This volume contains the proceedings of the AMS Special Session on Differential Geometry and Global Analysis, Honoring the Memory of Tadashi Nagano (1930?2017), held January 16, 2020, in Denver, Colorado.
Tadashi Nagano was one of the great Japanese differential geometers, whose fundamental and seminal work still attracts much interest today. This volume is inspired by his work and his legacy and, while reminding historical results obtained in the past, presents recent developments in the geometry of symmetric spaces as well as generalizations of symmetric spaces; minimal surfaces and minimal submanifolds; totally geodesic submanifolds and their classification; Riemannian, affine, projective, and conformal connections; the (M+,M?) method and its applications; and maximal antipodal subsets. Additionally, the volume features recent achievements related to biharmonic and biconservative hypersurfaces in space forms, the geometry of Laplace operator on Riemannian manifolds, and Chen-Ricci inequalities for Riemannian maps, among other topics that could attract the interest of any scholar working in differential geometry and global analysis on manifolds.
Graduate students and research mathematicians interested in differential geometry and global analysis on manifolds.
Contemporary Mathematics, Volume: 777
2022; Softcover
MSC: Primary 53; 58;
Print ISBN: 978-1-4704-6015-0
Product Code: CONM/777
While partial differential equations (PDEs) are fundamental in mathematics and throughout the sciences, most undergraduate students are only exposed to PDEs through the method of separation of variations. This text is written for undergraduate students from different cohorts with one sole purpose: to facilitate a proficiency in many core concepts in PDEs while enhancing the intuition and appreciation of the subject. For mathematics students this will in turn provide a solid foundation for graduate study. A recurring theme is the role of concentration as captured by Dirac's delta function. This both guides the student into the convolution structure of the solution to the diffusion equation and PDEs involving the Laplacian and invites them to develop a cognizance for the theory of distributions. Both distributions and the Fourier transform are given full treatment.
The book is rich with physical motivations and interpretations, and it takes special care to clearly explain all the technical mathematical arguments, often with pre-motivations and post-reflections. Through these arguments the reader will develop a deeper proficiency and understanding of advanced calculus. While the text is comprehensive, the material is divided into short sections, allowing particular issues/topics to be addressed in a concise fashion. Sections which are more fundamental to the text are highlighted, allowing the instructor several alternative learning paths. The author's unique pedagogical style also makes the text ideal for self-learning.
Undergraduate and graduate students interested in partial differential equations.
Pure and Applied Undergraduate Texts, Volume: 54
2022; Softcover
MSC: Primary 35;
Print ISBN: 978-1-4704-6491-2
Product Code: AMSTEXT/54
Not yet published - available from June 2022
FORMAT: Hardback ISBN: 9781108489676
400 pagesDIMENSIONS: 228 x 152 mm
This compact course is written for the mathematically literate reader who wants to learn to analyze data in a principled fashion. The language of mathematics enables clear exposition that can go quite deep, quite quickly, and naturally supports an axiomatic and inductive approach to data analysis. Starting with a good grounding in probability, the reader moves to statistical inference via topics of great practical importance ? simulation and sampling, as well as experimental design and data collection ? that are typically displaced from introductory accounts. The core of the book then covers both standard methods and such advanced topics as multiple testing, meta-analysis, and causal inference.
Preface
Acknowledgments
Part I. Elements of Probability Theory:
1. Axioms of probability theory
2. Discrete probability spaces
3. Distributions on the real line
4. Discrete distributions
5. Continuous distributions
6. Multivariate distributions
7. Expectation and concentration
8. Convergence of random variables
9. Stochastic processes
Part II. Practical Considerations:
10. Sampling and simulation
11. Data collection
Part III. Elements of Statistical Inference:
12. Models, estimators, and tests
13. Properties of estimators and tests
14. One proportion
15. Multiple proportions
16. One numerical sample
17. Multiple numerical samples
18. Multiple paired numerical samples
19. Correlation analysis
20. Multiple testing
21. Regression analysis
22. Foundational issues
References
Index.
Part of Cambridge Monographs on Applied and Computational Mathematics
Not yet published - available from April 2022
FORMAT: HardbackI SBN: 9781108838061
LENGTH: 188 pagesDIMENSIONS: 229 x 152 mm
The Christoffel?Darboux kernel, a central object in approximation theory, is shown to have many potential uses in modern data analysis, including applications in machine learning. This is the first book to offer a rapid introduction to the subject, illustrating the surprising effectiveness of a simple tool. Bridging the gap between classical mathematics and current evolving research, the authors present the topic in detail and follow a heuristic, example-based approach, assuming only a basic background in functional analysis, probability and some elementary notions of algebraic geometry. They cover new results in both pure and applied mathematics and introduce techniques that have a wide range of potential impacts on modern quantitative and qualitative science. Comprehensive notes provide historical background, discuss advanced concepts and give detailed bibliographical references. Researchers and graduate students in mathematics, statistics, engineering or economics will find new perspectives on traditional themes, along with challenging open problems.
Foreword Francis Bach
Preface
1. Introduction
Part I. Historical and Theoretical Background:
2. Positive definite kernels and moment problems
3. Univariate Christoffel?Darboux analysis
4. Multivariate Christoffel?Darboux analysis
5. Singular supports
Part II. Statistics and Applications to Data Analysis:
6. Empirical Christoffel?Darboux analysis
7. Applications and occurrences in data analysis
Part III. Complementary Topics:
8. Further applications
9. Transforms of Christoffel?Darboux kernels
10. Spectral characterization and extensions of the Christoffel function
References
Index.
Copyright Year 2022
Available for pre-order. Item will ship after May 16, 2022
ISBN 9780367537944
May 16, 2022
512 Pages 272 B/W Illustrations
Data Science students and practitioners want to find a forecast that gworksh and donft want to be constrained to a single forecasting strategy, Practical Time Series Analysis for Data Science discusses techniques of ensemble modelling for combining information from several strategies. Covering time series regression models, exponential smoothing, Holt-Winters forecasting, and Neural Networks. It places a particular emphasis on classical ARMA and ARIMA models that is often lacking from other textbooks on the subject.
Practical Time Series Analysis for Data Science is an accessible guide that doesnft require a background in calculus to be engaging but does not shy away from deeper explanations of the techniques discussed.
Provides a thorough coverage and comparison of a wide array of time series models and methods: Exponential Smoothing, Holt Winters, ARMA and ARIMA, deep learning models including RNNs, LSTMs, GRUs, and ensemble models composed of combinations of these models.
Introduces the factor table representation of ARMA and ARIMA models. This representation is not available in any other book at this level and is extremely useful in both practice and pedagogy.
Uses real world examples that can be readily found via web links from sources such as the US Bureau of Statistics, Department of Transportation and the World Bank.
There is an accompanying R package that is easy to use and requires little or no previous R experience. The package implements the wide variety of models and methods presented in the book and has tremendous pedagogical use.
EMS Tracts in Mathematics Vol. 34
ISBN print 978-3-98547-009-9, ISBN online 978-3-98547-509-4
DOI 10.4171/ETM/34
November 2021, 288 pages, hardcover, 16.5 x 23.5 cm.
This book studies the motion of suspensions, that is, of mixtures of a viscous incompressible fluid with small solid particles that can interact with each other through forces of non-hydrodynamic origin. In view of the complexity of the original (microscopic) system of equations that describe such phenomena, which appear both in nature and in engineering processes, the problem is reduced to a macroscopic description of the motion of mixtures as an effective continuous medium.
The focus is on developing mathematical methods for constructing such homogenized models for the motion of suspensions with an arbitrary distribution of solid particles in a fluid. In particular, the results presented establish that depending on the concentration of the solid phase of the mixture, the motion of suspensions can occur in two qualitatively different modes: that of frozen or of filtering particles.
Being one of the first mathematically rigorous treatises on suspensions from the viewpoint of homogenization theory, this book will be useful to graduate students and researchers in applied analysis and partial differential equations as well as to physicists and engineers interested in the theory of complex fluids with microstructure.
Keywords: suspension, asymptotic behavior of solutions, mesoscopic characteristics of microstructure, homogenized equations, frozen particles mode, filtering particles mode, cell problem