of nets to study arbitrary topological spaces
* Illustrates the insufficiency of sequences with simple but rarely
presented examples
* Elaborates on the historical background of most notions and results
treated in this volume
Presenting basic results of topology, calculus of several variables, and approximation
theory which are rarely treated in a single volume, this textbook includes several beautiful,
but almost forgotten, classical theorems of Descartes, Erd*s, Fejer, Stieltjes, and Turan.
The exposition style of Topology, Calculus and Approximation follows the Hungarian
mathematical tradition of Paul Erd*s and others. In the first part, the classical results
of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate
the theories of metric, topological and normed spaces. Following this, the general
framework of normed spaces and Caratheodory's definition of the derivative are shown to
simplify the statement and proof of various theorems in calculus and ordinary differential
equations. The third and final part is devoted to interpolation, orthogonal polynomials,
numerical integration, asymptotic expansions and the numerical solution of algebraic and
differential equations.
Students of both pure and applied mathematics, as well as physics and engineering
should find this textbook useful. Only basic results of one-variable calculus and linear
algebra are used, and simple yet pertinent examples and exercises illustrate the
usefulness of most theorems. Many of these examples are new or difficult to locate in the
literature, and so the original sources of most notions and results are given to help readers
understand the development of the field.
1st ed. 2017, IX, 671 p. 261 illus., 5 illus. in color.
Hardcover
ISBN 978-3-319-55079-4
Series: Problem Books in Mathematics
* Contains more than 1,000 problems
* Provides an easy-to-understand approach to train for mathematic olympiads
* Promotes creativity for solving math problems while learning new approaches
* Includes classical, well-known solutions combined with new problems
This unique collection of new and classical problems provides full coverage of
geometric inequalities. Many of the 1,000 exercises are presented with detailed
author-prepared-solutions, developing creativity and an arsenal of new approaches
for solving mathematical problems. This book can serve teachers, high-school
students, and mathematical competitors. It may also be used as supplemental reading,
providing readers with new and classical methods for proving geometric inequalities.
2017, XVI, 528 p. 29 illus.
Softcover
ISBN 978-3-319-52206-7
Series: Springer Texts in Statistics
* Still up front and central in the book, Chapters 1-5 provide the
"measure theory" necessary for the rest of the textbook and Chapters
6-7 adapt that measure-theoretic background to the special needs of
probability theory
* Develops both mathematical tools and specialized probabilistic tools
* Chapters organized by number of lectures to cover requisite topics,
optional lectures, and self-study
* Exercises interspersed within the text
* Guidance provided to instructors to help in choosing topics of emphasis
This 2nd edition textbook offers a rigorous introduction to measure theoretic probability
with particular attention to topics of interest to mathematical statisticians*a textbook
for courses in probability for students in mathematical statistics. It is recommended
to anyone interested in the probability underlying modern statistics, providing a solid
grounding in the probabilistic tools and techniques necessary to do theoretical research in
statistics. For the teaching of probability theory to post graduate statistics students, this is
one of the most attractive books available.
Of particular interest is a presentation of the major central limit theorems via Stein's
method either prior to or alternative to a characteristic function presentation.
Additionally, there is considerable emphasis placed on the quantile function as well as
the distribution function. The bootstrap and trimming are both presented. Martingale
coverage includes coverage of censored data martingales. The text includes measure
theoretic preliminaries, from which the authors own course typically includes selected
coverage.
This is a heavily reworked and considerably shortened version of the first edition of this
textbook. "Extra" and background material has been either removed or moved to the
appendices and important rearrangement of chapters has taken place to facilitate this
book's intended use as a textbook.
1st ed. 2017, XV, 380 p. 6 illus., 1 illus. in color.
Hardcover
ISBN 978-981-10-4225-6
Series: Developments in Mathematics, Vol. 47
* Equips the reader with an understanding of integrability
* Summarizes the classical results of Darboux integrability and its
modern development
* Connects analysis, algebraic geometry, field extension, differential
form, Lie symmetry and normal form theory
This is the first book to systematically state the fundamental theory of integrability and
its development of ordinary differential equations with emphasis on the Darboux theory
of integrability and local integrability together with their applications. It summarizes
the classical results of Darboux integrability and its modern development together with
their related Darboux polynomials and their applications in the reduction of Liouville
and elementary integrabilty and in the center*focus problem, the weakened Hilbert
16th problem on algebraic limit cycles and the global dynamical analysis of some realistic
models in fields such as physics, mechanics and biology.
Although it can be used as a textbook for graduate students in dynamical systems, it is
intended as supplementary reading for graduate students from mathematics, physics,
mechanics and engineering in courses related to the qualitative theory, bifurcation theory
and the theory of integrability of dynamical systems.