Munster Lectures in Mathematics
ISBN print 978-3-03719-184-2, ISBN online 978-3-03719-684-7
DOI 10.4171/184
April 2018, 222 pages, softcover, 17 x 24 cm.
38.00 Euro
Model theory is a thriving branch of mathematical logic with strong connections to other fields of mathematics. Its versatility has recently led to spectacular applications in areas ranging from diophantine geometry, algebraic number theory and group theory to combinatorics.
This volume presents lecture notes from a spring school in model theory which took place in Munster, Germany. The notes are aimed at PhD students but should also be accessible to undergraduates with some basic knowledge in model theory. They contain the core of stability theory (Bays, Palacin), two chapters connecting generalized stability theory with group theory (Clausen and Tent, Simon), as well as introductions to the model theory of valued fields (Hils, Jahnke) and motivic integration (Halupczok).
Keywords: Model theory, stability theory, NIP theories, definably amenable groups, profinite groups, valuation theory, algebraically closed valued fields, motivic integration
ISBN: 978-1-118-66930-3
Jul 2018
240 pages
A preeminent expert in the field explores new and exciting methodologies in the ever-growing field of robust statistics
Used to develop data analytical methods, which are resistant to outlying observations in the data, while capable of detecting outliers, robust statistics is extremely useful for solving an array of common problems, such as estimating location, scale, and regression parameters. Written by an internationally recognized expert in the field of robust statistics, this book addresses a range of well-established techniques while exploring, in depth, new and exciting methodologies. Local robustness and global robustness are discussed, and problems of non-identifiability and adaptive estimation are considered. Rather than attempt an exhaustive investigation of robustness, the author provides readers with a timely review of many of the most important problems in statistical inference involving robust estimation, along with a brief look at confidence intervals for location. Throughout, the author meticulously links research in maximum likelihood estimation with the more general M-estimation methodology. Specific applications and R and some MATLAB subroutines with accompanying data sets?available both in the text and online?are employed wherever appropriate.
Providing invaluable insights and guidance, Robustness Theory and Application:
Offers a balanced presentation of theory and applications within each topic-specific discussion
Features solved examples throughout which help clarify complex and/or difficult concepts
Meticulously links research in maximum likelihood type estimation with the more general M-estimation methodology
Delves into new methodologies which have been developed over the past decade without stinting on coverage of “tried-and-true” methodologies
Includes R and some MATLAB subroutines with accompanying data sets, which help illustrate the power of the methods described
Robustness Theory and Application is an important resource for all statisticians interested in the topic of robust statistics. This book encompasses both past and present research, making it a valuable supplemental text for graduate-level courses in robustness.
ISBN: 978-1-119-26407-1
Aug 2018
544 pages
A comprehensive resource that draws a balance between theory and applications of nonlinear time series analysis
Nonlinear Time Series Analysis offers an important guide to both parametric and nonparametric methods, nonlinear state-space models, and Bayesian as well as classical approaches to nonlinear time series analysis. The authors?noted experts in the field?explore the advantages and limitations of the nonlinear models and methods and review the improvements upon linear time series models.
The need for this book is based on the recent developments in nonlinear time series analysis, statistical learning, dynamic systems and advanced computational methods. Parametric and nonparametric methods and nonlinear and non-Gaussian state space models provide a much wider range of tools for time series analysis. In addition, advances in computing and data collection have made available large data sets and high-frequency data. These new data make it not only feasible, but also necessary to take into consideration the nonlinearity embedded in most real-world time series. This vital guide:
* Offers research developed by leading scholars of time series analysis
* Presents R commands making it possible to reproduce all the analyses included in the text
* Contains real-world examples throughout the book*? Recommends exercises to test understanding of material presented
* Includes an instructor solutions manual and companion website
Written for students, researchers, and practitioners who are interested in exploring nonlinearity in time series, Nonlinear Time Series Analysis offers a comprehensive text that explores the advantages and limitations of the nonlinear models and methods and demonstrates the improvements upon linear time series models.
Fifth and final volume examining some of Ramanujan's deepest work in the last year of his life
Proves mock theta conjectures first introduced in Ramanujan's famous Last Letter
Features Ramanujan’s Euler products and several continued fractions
In the spring of 1976, George Andrews of Pennsylvania State University visited the library at
Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers,
Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This
manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently
been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This fifth
and final installment of the authors’ examination of Ramanujan’s lost notebook focuses on the
mock theta functions first introduced in Ramanujan’s famous Last Letter. This volume proves
all of the assertions about mock theta functions in the lost notebook and in the Last Letter,
particularly the celebrated mock theta conjectures. Other topics feature Ramanujan’s many
elegant Euler products and the remaining entries on continued fractions not discussed in the
preceding volumes. Review from the second volume: "Fans of Ramanujan's mathematics are
sure to be delighted by this book. While some of the content is taken directly from published
papers, most chapters contain new material and some previously published proofs have been
improved. Many entries are just begging for further study and will undoubtedly be inspiring
research for decades to come. The next installment in this series is eagerly awaited." -
MathSciNet Review from the first volume: "Andrews and Berndt are to be congratulated on the
job they are doing. This is the first step...on the way to an understanding of the work of the
genius Ramanujan. It should act as an inspiration to future generations of mathematicians to
tackle a job that will never be complete." - Gazette of the Australian Mathematical Society
ISBN 978-3-319-77832-7 f
Updated Edition of the first comprehensive monograph on the topic
Contains new material and a thorough presentation of the historical development
Numerous attractive figures and original photos
Connections to various mathematical fields and applications to fields like
computer science and psychology
Exercises with hints and solutions
The solitaire game “The Tower of Hanoi" was invented in the 19th century by the French
number theorist Edouard Lucas. The book presents its mathematical theory and offers a survey
of the historical development from predecessors up to recent research. In addition to longstanding
myths, it provides a detailed overview of the essential mathematical facts with
complete proofs, and also includes unpublished material, e.g., on some captivating integer
sequences. The main objects of research today are the so-called Hanoi graphs and the related
Sierpiski graphs. Acknowledging the great popularity of the topic in computer science,
algorithms, together with their correctness proofs, form an essential part of the book. In view
of the most important practical applications, namely in physics, network theory and cognitive
(neuro)psychology, the book also addresses other structures related to the Tower of Hanoi and
its variants. The updated second edition includes, for the first time in English, the breakthrough
reached with the solution of the “The Reve's Puzzle" in 2014. This is a special case of the
famed Frame-Stewart conjecture which is still open after more than 75 years. Enriched with
elaborate illustrations, connections to other puzzles and challenges for the reader in the form
of (solved) exercises as well as problems for further exploration, this book is enjoyable reading
for students, educators, game enthusiasts and researchers alike. Excerpts from reviews of the
first edition: “The book is an unusual, but very welcome, form of mathematical writing:
recreational mathematics taken seriously and serious mathematics treated historically. I don’t
hesitate to recommend this book to students, professional research mathematicians, teachers,
and to readers of popular mathematics who enjoy more technical expository detail.
ISBN 978-3-319-73778-2