Geometric Function Theory

Explorations in Complex Analysis

Author: Steven G. Krantz

Publisher: Springer Science & Business Media

ISBN: 0817644407

Category: Mathematics

Page: 314

View: 6901

* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations

Function Theory of Several Complex Variables

Author: Steven George Krantz

Publisher: American Mathematical Soc.

ISBN: 0821827243

Category: Mathematics

Page: 564

View: 9983

The theory of several complex variables can be studied from several different perspectives. In this book, Steven Krantz approaches the subject from the point of view of a classical analyst, emphasizing its function-theoretic aspects. He has taken particular care to write the book with the student in mind, with uniformly extensive and helpful explanations, numerous examples, and plentiful exercises of varying difficulty. In the spirit of a student-oriented text, Krantz begins with an introduction to the subject, including an insightful comparison of analysis of several complex variables with the more familiar theory of one complex variable. The main topics in the book include integral formulas, convexity and pseudoconvexity, methods from harmonic analysis, and several aspects of the $\overline{\partial}$ problem. Some further topics are zero sets of holomorphic functions, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and holomorphic mappings. While due attention is paid to algebraic aspects of several complex variables (sheaves, Cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment. This book is suitable for a first graduate course in several complex variables.

Algebra and Geometry

Author: Alan F. Beardon

Publisher: Cambridge University Press

ISBN: 9781139443494

Category: Mathematics

Page: N.A

View: 3343

Describing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry. It covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups and aspects of geometry including groups of isometries, rotations, and spherical geometry. The book emphasises the interactions between topics, and each topic is constantly illustrated by using it to describe and discuss the others. Many ideas are developed gradually, with each aspect presented at a time when its importance becomes clearer. To aid in this, the text is divided into short chapters, each with exercises at the end. The related website features an HTML version of the book, extra text at higher and lower levels, and more exercises and examples. It also links to an electronic maths thesaurus, giving definitions, examples and links both to the book and to external sources.

Communication as Organizing

Empirical and Theoretical Explorations in the Dynamic of Text and Conversation

Author: Francois Cooren,James R. Taylor,Elizabeth J. Van Every

Publisher: Routledge

ISBN: 1136683771

Category: Business & Economics

Page: 256

View: 5685

Communication as Organizing unites multiple reflections on the role of language under a single rubric: the organizing role of communication. Stemming from Jim Taylor's earlier work, The Emergent Organization: Communication as Its Site and Surface (LEA, 2000), the volume editors present a communicational answer to the question, "what is an organization?" through contributions from an international set of scholars and researchers. The chapter authors synthesize various lines of research on constituting organizations through communication, describing their explorations of the relation between language, human practice, and the constitution of organizational forms. Each chapter develops a dimension of the central theme, showing how such concepts as agency, identity, sensemaking, narrative and account may be put to work in discursive analysis to develop effective research into organizing processes. The contributions employ concrete examples to show how the theoretical concepts can be employed to develop effective research. This distinctive volume encourages readers to discover and develop a truly communicational means of addressing the question of organization, addressing how organization itself emerges in the course of communicational transactions. In presenting a single and entirely communicational perspective for exploring organizational phenomena, grounded in the discourse of communicational transactions and the establishment of relationships through language, it is required reading for scholars, researchers, and graduate students working in organizational communication, management, social psychology, pragmatics of language, and organizational studies.

The Corona Problem

Connections Between Operator Theory, Function Theory, and Geometry

Author: Ronald G Douglas,Steven G Krantz,Eric T. Sawyer,Sergei Treil,Brett D. Wick

Publisher: Springer

ISBN: 1493912550

Category: Mathematics

Page: 231

View: 8766

The purpose of the corona workshop was to consider the corona problem in both one and several complex variables, both in the context of function theory and harmonic analysis as well as the context of operator theory and functional analysis. It was held in June 2012 at the Fields Institute in Toronto, and attended by about fifty mathematicians. This volume validates and commemorates the workshop, and records some of the ideas that were developed within. The corona problem dates back to 1941. It has exerted a powerful influence over mathematical analysis for nearly 75 years. There is material to help bring people up to speed in the latest ideas of the subject, as well as historical material to provide background. Particularly noteworthy is a history of the corona problem, authored by the five organizers, that provides a unique glimpse at how the problem and its many different solutions have developed. There has never been a meeting of this kind, and there has never been a volume of this kind. Mathematicians—both veterans and newcomers—will benefit from reading this book. This volume makes a unique contribution to the analysis literature and will be a valuable part of the canon for many years to come.

Complex Analysis 2

Riemann Surfaces, Several Complex Variables, Abelian Functions, Higher Modular Functions

Author: Eberhard Freitag

Publisher: Springer Science & Business Media

ISBN: 9783642205545

Category: Mathematics

Page: 506

View: 2894

The book contains a complete self-contained introduction to highlights of classical complex analysis. New proofs and some new results are included. All needed notions are developed within the book: with the exception of some basic facts which can be found in the ̄rst volume. There is no comparable treatment in the literature.

Harmonic and Complex Analysis in Several Variables

Author: Steven G. Krantz

Publisher: Springer

ISBN: 3319632310

Category: Mathematics

Page: 424

View: 7632

Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.

Mathematical Olympiad Treasures

Author: Titu Andreescu,Bogdan Enescu

Publisher: Springer Science & Business Media

ISBN: 9780817682538

Category: Mathematics

Page: 253

View: 5854

Mathematical Olympiad Treasures aims at building a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts in undergraduate mathematics. The book contains a stimulating collection of problems in the subjects of algebra, geometry, trigonometry, number theory and combinatorics. While it may be considered a sequel to "Mathematical Olympiad Challenges," the focus is on engaging a wider audience to apply techniques and strategies to real-world problems. Throughout the book students are encouraged to express their ideas, conjectures, and conclusions in writing. The goal is to help readers develop a host of new mathematical tools that will be useful beyond the classroom and in a number of disciplines.

Geometric Analysis of the Bergman Kernel and Metric

Author: Steven G. Krantz

Publisher: Springer Science & Business Media

ISBN: 146147924X

Category: Mathematics

Page: 292

View: 5987

This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties, boundary asymptotics, and asymptotic expansion of the Bergman kernel and metric. Moreover, it presents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretations in the language of functional analysis, with emphasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection of exercises which will be of interest to both graduate students and experienced mathematicians. Graduate students who have taken courses in complex variables and have a basic background in real and functional analysis will find this textbook appealing. Applicable courses for either main or supplementary usage include those in complex variables, several complex variables, complex differential geometry, and partial differential equations. Researchers in complex analysis, harmonic analysis, PDEs, and complex differential geometry will also benefit from the thorough treatment of the many exciting aspects of Bergman's theory.

The Theory and Practice of Conformal Geometry

Author: Steven G. Krantz

Publisher: Courier Dover Publications

ISBN: 0486793443

Category: Mathematics

Page: 285

View: 3887

An expert on conformal geometry introduces some of the subject's modern developments. Topics include the Riemann mapping theorem, invariant metrics, automorphism groups, harmonic measure, extremal length, analytic capacity, invariant geometry, and more. 2016 edition.

Complex Analysis

The Geometric Viewpoint

Author: Steven George Krantz

Publisher: MAA

ISBN: 9780883850350

Category: Mathematics

Page: 219

View: 3676

In this second edition of a Carus Monograph Classic, Steven G. Krantz, a leading worker in complex analysis and a winner of the Chauvenet Prize for outstanding mathematical exposition, develops material on classical non-Euclidean geometry. He shows how it can be developed in a natural way from the invariant geometry of the complex disk. He also introduces the Bergmann kernel and metric and provides profound applications, some of which have never appeared in print before. In general, the new edition represents a considerable polishing and re-thinking of the original successful volume. A minimum of geometric formalism is used to gain a maximum of geometric and analytic insight. The climax of the book is an introduction to several complex variables from the geometric viewpoint. Poincar's theorem, that the ball and bidisc are biholomorphically inequivalent, is discussed and proved.

Differential Equations

Author: Paul Blanchard,Robert L. Devaney,Glen R. Hall

Publisher: Cengage Learning

ISBN: 1133388086

Category: Mathematics

Page: 864

View: 8102

Incorporating an innovative modeling approach, this book for a one-semester differential equations course emphasizes conceptual understanding to help users relate information taught in the classroom to real-world experiences. Certain models reappear throughout the book as running themes to synthesize different concepts from multiple angles, and a dynamical systems focus emphasizes predicting the long-term behavior of these recurring models. Users will discover how to identify and harness the mathematics they will use in their careers, and apply it effectively outside the classroom. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Intelligent Data Analysis for Real-Life Applications: Theory and Practice

Theory and Practice

Author: Magdalena-Benedito, Rafael

Publisher: IGI Global

ISBN: 1466618078

Category: Computers

Page: 444

View: 3973

With the recent and enormous increase in the amount of available data sets of all kinds, applying effective and efficient techniques for analyzing and extracting information from that data has become a crucial task. Intelligent Data Analysis for Real-Life Applications: Theory and Practice investigates the application of Intelligent Data Analysis (IDA) to these data sets through the design and development of algorithms and techniques to extract knowledge from databases. This pivotal reference explores practical applications of IDA, and it is essential for academic and research libraries as well as students, researchers, and educators in data analysis, application development, and database management.


A Brief History of Humankind

Author: Yuval Noah Harari

Publisher: Harper Collins

ISBN: 0062316109

Category: Science

Page: 464

View: 5905

New York Times Bestseller A Summer Reading Pick for President Barack Obama, Bill Gates, and Mark Zuckerberg From a renowned historian comes a groundbreaking narrative of humanity’s creation and evolution—a #1 international bestseller—that explores the ways in which biology and history have defined us and enhanced our understanding of what it means to be “human.” One hundred thousand years ago, at least six different species of humans inhabited Earth. Yet today there is only one—homo sapiens. What happened to the others? And what may happen to us? Most books about the history of humanity pursue either a historical or a biological approach, but Dr. Yuval Noah Harari breaks the mold with this highly original book that begins about 70,000 years ago with the appearance of modern cognition. From examining the role evolving humans have played in the global ecosystem to charting the rise of empires, Sapiens integrates history and science to reconsider accepted narratives, connect past developments with contemporary concerns, and examine specific events within the context of larger ideas. Dr. Harari also compels us to look ahead, because over the last few decades humans have begun to bend laws of natural selection that have governed life for the past four billion years. We are acquiring the ability to design not only the world around us, but also ourselves. Where is this leading us, and what do we want to become? Featuring 27 photographs, 6 maps, and 25 illustrations/diagrams, this provocative and insightful work is sure to spark debate and is essential reading for aficionados of Jared Diamond, James Gleick, Matt Ridley, Robert Wright, and Sharon Moalem.

The Proof is in the Pudding

The Changing Nature of Mathematical Proof

Author: Steven G. Krantz

Publisher: Springer Science & Business Media

ISBN: 9780387487441

Category: Mathematics

Page: 264

View: 8354

This text explores the many transformations that the mathematical proof has undergone from its inception to its versatile, present-day use, considering the advent of high-speed computing machines. Though there are many truths to be discovered in this book, by the end it is clear that there is no formalized approach or standard method of discovery to date. Most of the proofs are discussed in detail with figures and equations accompanying them, allowing both the professional mathematician and those less familiar with mathematics to derive the same joy from reading this book.

Musical Creativity

Multidisciplinary Research in Theory and Practice

Author: Irène Deliège,Geraint A. Wiggins

Publisher: Psychology Press

ISBN: 1135422672

Category: Music

Page: 448

View: 1066

This collection initiates a resolutely interdisciplinary research dynamic specifically concerning musical creativity. Creativity is one of the most challenging issues currently facing scientific psychology and its study has been relatively rare in the cognitive sciences, especially in artificial intelligence. This book will address the need for a coherent and thorough exploration. Musical Creativity: Multidisciplinary Research in Theory and Practice comprises seven sections, each viewing musical creativity from a different scientific vantage point, from the philosophy of computer modelling, through music education, interpretation, neuroscience, and music therapy, to experimental psychology. Each section contains discussions by eminent international specialists of the issues raised, and the book concludes with a postlude discussing how we can understand creativity in the work of eminent composer, Jonathan Harvey. This unique volume presents an up-to-date snapshot of the scientific study of musical creativity, in conjunction with ESCOM (the European Society for the Cognitive Sciences of Music). Describing many of the different aspects of musical creativity and their study, it will form a useful springboard for further such study in future years, and will be of interest to academics and practitioners in music, psychology, cognitive science, artificial intelligence, neuroscience and other fields concerning the study of human cognition in this most human of behaviours.

Advanced Calculus


Author: Lynn Harold Loomis,Shlomo Sternberg

Publisher: World Scientific Publishing Company

ISBN: 9814583952

Category: Mathematics

Page: 596

View: 9894

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

A First Course in General Relativity

Author: Bernard Schutz

Publisher: Cambridge University Press

ISBN: 0521887054

Category: Science

Page: 393

View: 7377

Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.

Calculus DeMYSTiFieD, Second Edition

Author: Steven Krantz

Publisher: McGraw Hill Professional

ISBN: 0071743642

Category: Mathematics

Page: 416

View: 817

Calculate this: learning CALCULUS just got a whole lot easier! Stumped trying to understand calculus? Calculus Demystified, Second Edition, will help you master this essential mathematical subject. Written in a step-by-step format, this practical guide begins by covering the basics--number systems, coordinates, sets, and functions. You'll move on to limits, derivatives, integrals, and indeterminate forms. Transcendental functions, methods of integration, and applications of the integral are also covered. Clear examples, concise explanations, and worked problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key concepts. It's a no-brainer! You'll get: Applications of the derivative and the integral Rules of integration Coverage of improper integrals An explanation of calculus with logarithmic and exponential functions Details on calculation of work, averages, arc length, and surface area Simple enough for a beginner, but challenging enough for an advanced student, Calculus Demystified, Second Edition, is one book you won't want to function without!

Essential Topology

Author: Martin D. Crossley

Publisher: Springer Science & Business Media

ISBN: 9781852337827

Category: Mathematics

Page: 224

View: 7443

This thoroughly modern introduction to undergraduate topology brings the most exciting and useful aspects of modern topology to the reader. Containing all the key results of basic topology, this book concentrates on uniting the most interesting aspects of the subject with aspects that are most useful to research. It is suitable for self-study, and will leave the reader both motivated and well prepared for further study.