Steven George Krantz Knihy

This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.

This book is written to be a convenient reference for the working scientist, student, or engineer who needs to know and use basic concepts in complex analysis. It is not a book of mathematical theory. It is instead a book of mathematical practice. All the basic ideas of complex analysis, as well as many typical applica tions, are treated. Since we are not developing theory and proofs, we have not been obliged to conform to a strict logical ordering of topics. Instead, topics have been organized for ease of reference, so that cognate topics appear in one place. Required background for reading the text is minimal: a good ground ing in (real variable) calculus will suffice. However, the reader who gets maximum utility from the book will be that reader who has had a course in complex analysis at some time in his life. This book is a handy com pendium of all basic facts about complex variable theory. But it is not a textbook, and a person would be hard put to endeavor to learn the subject by reading this book.

The book features an enhanced Preface designed to guide instructors in tailoring their courses effectively. It includes clear prerequisites and a structured roadmap to facilitate course development. Additionally, sample syllabi are provided to assist in planning and organization, making it a valuable resource for educators.

The book systematically explores the fundamental analytic and geometric aspects of Bergman's classic kernel theory, focusing on its invariance properties. Each chapter is enriched with illustrative examples to enhance understanding, alongside a collection of exercises designed to reinforce the concepts presented.

* 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

The evolution of mathematical proof is traced from its origins with ancient figures like Euclid and Pythagoras to its contemporary applications. The narrative spans across different cultures and historical periods, highlighting significant transformations in the understanding and significance of mathematical proof throughout the ages. This exploration reveals the profound impact of mathematics on various fields and illustrates its ongoing relevance in today's world.

The perfect supplement to the standard Discrete Mathematics texts, which tend to be dry, complicated, abstract, and inordinately expensive.

Focusing on the essential role of logic in modern mathematics, this handbook aims to bridge the gap between complex mathematical concepts and those with basic mathematical knowledge. Unlike more specialized texts, it introduces key terminology and ideas in a clear manner, making it accessible to mathematical scientists who may not have a deep background in logic. The work is designed to provide a foundational understanding of modern logic, including contemporary topics, catering specifically to readers seeking to enhance their familiarity with the subject.

In this original text, prolific mathematics author Steven G. Krantz addresses conformal geometry, a subject that has occupied him for four decades and for which he helped to develop some of the modern theory. This book takes readers with a basic grounding in complex variable theory to the forefront of some of the current approaches to the topic. "Along the way," the author notes in his Preface, "the reader will be exposed to some beautiful function theory and also some of the rudiments of geometry and analysis that make this subject so vibrant and lively."More up-to-date and accessible to advanced undergraduates than most of the other books available in this specific field, the treatment discusses the history of this active and popular branch of mathematics as well as recent developments. Topics include the Riemann mapping theorem, invariant metrics, normal families, automorphism groups, the Schwarz lemma, harmonic measure, extremal length, analytic capacity, and invariant geometry. A helpful Bibliography and Index complete the text.

A bewitching tale showcasing the timeless lesson that a good deed always triumphs over a bad one, even at Miss Mildred Mildew's School of Magic! Whatever you chant, Whatever you brew, Sooner or later Comes back to you! Alice and Greta attended the same school of magic, but they each have their own ideas about how to put their skills to the best use. Alice spends her days waving her wand to cast splendid spells. Greta only uses hers to stir up trouble. When their wands and witching styles clash, it turns out Greta should have paid more attention to those early magic lessons. An enchanting tale of two very different fates.