1st ed. 2016, Approx. 740 p. 3 volume-set.
Softcover
ISBN 978-3-662-49515-5
* New translation of the three classic volumes
* Invaluable treatise for any mathematics educator
* Exhibits the connections between geometry and more formalistic
mathematics
These three volumes constitute the first complete English translation of Felix Klein’s
seminal series “Elementarmathematik vom hoheren Standpunkte aus”. “Complete” has
a twofold meaning here: First, there now exists a translation of volume III into English,
while until today the only translation had been into Chinese. Second, the English versions
of volume I and II had omitted several, even extendedparts of the original, while we now
present a complete revised translation into modern English.
The volumes, first published between 1902 and 1908, are lecture notes of courses that
Klein offered to future mathematics teachers, realizing a new form of teacher training
that remained valid and effective until today: Klein leads the students to gain a more
comprehensive and methodological point of view on school mathematics. The volumes
enable us to understand Klein’s far-reaching conception of elementarisation, of the
“elementary from a higher standpoint”, in its implementation for school mathematics.
1st ed. 2016, X, 485 p. 50 illus.
Hardcover
ISBN 978-3-319-32593-4
* Provides a detailed survey of leading results in bent
functions Presents a systematic overview of their generalizations
and applications Considers open problems in classification and
systematization of bent functions Discusses proofs of several results
and reflects on recent developments and trends in the field
This book gives a detailed survey of the main results on bent functions over finite fields,
presents a systematic overview of their generalizations, variations and applications,
considers open problems in classification and systematization of bent functions,
and discusses proofs of several results.
This book uniquely provides a necessary comprehensive coverage of bent functions.
It serves as a useful reference for researchersin discrete mathematics, coding and cryptography.
Students and professors in mathematics and computer science will also find the content valuable, especially
those interested in mathematical foundations of cryptography. It can be used as a
supplementary text for university courses on discrete mathematics, Boolean functions, or
cryptography, and is appropriate for both basic classes for under-graduate students and
advanced courses for specialists in cryptography and mathematics.
1st ed. 2016, Approx. 750 p.
Hardcover
ISBN 978-3-319-33300-7
* Collects integral and discrete inequalities established by many
different authors
* Presents some integral and discrete inequalities and their
applications in (partial) differential equations, integral equations and
discrete equations
* Introduces Gronwall-Bellman, Henry, Bihari and Ou-Yang inequalities
* Presents numerous inequalities, which cannot be found in other books
This book focuses on one- and multi-dimensional linear integral and discrete inequalities
of Gronwall-Bellman type. It provides a useful collection and systematic presentation
of known and new results, as well as many applications to differential (ODE and PDE),
difference, and integral equations. With this work the author fills a gap in the literature on
inequalities, offering an ideal source for researchers in these topics.
The present volume is part 1 (Chapters 1-4) of the author’s two-volume work on
inequalities.
Integral and discrete inequalities are a very important tool in classical analysis and play a
crucial role in establishing the well-posedness of the related equations, i.e., differential,
difference and integral equations.
1st ed. 2016, Approx. 820 p.
Hardcover
ISBN 978-3-319-33303-8
* Collects integral and discrete inequalities established by many
different authors
* Presents some integral and discrete inequalities and their
applications in (partial) differential equations, integral equations and
discrete equations
* Introduces Gronwall-Bellman, Henry, Bihari and Ou-Yang inequalities
* Presents numerous inequalities, which cannot be found in other books
This book concentrates on one- and multi-dimensional nonlinear integral and discrete
inequalities of Gronwall-Bellman type. It complements the author’s book on linear
inequalities and serves as an essential tool for researchers interested in differential (ODE
and PDE), difference, and integral equations.
The present volume is part 2 (Chapters 5-8) of the author’s two-volume work on
inequalities.
Integral and discrete inequalities are a very important tool in classical analysis and play a
crucial role in establishing the well-posedness of the related equations, i.e., differential,
difference and integral equations.
2016, XXX, 549 p. 4 illus.
Hardcover
ISBN 978-1-4939-4003-5
Series: Birkhauser Advanced Texts Basler Lehrbucher
* Clear, user-friendly presentation of techniques used for further study
and research in applied math and partial differential equations
* Second Edition provides new content and expanded coverage of key
topics
* Each chapter contains a "Problems and Complements" section
consisting of exercises and suggestions for further developments of
the material contained in that chapter
* Ideal for classroom use or self study
The second edition of this classic textbook presents a rigorous and self-contained
introduction to real analysis with the goal of providing a solid foundation for future
coursework and research in applied mathematics. Written in a clear and concise style,
it covers all of the necessary subjects as well as those often absent from standard
introductory texts. Each chapter features a “Problems and Complements” section that
includes additional material that briefly expands on certain topics within the chapter and
numerous exercises for practicing the key concepts.
The first eight chapters explore all of the basic topics for training in real analysis,
beginning with a review of countable sets before moving on to detailed discussions
of measure theory, Lebesgue integration, Banach spaces, functional analysis, and
weakly differentiable functions. More topical applications are discussed in the
remaining chapters, such as maximal functions, functions of bounded mean oscillation,
rearrangements, potential theory, and the theory of Sobolev functions.
This second edition has been completely revised and updated and contains a variety of new
content and expanded coverage of key topics, such as new exercises on the calculus of
distributions, a proof of the Riesz convolution, Steiner symmetrization, and embedding
theorems for functions in Sobolev spaces.
Ideal for either classroom use or self-study, Real Analysis is an excellent textbook both
for students discovering real analysis for the first time and for mathematicians and
researchers looking for a useful resource for reference or review.
“[This book will be extremely useful as a text. There is certainly enough material for a
year-long graduate course, but judicious selection would make it possible to use this most
appealing book in a one-semester course for well-prepared students.” - Mathematical Reviews.
1st ed. 2016, Approx. 660 p.
Softcover
ISBN 978-3-319-32409-8
Series: Universitext
* Presents results of analysis that can be applied to a wealth of
concrete problemsStarts from the foundations and leads to powerful
resultsTreats less traditional topics such as convex analysis,
monotone operators, and the Laplace and Radon transforms
This textbook covers the main results and methods of real analysis in a single volume.
Taking a progressive approach to equations and transformations, this book starts with
the very foundations of real analysis (set theory, order, convergence, and measure theory)
before presenting powerful results that can be applied to concrete problems.
In addition to classical results of functional analysis, differential calculus and integration,
Analysis discusses topics such as convex analysis, dissipative operators and semigroups
which are often absent from classical treatises. Acknowledging that analysis has
significantly contributed to the understanding and development of the present world,
the book further elaborates on techniques which pervade modern civilization, including
wavelets in information theory, the Radon transform in medical imaging and partial
differential equations in various mechanical and physical phenomena.
Advanced undergraduate and graduate students, engineers as well as practitioners
wishing to familiarise themselves with concepts and applications of analysis will find
this book useful. With its content split into several topics of interest, the book’s style and
layout make it suitable for use in several courses, while its self-contained character make it
appropriate for self-study.