Item will ship after November 24, 2021
ISBN 9780367698652
November 24, 2021 Forthcoming by Chapman and Hall/CRC
230 Pages
Banach Limit and Applications provides all the results in the area of Banach Limit, its extensions, generalizations, and applications to various fields in one go (as far as possible). All the results in this field, after Banach introduced this concept in 1932, were scattered till now.
Sublinear functionals generating and dominating Banach Limit, unique Banach Limit (almost convergence), invariant means and invariant limits, absolute and strong almost convergence, applications to ergodicity, law of large numbers, Fourier series, uniform distribution of sequences, uniform density, core theorems, and functional Banach limits are discussed in this book. The discovery of functional analysis, such as the Hahn-Banach Theorem and the Banach-Steinhaus Theorem, helped the researchers to develop a modern, rich, and unified theory of sequence spaces by encompassing classical summability theory via matrix transformations and the topics related to sequence spaces, which arose from the concept of Banach limits, all of which are presented in this book.
The unique features of this book are as follows:
All the results in this area which were scattered till now are in one place.
The book is the first of its kind in the sense that there is no other competitive book.
The contents of this monograph did not appear in any book form before.
The audience of this book are the researchers in this area and Ph.D. and advanced masterfs students. The book is suitable for one- or two-semester course work for Ph.D. students, M.S. students in North America and Europe, and M.Phil. and masterfs students in India.
Introduction. Hahn-Banach Theorem and Generalizations. Banach and Generalized Limits. Almost Convergence Core Theorems. Absolute Almost Convergence. The space. Strong Almost Convergence. Functional Banach Limits. Matrix Transformations. Absolutely Almost and Strongly Almost Summable Sequences. Bibliography. Index.
Copyright Year 2022
ISBN 9780367748456
November 22, 2021 Forthcoming
486 Pages 104 Color & 3 B/W Illustrations
Foundations of Statistics for Data Scientists: With R and Python is designed as a textbook for a one- or two-term introduction to mathematical statistics for students training to become data scientists. It is an in-depth presentation of the topics in statistical science with which any data scientist should be familiar, including probability distributions, descriptive and inferential statistical methods, and linear modeling. The book assumes knowledge of basic calculus, so the presentation can focus on "why it works" as well as "how to do it." Compared to traditional "mathematical statistics" textbooks, however, the book has less emphasis on probability theory and more emphasis on using software to implement statistical methods and to conduct simulations to illustrate key concepts. All statistical analyses in the book use R software, with an appendix showing the same analyses with Python.
The book also introduces modern topics that do not normally appear in mathematical statistics texts but are highly relevant for data scientists, such as Bayesian inference, generalized linear models for non-normal responses (e.g., logistic regression and Poisson loglinear models), and regularized model fitting. The nearly 500 exercises are grouped into "Data Analysis and Applications" and "Methods and Concepts." Appendices introduce R and Python and contain solutions for odd-numbered exercises. The book's website has expanded R, Python, and Matlab appendices and all data sets from the examples and exercises.
1. Introduction to Statistical Science 2. Probability Distributions 3. Sampling Distributions 4. Statistical Inference: Estimation Skip Product Menu 5. Statistical Inference: Significance Testing 6. Linear Models and Least Squares 7. Generalized Linear Models 8. Classification and Clustering 9. Statistical Science: A Historical Overview Appendices
Copyright Year 2022
ISBN 9780367700812
286 Pages
This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The book assumes almost no prerequisite for the most part. However, familiarity with the basic convergence concepts in probability and a bit of mathematical maturity will be helpful.
Combinatorial properties of non-crossing partitions, including the Mobius function play a central role in introducing free probability.
Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants.
Free cumulants are introduced through the Mobius function.
Free product probability spaces are constructed using free cumulants.
Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed.
Convergence of the empirical spectral distribution is discussed for symmetric matrices.
Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices.
Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices.
Exercises, at advanced undergraduate and graduate level, are provided in each chapter.
Copyright Year 2022
ISBN 9780367705053
Published November 10, 2021
248 Pages 32 B/W Illustrations
One of the primary motivations for clinical trials and observational studies of humans is to infer cause and effect. Disentangling causation from confounding is of utmost importance. Fundamentals of Causal Inference explains and relates different methods of confounding adjustment in terms of potential outcomes and graphical models, including standardization, difference-in-differences estimation, the front-door method, instrumental variables estimation, and propensity score methods. It also covers effect-measure modification, precision variables, mediation analyses, and time-dependent confounding. Several real data examples, simulation studies, and analyses using R motivate the methods throughout. The book assumes familiarity with basic statistics and probability, regression, and R and is suitable for seniors or graduate students in statistics, biostatistics, and data science as well as PhD students in a wide variety of other disciplines, including epidemiology, pharmacy, the health sciences, education, and the social, economic, and behavioral sciences.
Beginning with a brief history and a review of essential elements of probability and statistics, a unique feature of the book is its focus on real and simulated datasets with all binary variables to reduce complex methods down to their fundamentals. Calculus is not required, but a willingness to tackle mathematical notation, difficult concepts, and intricate logical arguments is essential. While many real data examples are included, the book also features the Double What-If Study, based on simulated data with known causal mechanisms, in the belief that the methods are best understood in circumstances where they are known to either succeed or fail. Datasets, R code, and solutions to odd-numbered exercises are available at www.routledge.com.
1. Introduction. 2. Conditional Probability and Expectation. 3. Potential Outcomes and the Fundamental Problem of Causal Inference. 4. Effect-measure Modification and Causal Interaction. 5. Causal Directed Acyclic Graphs. 6. Adjusting for Confounding: Back-door method via Standardization. 7. Adjusting for Confounding: Difference-in-Differences Estimators. 8. Adjusting for Confounding: Front-door method. 9. Adjusting for Confounding: Instrumental Variables. 10. Adjusting for Confounding: Propensity-score Methods. 11. Efficiency with Precision Variables. 12. Mediation.
Copyright Year 2022
ISBN 9781032150468
November 29, 2021 Forthcoming
432 Pages 8 Color & 184 B/W Illustrations
There is an explosion of interest in dynamical systems in the mathematical community as well as in many areas of science. The results have been truly exciting: systems which once seemed completely intractable from an analytic point of view can now be understood in a geometric or qualitative sense rather easily.
Scientists and engineers realize the power and the beauty of the geometric and qualitative techniques. These techniques apply to a number of important nonlinear problems ranging from physics and chemistry to ecology and economics.
Computer graphics have allowed us to view the dynamical behavior geometrically. The appearance of incredibly beautiful and intricate objects such as the Mandelbrot set, the Julia set, and other fractals have really piqued interest in the field.
This is text is aimed primarily at advanced undergraduate and beginning graduate students. Throughout, the author emphasizes the mathematical aspects of the theory of discrete dynamical systems, not the many and diverse applications of this theory.
The field of dynamical systems and especially the study of chaotic systems has been hailed as one of the important breakthroughs in science in the past century and its importance continues to expand. There is no question that the field is becoming more and more important in a variety of scientific disciplines.
?Greatly expanded coverage complex dynamics now in Chapter 2
?The third chapter is now devoted to higher dimensional dynamical systems.
?Chapters 2 and 3 are independent of one another.
?New exercises have been added throughout.
Copyright Year 2022
ISBN 9781032079882
Published November 8, 2021
230 Pages
Noncommutative Polynomial Algebras of Solvable Type and Their Modules is the ?rst book to systematically introduce the basic constructive-computational theory and methods developed for investigating solvable polynomial algebras and their modules. In doing so, this book covers:
A constructive introduction to solvable polynomial algebras and Grobner basis theory for left ideals of solvable polynomial algebras and submodules of free modules
The new ?ltered-graded techniques combined with the determination of the existence of graded monomial orderings
The elimination theory and methods (for left ideals and submodules of free modules) combining the Grobner basis techniques with the use of Gelfand-Kirillov dimension, and the construction of di?erent kinds of elimination orderings
The computational construction of ?nite free resolutions (including computation of syzygies, construction of di?erent kinds of ?nite minimal free resolutions based on computation of di?erent kinds of minimal generating sets), etc.
This book is perfectly suited to researchers and postgraduates researching noncommutative computational algebra and would also be an ideal resource for teaching an advanced lecture course.
Copyright Year 2022
ISBN 9780367252571
November 22, 2021 Forthcoming
736 Pages 99 B/W Illustrations
Through the previous three editions, Handbook of Differential Equations has proven an invaluable reference for anyone working within the field of mathematics, including academics, students, scientists, and professional engineers.
The book is a compilation of methods for solving and approximating differential equations. These include the most widely applicable methods for solving and approximating differential equations,@as well as@numerous methods. Topics include methods for ordinary differential equations, partial differential equations, stochastic differential equations, and systems of such equations.
Included for nearly every method are:
The types of equations to which the method is applicable
The idea behind the method
The procedure for carrying out the method
At least one simple example of the method
Any cautions that should be exercised
Notes for more advanced users
The fourth edition includes corrections, many supplied by readers, as well as many new methods and techniques. These new and corrected entries make necessary improvements in this edition.