A publication of the Societe Mathematique de France
This is the first of two volumes that celebrate the memory of Jean-Christophe Yoccoz.
These volumes present research articles on various aspects of the theory of dynamical systems
and related topics that were dear to him.
Graduate students and research mathematicians.
Mathematics : History of Mathematics
Godel's Shorthand Notes & Lectures on Incompleteness
Contains a thorough introduction to a very important mathematician's research
Features a series of lectures and seminars based on Godel's results
Includes a translation of Godel's manuscripts from German Gabelsberger shorthand to English
Kurt Godel (1906?1978) shook the mathematical world in 1931 by a result that has become
an icon of 20th century science: The search for rigour in proving mathematical theorems had
led to the formalization of mathematical proofs, to the extent that such proving could be
reduced to the application of a few mechanical rules. Godel showed that whenever the part of
mathematics under formalization contains elementary arithmetic, there will be arithmetical
statements that should be formally provable but aren’t. The result is known as Godel’s first
incompleteness theorem, so called because there is a second incompleteness result, embodied
in his answer to the question "Can mathematics be proved consistent?" This book offers the
first examination of Godel’s preserved notebooks from 1930, written in a long-forgotten
German shorthand, that show his way to the results: his first ideas, how they evolved, and how
the jewel-like final presentation in his famous publication On formally undecidable propositions
was composed.The book also contains the original version of Godel’s incompleteness article, as
handed in for publication with no mentioning of the second incompleteness theorem, as well
as six contemporary lectures and seminars Godelgave between 1931 and 1934 in Austria,
Germany, and the United States. The lectures are masterpieces of accessible presentations of
deep scientific results, readable even for those without special mathematical training, and
published here for the first time.
1st ed. 2020, IX, 263 p.
Hardcover
ISBN 978-3-030-50875-3
Product category : Monograph
Series : Sources and Studies in the History of Mathematics and Physical Sciences
Mathematics : Mathematical Applications in the Physical Sciences
Highlights state-of-the-art tools for the identification and reconstruction of
unknown coefficients, control of coupled phenomena, and regularization
Gathers papers from a diverse mix of fields, so as to promote the exchange of
ideas on possible improvements and cross-fertilization
Shares valuable insights on the practical implementation of algorithms and co-design
This proceedings volume gathers peer-reviewed, selected papers presented at the
“Mathematical and Numerical Approaches for Multi-Wave Inverse Problems” conference at the
Centre Internacional de Rencontres Mathematiques (CIRM) in Marseille, France, in April 2019.
It brings the latest research into new, reliable theoretical approaches and numerical techniques
for solving nonlinear and inverse problems arising in multi-wave and hybrid systems.
Multiwave inverse problems have a wide range of applications in acoustics, electromagnetics, optics,
medical imaging, and geophysics, to name but a few. In turn, it is well known that inverse
problems are both nonlinear and ill-posed: two factors that pose major challenges for the
development of new numerical methods for solving these problems, which are discussed in
detail. These papers will be of interest to all researchers and graduate students working in the
fields of nonlinear and inverse problems and its applications.
1st ed. 2020, VII, 142 p. 29 illus., 24 illus. in color.
Hardcover
ISBN 978-3-030-48633-4
Product category : Proceedings
Series : Springer Proceedings in Mathematics & Statistics
The Legacy of Gaspard Monge
Presents a new perspective on the history of mathematics teaching by looking
at descriptive geometry in the 19th century
Offers myriad international viewpoints on history of mathematics teaching
from renowned specialists across the field
Concerns relations between technics, arts and mathematics
This book seeks to explore the history of descriptive geometry in relation to its circulation in
the 19th century, which had been favoured by the transfers of the model of the Ecole
Polytechnique to other countries. The book also covers the diffusion of its teaching from higher
instruction to technical and secondary teaching. In relation to that, there is analysis of the role
of the institution ? similar but definitely not identical in the different countries ? in the field
under consideration. Thebook contains chapters focused on different countries, areas, and
institutions, written by specialists of the history of the field. Insights on descriptive geometry
are provided in the context of the mathematical aspect, the aspect of teaching in particular to
non-mathematicians, and the institutions themselves
1st ed. 2019, XXVI, 437 p. 87 illus., 24 illus. in color.
Hardcover
ISBN 978-3-030-14807-2
Product category : Contributed volume
Series : International Studies in the History of Mathematics and its Teaching
Softcover
ISBN 978-3-030-14810-2
Statistics : Statistical Theory and Methods
Highlights modern analytical methods in statistics and their extensions
Focuses on estimation, asymptotics, robustness, and stochastics models
Gathers contributions by experts in the field
This book collects peer-reviewed contributions on modern statistical methods and topics,
stemming from the third workshop on Analytical Methods in Statistics, AMISTAT 2019, held in
Liberec, Czech Republic, on September 16-19, 2019. Real-life problems demand statistical
solutions, which in turn require new and profound mathematical methods. As such, the book is
not only a collection of solved problems but also a source of new methods and their practical
extensions. The authoritative contributions focus on analytical methods in statistics, asymptotics,
estimation and Fisher information, robustness, stochastic models and inequalities, and other
related fields; further, they address e.g. average autoregression quantiles, neural networks,
weighted empirical minimum distance estimators, implied volatility surface estimation, the
Grenander estimator, non-Gaussian component analysis, meta learning, and high-dimensional
errors-in-variables models.
1st ed. 2020, X, 156 p. 15 illus., 8 illus. in color.
Hardcover
ISBN 978-3-030-48813-0
Product category : Proceedings
Series : Springer Proceedings in Mathematics & Statistics
Mathematics : Convex and Discrete Geometry
The text provides a self-contained and efficient one-semester introduction to
the main concepts and results in convex geometry.
The selected topics highlight the interactions between geometry and analysis,
treating several topics for the first time in an introductory textbook.
Suggestions for further reading and a large number of solved exercises complement the main text
This book providesa self-contained introduction toconvex geometry in Euclidean space.After
covering the basic concepts and results, it developsBrunn?Minkowskitheory, with an exposition
of mixed volumes, the Brunn?Minkowski inequality, and some of its consequences,includingthe
isoperimetric inequality.Further centraltopics are then treated, such as surface area measures,
projection functions, zonoids, and geometric valuations.Finally, an introduction tointegralgeometric
formulas in Euclidean space is provided.The numerous exercises and the
supplementary material at the end of each sectionform an essential partof the book. Convexity
is an elementary and naturalconcept.It plays a key role in many mathematical fields, including
functional analysis,optimization,probability theory,and stochastic geometry. Paving the way to
the more advanced and specialized literature, thematerialwill beaccessible to students in the
third year and can be coveredin one semester.
Due 2020-11-09
1st ed. 2020, XVIII, 287 p.11 illus., 9 illus. in color.
Hardcover
ISBN 978-3-030-50179-2
Product category : Graduate/advanced undergraduate textbook
Series : Graduate Texts in Mathematics