Format: Hardback, 268 pages, height x width: 235x155 mm, 13 Tables, color; 15 Illustrations, color;
12 Illustrations, black and white; X, 268 p. 27 illus., 15 illus. in color.
Series: Applied and Numerical Harmonic Analysis
Pub. Date: 04-Oct-2023
ISBN-13: 9783031377990
Over the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis on fractals. This is the first volume of a tribute to his work and legacy, featuring chapters that reflect his mathematical interests, written by his colleagues and friends. An introductory chapter summarizes his broad and varied mathematical work and highlights his profound contributions as a mathematical mentor. The remaining articles are grouped into three sections ? functional and harmonic analysis on Euclidean spaces, analysis on manifolds, and analysis on fractals ? and explore Strichartz’ contributions to these areas, as well as some of the latest developments.
Part I. Introduction to this volume.- From Strichartz Estimates to
Differential Equations on Fractals.- Part II. Functional and harmonic
analysis on Euclidean spaces.- A new proof of Strichartz estimates for the
Schroedinger equation in 2 + 1 dimensions.- Modulational instability of
classical water waves.- Convergence Analysis of the Deep Galerkin Method for
Weak Solutions.- The 4-player gambler's ruin problem.- Part III. Analysis on
Manifolds.- Product Manifolds with Improved Spectral Cluster and Weyl
Remainder Estimates.- A scalar valued Fourier transform for the Heisenberg
group.- Asymptotic behavior of the heat semigroup on certain Riemannian
manifolds.- Part IV. Intrinsic Analysis on Fractals.- Fourier Series for
Fractals in 2 Dimensions.- Blowups and Tops of Overlapping Iterated Function
Systems.- Estimates of the local spectral dimension of the Sierpinski
gasket.- Heat kernel fluctuations for stochastic processes on fractals and
random media.- Index.
Format: Paperback / softback, 333 pages, height x width: 235x155 mm, 32 Illustrations, black and white; X, 333 p. 32 illus.
Series: Universitext
Pub. Date: 07-Oct-2023
ISBN-13: 9783031384912
This textbook offers a complete one-semester course in probability, covering the essential topics necessary for further study in the areas of probability and statistics.
The book begins with a review of the fundamentals of measure theory and integration. Probability measures, random variables, and their laws are introduced next, along with the main analytic tools for their investigation, accompanied by some applications to statistics. Questions of convergence lead to classical results such as the law of large numbers and the central limit theorem with their applications also to statistical analysis and more. Conditioning is the next main topic, followed by a thorough introduction to discrete time martingales. Some attention is given to computer simulation. Through the text, over 150 exercises with full solutions not only reinforce the concepts presented, but also provide students with opportunities to develop their problem-solving skills, and make this textbook suitable for guided self-study.
Based on years of teaching experience, the author's expertise will be evident in the clear presentation of material and the carefully chosen exercises. Assuming familiarity with measure and integration theory as well as elementary notions of probability, the book is specifically designed for teaching in parallel with a first course in measure theory. An invaluable resource for both instructors and students alike, it offers ideal preparation for further courses in statistics or probability, such as stochastic calculus, as covered in the author's book on the topic.
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1 Elements of Measure Theory.- 2 Probability.- 3 Convergence.- 4 Conditioning.- 5 Martingales.- 6 Complements.- 7 Solutions.
Format: Hardback, 305 pages, height x width: 235x155 mm, 3 Illustrations, black and white; XVI, 305 p. 3 illus
Series: CMS/CAIMS Books in Mathematics 8
Pub. Date: 10-Oct-2023
ISBN-13: 9783031372377
Although the Lucas sequences were known to earlier investigators such as Lagrange, Legendre and Genocchi, it is because of the enormous number and variety of results involving them, revealed by Edouard Lucas between 1876 and 1880, that they are now named after him. Since Lucas' early work, much more has been discovered concerning these remarkable mathematical objects, and the objective of this book is to provide a much more thorough discussion of them than is available in existing monographs. In order to do this a large variety of results, currently scattered throughout the literature, are brought together. Various sections are devoted to the intrinsic arithmetic properties of these sequences, primality testing, the Lucasnomials, some associated density problems and Lucas' problem of finding a suitable generalization of them. Furthermore, their application, not only to primality testing, but also to integer factoring, efficient solution of quadratic and cubic congruences, cryptography and Diophantine equations are briefly discussed. Also, many historical remarks are sprinkled throughout the book, and a biography of Lucas is included as an appendix.Much of the book is not intended to be overly detailed. Rather, the objective is to provide a good, elementary and clear explanation of the subject matter without too much ancillary material. Most chapters, with the exception of the second and the fourth, will address a particular theme, provide enough information for the reader to get a feel for the subject and supply references to more comprehensive results. Most of this work should be accessible to anyone with a basic knowledge of elementary number theory and abstract algebra. The book's intended audience is number theorists, both professional and amateur, students and enthusiasts.
1. Introduction.-
2. Basic theory of Lucas sequences.-
3. Applications.-
4. Further Properties.-
5. Some Properties of Lucasnomials.-
6. Cubic
Extensions of the Lucas Sequences.-
7. Linear Recurrence Sequences and
Further Generalizations.-
8. Divisibility Sequences and Further
Generalizations.-
9. Prime Density of Companion Lucas Sequences.-
10.
Epilogue and Open Problems.
Format: Hardback, 796 pages, height x width: 235x155 mm, 27 Illustrations, black and white; XXVI, 796 p. 27 illus.
Series: Theoretical and Mathematical Physics
Pub. Date: 15-Sep-2023
ISBN-13: 9783031365294
Graduate students typically enter into courses on string theory having little to no familiarity with the mathematical background so crucial to the discipline. As such, this book, based on lecture notes, edited and expanded, from the graduate course taught by the author at SISSA and BIMSA, places particular emphasis on said mathematical background. The target audience for the book includes students of both theoretical physics and mathematics. This explains the book’s "strange" style: on the one hand, it is highly didactic and explicit, with a host of examples for the physicists, but, in addition, there are also almost 100 separate technical boxes, appendices, and starred sections, in which matters discussed in the main text are put into a broader mathematical perspective, while deeper and more rigorous points of view (particularly those from the modern era) are presented. The boxes also serve to further shore up the reader’s understanding of the underlying math. In writing this book, the author’s goal was not to achieve any sort of definitive conciseness, opting instead for clarity and "completeness". To this end, several arguments are presented more than once from different viewpoints and in varying contexts.
Chapter
1. The Polyakov path integral.
Chapter
2. Introduction to 2d conformal field theories.
Chapter
3. Spectrum, vertices, and BRST quantization.
Chapter
4. Tree and one-loop amplitudes in the bosonic string.
Chapter
5. Consistent 10d superstring, modular invariance, and all that.
Chapter
6. The Heterotic string: part I.
Chapter
7. Toroidal compactifications and T-duality (bosonic string).
Chapter
8. The Heterotic string: part II.
Chapter
9. Superstring interactions and anomalies.
Chapter
10. Superstring D-branes.
Chapter
11. Strings at strong coupling.
Chapter
12. Calabi-Yau compactifications. Appendix.
Format: Hardback, 936 pages, height x width: 235x155 mm, 81 Tables, color; 81 Illustrations, color;
58 Illustrations, black and white; XVII, 936 p. 139 illus., 81 illus. in color.
Pub. Date: 26-Sep-2023
ISBN-13: 9783031308314
This book provides an introduction to real analysis, a fundamental topic that is an essential requirement in the study of mathematics. It deals with the concepts of infinity and limits, which are the cornerstones in the development of calculus.
Beginning with some basic proof techniques and the notions of sets and functions, the book rigorously constructs the real numbers and their related structures from the natural numbers. During this construction, the readers will encounter the notions of infinity, limits, real sequences, and real series. These concepts are then formalised and focused on as stand-alone objects. Finally, they are expanded to limits, sequences, and series of more general objects such as real-valued functions. Once the fundamental tools of the trade have been established, the readers are led into the classical study of calculus (continuity, differentiation, and Riemann integration) from first principles. The book concludes with an introduction to the study of measures and how one can construct the Lebesgue integral as an extension of the Riemann integral.
This textbook is aimed at undergraduate students in mathematics. As its title suggests, it covers a large amount of material, which can be taught in around three semesters. Many remarks and examples help to motivate and provide intuition for the abstract theoretical concepts discussed. In addition, more than 600 exercises are included in the book, some of which will lead the readers to more advanced topics and could be suitable for independent study projects. Since the book is fully self-contained, it is also ideal for self-study.
Preface.-
1. Logic and Sets.-
2. Integers.-
3. Construction of the Real Numbers.-
4. The Real Numbers.-
5. Real Sequences.-
6. Some Applications of Real Sequences.-
7. Real Series.-
8. Additional Topics in Real Series.-
9. Functions and Limits.-
10. Continuity.-
11. Function Sequences and Series.-
12. Power Series.-
13. Differentiation.-
14. Some Applications of Differentiation.-
15. Riemann and Darboux Integration.-
16. The Fundamental Theorem of Calculus.-
17. Taylor and MacLaurin Series.-
18. Introduction to Measure Theory.-
19. Lebesgue Integration.-
20. Double Integrals.- Solutions to the Exercises.- Bibliography.- Index.
Format: Hardback, 466 pages, height x width: 235x155 mm, XX, 466 p.
Pub. Date: 29-Sep-2023
ISBN-13: 9789819937875
This book offers a concise and thorough introduction to the topic of applied functional analysis. Targeted to graduate students of mathematics, it presents standard topics in a self-contained and accessible manner. Featuring approximately 300 problems sets to aid in understanding the content, this text serves as an ideal resource for independent study or as a textbook for classroom use. With its comprehensive coverage and reader-friendly approach, it is equally beneficial for both students and teachers seeking a detailed and in-depth understanding of the subject matter.
Chapter
1. Operator Theory.
Chapter
2. Distribution Theory.
Chapter
3. Theory of Sobolev Spaces.
Chapter
4. Elliptic Theory.
Chapter
5. Calculus of Variations.
Format: Paperback / softback, 86 pages, height x width: 235x155 mm, X, 86 p.,
Series: SpringerBriefs in Statistics
Pub. Date: 05-Nov-2023
ISBN-13: 9783031345524
This book provides a compact and systematic overview of closure properties of heavy-tailed and related distributions, including closure under tail equivalence, convolution, finite mixing, maximum, minimum, convolution power and convolution roots, and product-convolution closure. It includes examples and counterexamples that give an insight into the theory and provides numerous references to technical details and proofs for a deeper study of the subject. The book will serve as a useful reference for graduate students, young researchers, and applied scientists.
Preface.- Introduction.- Heavy-Tailed and Related Classes of
Distributions.- Closure Properties under Tail-Equivalence, Convolution,
Finite Mixing, Maximum and Minimum.- Convolution-Root Closure.-
Product-Convolution of Heavy-tailed and Related Distributions.- Summary of
Closure Properties.-References.- Index.