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Siu Yum-Tong: Introduction to Several
Complex Variables

Introduction to Several Complex Variables

The Handbook of Complex Analysis will be an entree for advanced undergraduates and beginning graduate students in the subject of complex analysis. The subject of complex analysis of increasing importance. Even the function theory of several complex variables has seen applications in cosmology, geophysics, and engineering.

The Handbook of Complex Analysis will be an entree for advanced undergraduates and beginning graduate students in the subject of complex analysis. The subject of complex analysis of increasing importance. Even the function theory of several complex variables has seen applications in cosmology, geophysics, and engineering.

Handbook of Complex Analysis

This book provides an overview of the most up-to-date developments in the field, presenting original contributions and surveys from a spectrum of respected academics in Mathematical Analysis. Each chapter highlights new research directions, making this book suitable for graduate students, faculty, and researchers.

This book provides an overview of the most up-to-date developments in the field, presenting original contributions and surveys from a spectrum of respected academics in Mathematical Analysis. Each chapter highlights new research directions, making this book suitable for graduate students, faculty, and researchers.

Theory and Applications

Mathematical Analysis

It is a curious fact that even notoriously difficult computational problems can be expressed in the form of a high-dimensional Venn diagram, where solutions lie in the overlap of a pair of remarkably simple sets, A and B. The simplicity of these sets enables operations called projections that locate the nearest point of A, or B, starting anywhere within the high-dimensional space.&nbsp; This book introduces a novel method for tackling complex problems that exploits projections and the two-set structure, offering an effective alternative to traditional, gradient-based approaches. Beginning with phase retrieval, where A and B address the properties of an image and its Fourier transform, it progresses to more diverse challenges, such as sphere packing, origami design, sudoku and tiling puzzles, data dimension reduction, and neural network training. The text presents a detailed description of this powerful and original approach and is essential reading for physicists and applied mathematicians.

From Phase Retrieval to Packing

Solving Problems with Projections

Textbooks in Mathematics

The idea of complex numbers dates back at least 300 years-to Gauss and Euler, among others. Today complex analysis is a central part of modern analytical thinking. It is used in engineering, physics, mathematics, astrophysics, and many other fields. It provides powerful tools for doing mathematical analysis, and often yields pleasing and unanticipated answers.


This book makes the subject of complex analysis accessible to a broad audience. The complex numbers are a somewhat mysterious number system that seems to come out of the blue. It is important for students to see that this is really a very concrete set of objects that has very concrete and meaningful applications. 





Features:









This new edition is a substantial rewrite, focusing on the accessibility, applied, and visual aspect of complex analysis





This book has an exceptionally large number of examples and a large number of figures. 








The topic is presented as a natural outgrowth of the calculus. It is not a new language, or a new way of thinking.








Incisive applications appear throughout the book.








Partial differential equations are used as a unifying theme.

Complex Variables: A Physical Approach with Applications, Second Edition offers a notable revision. The emphasis remains on theory and practice. The first part of the text focuses on the fundamental concepts. The author then moves on to a detailed look at how complex variables are used in the real world.

A Physical Approach with Applications

Complex Variables

Can networks unlock secrets of AI or make sense of a social media mess?

Hidden Networks in Social Media, AI, and Nature

Dots and Lines

Contemporary Mathematics And Its Applications: Monographs, Expositions And Lecture Notes

In this book, potential theory is presented in an inclusive and accessible manner, with the emphasis reaching from classical to modern, from analytic to probabilistic, and from Newtonian to abstract or axiomatic potential theory (including Dirichlet spaces). The reader is guided through stochastic analysis featuring Brownian motion in its early chapters to potential theory in its latter sections. This path covers the following themes: martingales, diffusion processes, semigroups and potential operators, analysis of super harmonic functions, Dirichlet problems, balayage, boundaries, and Green functions.

The wide range of applications encompasses random walk models, especially reversible Markov processes, and statistical inference in machine learning models. However, the present volume considers the analysis from the point of view of function space theory, using Dirchlet energy as an inner product. This present volume is an expanded and revised version of an original set of lectures in the Aarhus University Mathematics Institute Lecture Note Series.

Brownian Motion And Potential Theory, Modern And Classical

Typically, undergraduates see real analysis as one of the most di¿cult courses that a mathematics major is required to take. The main reason for this perception is twofold: Students must comprehend new abstract concepts and learn to deal with these concepts on a level of rigor and proof not previously encountered. A key challenge for an instructor of real analysis is to ¿nd a way to bridge the gap between a student's preparation and the mathematical skills that are required to be successful in such a course. 



Real Analysis: With Proof Strategies provides a resolution to the "bridging-the-gap problem." The book not only presents the fundamental theorems of real analysis, but also shows the reader how to compose and produce the proofs of these theorems. The detail, rigor, and proof strategies öered in this textbook will be appreciated by all readers. 



Features 



Explicitly shows the reader how to produce and compose the proofs of the basic theorems in real analysis 





Suitable for junior or senior undergraduates majoring in mathematics.

This book provides a resolution to the "bridging-the-gap problem." The book not only presents the fundamental theorems of real analysis, but also shows the reader how to compose and produce the proofs of these theorems.

With Proof Strategies

Real Analysis

This book covers complex analysis (the study of boundary behaviors of analytic functions) and its applications with engineering problems, especially control theory from the viewpoint of boundary functions. The metascience part is rather unique and illustrates a metascientific way of thinking engineering problems by examples of batteries which are cores of electric vehicles.This book gives a way of looking at the phenomena from a higher and brighter point of view through the windows of boundary behavior and metascience. In Chapter 1 which is meant for mathematics-oriented readers, we state materials in standard complex analysis with emphasis on similarity and Laurent expansions. Non-mathematical readers can also benefit by browsing through many examples and worked-out exercises. Chapter 2 gives some concrete examples of invoking novel ideas in the heap of stereo-typed contributions to a field. Possible replacement of LIB by ECaSS(R) is a typical example through which the reader can learn basics of electromagnetism and electrochemistry. The book also provides hints for a deeper understanding of environmental problems as well as how to manage and create a sustainable society.

From Complex Analysis To Metascience: A Stroll Around Boundary Behavior, Similarity And Duality

Query complexity addresses issues like the number of calls to a black box routine, the number of queries to a data structure or the number of steps made by a parallel processor. It has immense applications, and not surprisingly a large number of papers ha

Query Complexity

This book provides a better understanding of mutant strains and their pathogenicity by performing genomic sequences of samples. The book will benefit clinicians, educators, scientists, industrialists and policymakers in handling the crisis of the outbreak.

This book provides a better understanding of mutant strains and their pathogenicity by performing genomic sequences of samples. The book will benefit clinicians, educators, scientists, industrialists and policymakers in handling the crisis of the outbreak.

Recent Advances and Challenges

Frontiers of Fractal Analysis

This book presents the theory of dynamic equations on time scales and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results related to the qualitative properties of solutions like existence and uniqueness, stability, etc.

This book presents the theory of dynamic equations on time scales and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results related to the qualitative properties of solutions like existence and uniqueness, stability, etc.

Dynamic Equations on Time Scales and Applications

This book provides a comprehensive exploration of generalization in deep learning, focusing on both theoretical foundations and practical strategies. It delves deeply into how machine learning models, particularly deep neural networks, achieve robust performance on unseen data.

Theoretical Foundations and Practical Strategies

Deep Learning Generalization

Introduction to Several Complex Variables

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