Contains a consistent theory of smooth functions
Deals with critical values of smooth mappings
Uses a new technical approach that allows to clarify some of the technically
difficult proofs while maintaining full integrity
The book contains a consistent and sufficiently comprehensive theory of smooth functions and
maps insofar as it is connected with differential calculus. The scope of notions includes, among
others, Lagrange inequality, Taylor’s formula, finding absolute and relative extrema, theorems
on smoothness of the inverse map and on conditions of local invertibility, implicit function
theorem, dependence and independence of functions, classification of smooth functions up to
diffeomorphism. The concluding chapter deals with a more specific issue of critical values of
smooth mappings. In several chapters, a relatively new technical approach is used that allows
the authors to clarify and simplify some of the technically difficult proofs while maintaining full
integrity. Besides, the book includes complete proofs of some important results which until
now have only been published in scholarly literature or scientific journals (remainder estimates
of Taylor’s formula in a nonconvex area (Chapter I, §8), Whitney's extension theorem for
smooth function (Chapter I, §11) and some of its corollaries, global diffeomorphism theorem
(Chapter II, §5), results on sets of critical values of smooth mappings and the related Whitney
example (Chapter IV). The text features multiple examples illustrating the results obtained and
demonstrating their accuracy. Moreover, the book contains over 150 problems and 19
illustrations. Perusal of the book equips the reader to further explore any literature basing
upon multivariable calculus.
1st ed. 2021, XL, 244 p. 19 illus.
Hardcover
ISBN 978-3-030-79437-8
Product category : Graduate/advanced undergraduate textbook
Series : Moscow Lectures
Mathematics : Analysis
Presents an elemental method, assuming only standard linear algebra and
complex analysis
Allows target equations such as Painleve and Garnier systems to arise
naturally through suitable Pade problems
Provides a unique guide to continuous and discrete isomonodromic
deformation equations based on a simple method
The isomonodromic deformation equations such as the Painleve and Garnier systems are an
important class of nonlinear differential equations in mathematics and mathematical physics.
For discrete analogs of these equations in particular, much progress has been made in recent
decades. Various approaches to such isomonodromic equations are known: the Painleve test
/Painleve property, reduction of integrable hierarchy, the Lax formulation, algebro-geometric
methods, and others. Among them, the Pade method explained in this book provides a simple
approach to those equations in both continuous and discrete cases. For a given function f(x),
the Pade approximation/interpolation supplies the rational functions P(x), Q(x) as approximants
such as f(x)~P(x)/Q(x). The basic idea of the Pade method is to consider the linear differential
(or difference) equations satisfied by P(x) and f(x)Q(x). In choosing the suitable approximation
problem, the linear differential equations give the Lax pair for some isomonodromic equations.
Although this relation between the isomonodromic equations and Pade approximations has
been known classically, a systematic study including discrete cases has been conducted only
recently. By this simple and easy procedure, one can simultaneously obtain various results
such as the nonlinear evolution equation, its Lax pair, and their special solutions. In this way,
the method is a convenient means of approaching the isomonodromic deformation equations
Due 2021-10-07
1st ed. 2021, VIII, 90 p. 2 illus., 1 illus. in color.
Softcover
ISBN 978-981-16-2997-6
Product category : Brief
Series : SpringerBriefs in Mathematical Physics
Mathematics : Mathematical Physics
Provides a comprehensive review of thermodynamics and information theory
Introduces to Jarzynski's equality and Crooks' relation
Includes a unique primer on Shannon's entropy and information theory
Covers fundamental experiments on Maxwell's Demon and Landauer's
principle
Offers an in-depth review of the rapidly expanding field of quantum
computing quantum cryptography and verification
This eighteenth volume in the Poincare Seminar Series provides a thorough description of
Information Theory and some of its mostactive areas, in particular, its relation to
thermodynamics at the nanoscale and theMaxwell Demon, and the emergence of quantum
computation and of its counterpart,quantum verification. It also includes two introductory
tutorials, one on the fundamental relation between thermodynamics and information theory,
and a primer on Shannon's entropy and information theory. The book offers a unique and
manifold perspective on recent mathematical and physical developments inthis field.
1st ed. 2021, XII, 209 p. 56 illus.
Hardcover
ISBN 978-3-030-81479-3
Product category : Contributed volume
Series : Progress in Mathematical Physics
Physics : Mathematical Methods in Physics
Qualsiasi argomento viene discusso partendo dai principi primi fino al livello
di lavoro con esercizi
Il lettore puo scaricare piu di 100 routine scritte con il software statistico R
Ci sono circa 140 problemi completamente risolti
Il libro contiene in forma compatta il programma svolto negli insegnamenti introduttivi di
Statistica e tratta alcuni argomenti indispensabili per l'attivita di ricerca, come le tecniche di
simulazione Monte Carlo, i metodi di inferenza statistica, di best fit e di analisi dei dati di
laboratorio. Gli argomenti vengono sviluppati partendo dai fondamenti, evidenziandone gli
aspetti applicativi, fino alla descrizione dettagliata di molti casi di particolare rilevanza in ambito
scientifico e tecnico. Il testo e rivolto agli studenti universitari dei corsi ad indirizzo scientifico e
a tutti quei ricercatori che devono risolvere problemi concreti che coinvolgono l’analisi dei dati
e le tecniche di simulazione. In questa edizione, completamente rivista e corretta, sono stati
aggiunti alcuni importanti argomenti sul test d’ipotesi (a cui e stato dedicato un capitolo
interamente nuovo) e sul trattamento degli errori sistematici. Per la prima volta e stato
adottato il software R, con una ricca libreria di programmi originali accessibile al lettore.
4a ed. 2021, XV, 621 pagg.130 figg., 12 figg. a colori.
Softcover
ISBN 978-88-470-4009-0
Product category : Undergraduate textbook
Series : La Matematica per il 3+2
Statistics : Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences
Gives a concise introduction to exponential families
Includes a variety of detailed examples
Provides a rigorous course for graduate students of statistics and
mathematics as well as for researchers
This book provides a concise introduction to exponential families. Parametric families of
probability distributions and their properties are extensively studied in the literature on
statistical modeling and inference. Exponential families of distributions comprise density
functions of a particular form, which enables general assertions and leads to nice features.
With a focus on parameter estimation and hypotheses testing, the text introduces the reader to
distributional and statistical properties of multivariate and multiparameter exponential families
along with a variety of detailed examples. The material is widely self-contained and written in a
mathematical setting. It may serve both as a concise, mathematically rigorous course on
exponential families in a systematic structure and as an introduction to Mathematical Statistics
restricted to the use of exponential families.
Due 2021-10-06
1st ed. 2021, X, 130 p. 1 illus.
Softcover
ISBN 978-3-030-81899-9
Product category : Brief
Series : SpringerBriefs in Statistics
Statistics : Statistical Theory and Methods
Presents in-depth and accessible surveys of topics in singularity theory,
including their interrelationships and connections with other subjects
Ideal for graduate students and researchers in general who want to learn
about this active field, and as a reference for specialists
Emphasizes clarity and quality of exposition rather than technical details
Encourages readers to go deeper into the subject by offering illuminating
insights and useful bibliographies
This is the second volume of the Handbook of the Geometry and Topology of Singularities, a
series which aims to provide an accessible account of the state-of-the-art of the subject, its
frontiers, and its interactions with other areas of research. This volume consists of ten chapters
which provide an in-depth and reader-friendly survey of some of the foundational aspects of
singularity theory and related topics. Singularities are ubiquitous in mathematics and science in
general. Singularity theory interacts energetically with the rest of mathematics, acting as a
crucible where different types of mathematical problems interact, surprising connections are
born and simple questions lead to ideas which resonate in other parts of the subject, and in
other subjects. Authored by world experts, the various contributions deal with both classical
material and modern developments, covering a wide range of topics which are linked to each
other in fundamental ways. The book is addressed to graduate students and newcomers to the
theory, as well as to specialists who can use it as a guidebook
Due 2021-10-05
1st ed. 2021, XIV, 572 p. 24 illus., 13 illus. in color.
Hardcover
ISBN 978-3-030-78023-4
Product category : Handbook
Mathematics : Topology
Offers a broad set of problems in Mathematical Logic, starting from its
supporting fields and advancing toward key theorems
Enables the student to prove the main theorems himself, including Godel's
famous completeness and incompleteness theorems
Useful for instructors teaching introductory courses on topics such as
propositional logic, first-order logic, recursion theory, model theory, among
others
This book gathers together a colorful set of problems on classical Mathematical Logic, selected
from over 30 years of teaching. The initial chapters start with problems from supporting fields,
like set theory (ultrafilter constructions), full-information game theory (strategies), automata,
and recursion theory (decidability, Kleene’s theorems). The work then advances toward
propositional logic (compactness and completeness, resolution method), followed by first-order
logic, including quantifier elimination and the Ehrenfeucht? Fraisse game; ultraproducts; and
examples for axiomatizability and non-axiomatizability. The Arithmetic part covers Robinson’s
theory, Peano’s axiom system, and Godel’s incompleteness theorems. Finally, the book touches
universal graphs, tournaments, and the zero-one law in Mathematical Logic. Instructors
teaching Mathematical Logic, as well as students who want to understand its concepts and
methods, can greatly benefit from this work. The style and topics have been specially chosen
so that readers interested in the mathematical content and methodology could follow the
problems and prove the main theorems themselves, including Godel’s famous completeness
and incompleteness theorems. Examples of applications on axiomatizability and decidability of
numerous mathematical theories enrich this volume
Due 2021-10-04
1st ed. 2021, VIII, 312 p. 4 illus.
Hardcover
ISBN 978-3-030-79009-7
Product category : Undergraduate textbook
Series : Problem Books in Mathematics
Mathematics : Mathematical Logic and Foundations
Helps the reader to understand theory of distributions help students with
many examples
Solved problems problems with hints and problems with examples
Detailed proofs of the basic facts
This book explains many fundamental ideas on the theory of distributions. The theory of partial
differential equations is one of the synthetic branches of analysis that combines ideas and
methods from different fields of mathematics, ranging from functional analysis and harmonic
analysis to differential geometry and topology. This presents specific difficulties to those
studying this field. This second edition, which consists of 10 chapters, is suitable for upper
undergraduate/graduate students and mathematicians seeking an accessible introduction to
some aspects of the theory of distributions. It can also be used for one-semester course
Due 2021-09-24
2nd ed. 2021, XI, 262 p.
Softcover
ISBN 978-3-030-81264-5
Product category : Graduate/advanced undergraduate textbook
Mathematics : Functional Analysis