Format: 322 pages, height x width: 235x155 mm, weight: 516 g, 325 Illustrations, color;
65 Illustrations, black and white; XIV, 322 p. 390 illus., 325 illus. in color.
Pub. Date: 02-Oct-2023
ISBN-13: 9783030985608
Contents and treatment are fresh and very different from the standard treatments
Presents a fully constructive version of what it means to do algebra
The exposition is not only clear, it is friendly, philosophical, and considerate even to the most naive or inexperienced reader
Part I.-
1. A Fundamental Theorem.-
2. Topics in Algebra.-
3. Some Quadratic Problems.-
4. The Genus of an Algebraic Curve.-
5. Miscellany.
Part II.-
6. Constructive Algebra.-
7. The Algorithmic Foundation of Galois'sTheory.-
8. A Constructive Definition of Points on an Algebraic Curve.-
9. Abel's Theorem.
Format: 372 pages, height x width: 235x155 mm, weight: 587 g, 246 Tables, color;
246 Illustrations, color; 3 Illustrations, black and white; X, 372 p. 249 illus., 246 illus. in color.,
Series: Statistics and Computing
Pub. Date: 20-Oct-2023
ISBN-13: 9783031135866
This textbook presents methods and techniques for time series analysis and forecasting and shows how to use Python to implement them and solve data science problems. It covers not only common statistical approaches and time series models, including ARMA, SARIMA, VAR, GARCH and state space and Markov switching models for (non)stationary, multivariate and financial time series, but also modern machine learning procedures and challenges for time series forecasting. Providing an organic combination of the principles of time series analysis and Python programming, it enables the reader to study methods and techniques and practice writing and running Python code at the same time. Its data-driven approach to analyzing and modeling time series data helps new learners to visualize and interpret both the raw data and its computed results. Primarily intended for students of statistics, economics and data science with an undergraduate knowledge of probability and statistics, the book will equally appeal to industry professionals in the fields of artificial intelligence and data science, and anyone interested in using Python to solve time series problems.
1. Time Series Concepts and Python.- 2. Exploratory Time Series Data
Analysis.- 3. Stationary Time Series Models.- 4. ARMA and ARIMA Modeling and
Forecasting.- 5. Nonstationary Time Series Models.- 6. Financial Time Series
and Related Models.- 7. Multivariate Time Series Analysis.- 8. State Space
Models and Markov Switching Models.- 9. Nonstationarity and Cointegrations.-
10. Modern Machine Learning Methods for Time Series Analysis.
Format: 346 pages, height x width: 235x155 mm, weight: 551 g, 10 Illustrations, black and white; XIII, 346 p. 10 illus.,
Series: Applied Mathematical Sciences 211
Pub. Date: 18-Sep-2023
ISBN-13: 9783031127649
This book is intended to provide graduate students and researchers in graph theory with an overview of the elementary methods of graph Ramsey theory. It is especially targeted towards graduate students in extremal graph theory, graph Ramsey theory, and related fields, as the included contents allow the text to be used in seminars.
It is structured in thirteen chapters which are application-focused and largely independent, enabling readers to target specific topics and information to focus their study. The first chapter includes a true beginners overview of elementary examples in graph Ramsey theory mainly using combinatorial methods. The following chapters progress through topics including the probabilistic methods, algebraic construction, regularity method, but that's not all.
Many related interesting topics are also included in this book, such as the disproof for a conjecture of Borsuk on geometry, intersecting hypergraphs, Tur?n numbers and communication channels, etc.
Existence.- Small Ramsey Numbers.- Basic Probalistic Method.- Random
Graph.- Lov?sz Local Lemma.- Constructive Lower Bounds.- Tur?n Number and
Related Ramsey Number.- Communication Channels.- Dependent Random Choice.-
Quasi-Random Graphs.- Regularity Lemma and van der Waerden Number.- More
Ramsey Linear Functions.- Various Ramsey Problems.
Format: 921 pages, height x width: 279x210 mm, weight: 2300 g, 3 Illustrations, black and white; XXVII, 921 p. 3 illus
Pub. Date: 07-Oct-2023
ISBN-13: 9783030958664
This book explores topics in multivariate statistical analysis, relevant in the real and complex domains. It utilizes simplified and unified notations to render the complex subject matter both accessible and enjoyable, drawing from clear exposition and numerous illustrative examples. The book features an in-depth treatment of theory with a fair balance of applied coverage, and a classroom lecture style so that the learning process feels organic. It also contains original results, with the goal of driving research conversations forward. This will be particularly useful for researchers working in machine learning, biomedical signal processing, and other fields that increasingly rely on complex random variables to model complex-valued data. It can also be used in advanced courses on multivariate analysis. Numerous exercises are included throughout.
1. Mathematical Preliminaries.-
2. The Univariate Gaussian and Related Distribution.-
3. Multivariate Gaussian and Related Distributions.-
4. The Matrix-variate Gaussian Distribution.-
5. Matrix-variate Gamma and Beta Distributions.-
6. Hypothesis Testing and Null Distributions.-
7. Rectangular Matrix-variate Distributions.-
8. Distributions of Eigenvalues and Eigenvectors.-
9. Principal Component Analysis.-
10. Canonical Correlation Analysis.-
11. Factor Analysis.-
12. Classification Problems.-
13. Multivariate Analysis of Variance (MANOVA).-
14. Profile Analysis and Growth Curves.-
15. Cluster Analysis and Correspondence Analysis.
Format: 127 pages, height x width: 240x168 mm, 1 Illustrations, black and white; XI, 127 p. 1 illus., 1 Hardback
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 20-Dec-2023
ISBN-13: 9783031437120
This book is devoted to the study of multivariate discrete q-distributions, which is greatly facilitated by existing multivariate q-sequences and q-functions. Classical multivariate discrete distributions are defined on a sequence of independent and identically distributed Bernoulli trials, with either being a success of a certain rank (level) or a failure. The author relaxes the assumption that the probability of success of a trial is constant by assuming that it varies geometrically with the number of trials and/or the number of successes. The latter is advantageous in the sense that it permits incorporating the experience gained from the previous trials and/or successes, which leads to multivariate discrete q-distributions. Furthermore, q-multinomial and negative q-multinomial formulae are obtained. Next, the book addresses q-multinomial and negative q-multinomial distributions of the first and second kind. The author also examines multiple q-Polya urn model, multivariate q-Polya and inverse q-Polya distributions.
Preface.- Multivariate q-Combinatorics and q-Hypergeometric Series.-
Multivariate q-Distributions.- Appendix: Hints and Answers to Exercises.-
Bibliography.- Index.
Format: 748 pages, height x width: 235x155 mm, weight: 1328 g, 35 Illustrations, black and white; XXX, 748 p. 35 illus., 1 Hardback
Series: Cornerstones
Pub. Date: 22-Oct-2023
ISBN-13: 9783031466175
Other books in subject:
This book offers a self-contained introduction to partial differential equations (PDEs), primarily focusing on linear equations, and also providing perspective on nonlinear equations. The treatment is mathematically rigorous with a generally theoretical layout, with indications to some of the physical origins of PDEs. The Second Edition is rewritten to incorporate years of classroom feedback, to correct errors and to improve clarity. The exposition offers many examples, problems and solutions to enhance understanding. Requiring only advanced differential calculus and some basic Lp theory, the book will appeal to advanced undergraduates and graduate students, and to applied mathematicians and mathematical physicists.
Preliminaries.- Quasi-Linear Equations and the Cauchy-Kowalewski
Theorem.- The Laplace Equation.- Boundary Value Problems by Double-Layer
Potentials.- Integral Equations and Eigenvalue Problems.- The Heat Equation.-
The Wave Equation.- Quasi-Linear Equations of First Order.- Linear Elliptic
Equations with Measurable Coefficients.- Elliptic De Giorgi Classes.-
Navier-Stokes Equations.- Quasi-Linear Hyperbolic First Order Systems.-
Non-Linear Equations of the First Order.