Introduction To The Geometry Of Complex Numbers

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.

The second edition of this text has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginner

The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their

Leading experts present a unique, invaluable introduction to the study of the geometry and typology of fluid flows. From basic motions on curves and surfaces to the recent developments in knots and

Recent decades have seen profound changes in the way we understand complex analysis. This new work presents a much-needed modern treatment of the subject, incorporating the latest developments and pro

This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and profess

This book focuses on the elementary but essential problems in Riemann-Finsler Geometry, which include a repertoire of rigidity and comparison theorems, and an array of explicit examples, illustrating

In 1905, Albert Einstein offered a revolutionary theory--special relativity--to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards

A number of important topics in complex analysis and geometry are covered in this excellent introductory text. Written by experts in the subject, each chapter unfolds from the basics to the more comp

This textbook presents modern algebra from the ground up using numbers and symmetry. The idea of a ring and of a field are introduced in the context of concrete number systems. Groups arise from consi

In this introduction to commutative algebra, the author leads the beginning student through the essential ideas, without getting embroiled in technicalities. The route chosen takes the reader quickly to the fundamental concepts for understanding complex projective geometry, the only prerequisites being a basic knowledge of linear and multilinear algebra and some elementary group theory. In the first part, the general theory of Noetherian rings and modules is developed. A certain amount of homological algebra is included, and rings and modules of fractions are emphasised, as preparation for working with sheaves. In the second part, the central objects are polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalisation lemma and Hilbert's Nullstellensatz, affine complex schemes and their morphisms are introduced; Zariski's main theorem and Chevalley's semi-continuity theorem are then proved. Finally, a detailed study of Weil and Cart

The 1992/3 academic year at the Mathematical Sciences Research Institute was devoted to complex algebraic geometry. This 1996 volume collects survey articles that arose from this event, which took place at a time when algebraic geometry was undergoing a major change. To put it succinctly, algebraic geometry has opened up to ideas and connections from other fields that have traditionally been far away. The editors of the volume, Herbert Clemens and Janos Kollar, chaired the organizing committee. Activities were centered around themes, one per month, under the guidance of experts in each area. There were also four short workshops, which attracted many participants and helped considerably in communicating the new directions in algebraic geometry to a large audience. This book gives a good idea of the intellectual content of the special year and of the workshops.

Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such

Certainly the quality of any text entering its 5th edition will in general terms be well known to potential users well in advance of any review. The 1st edition of this classic appeared in 1960, and t

From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is

This classic work is now available in an unabridged paperback edition. The Second Edition retains all the characterisitcs that made the first edition so popular: brilliant exposition, the flexibility

These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 16-21, 1987. In 1982 Tsfasman, Vladut and Zink, using alg

The surreal numbers form a system which includes both the ordinary real numbers and the ordinals. Since their introduction by J. H. Conway, the theory of surreal numbers has seen a rapid development revealing many natural and exciting properties. These notes provide a formal introduction to the theory in a clear and lucid style. The the author is able to lead the reader through to some of the problems in the field. The topics covered include exponentiation and generalized e-numbers.

Number theory has a long and distinguished history and the concepts and problems relating to the subject have been instrumental in the foundation of much of mathematics. In this book, Professor Baker describes the rudiments of number theory in a concise, simple and direct manner. Though most of the text is classical in content, he includes many guides to further study which will stimulate the reader to delve into the great wealth of literature devoted to the subject. The book is based on Professor Baker's lectures given at the University of Cambridge and is intended for undergraduate students of mathematics.

"Introduction to Particle Therapy: An Educational Handbook" provides a clear and accessible overview of modern particle radiation therapy. Aimed at students, physicists and researchers in particle beam therapy, it explains the fundamental physics of proton and heavy-ion beams and how their distinctive depth-dose profiles enable highly targeted cancer treatment with minimal damage to healthy tissue.It explores the latest, cutting-edge research in accelerator technology, beam-delivery systems, treatment-planning methods, radiobiology, and dosimetry and safety. The book also examines the engineering design of particle therapy machines, outlining key components, system architectures and performance considerations. Chapters on particle radiation biology, image-guidance technologies and inverse optimization methods illustrate the principles required for precise and adaptive treatment delivery. Emerging developments, such as ultra-high-dose-rate (FLASH) therapy, next-generation planning strat

The Routledge Introduction to Asian Canadian Literature offers an engaging and wide-ranging survey of Asian Canadian literature as a formalized field of academic study.

The definitive translation of Plato's Republic, the most influential text in the history of Western philosophy "No one else has even come close to balancing Bloom's fidelity to Greek with intelligible English prose."--National Review Long regarded as the most accurate rendering of Plato's Republic that has yet been published, this widely acclaimed translation by Allan Bloom was the first to take a strictly literal approach. In addition to the annotated text, there is also a rich and valuable essay--as well as indices--which will enable readers to better understand the heart of Plato's intention. This edition includes an introduction by renowned critic Adam Kirsch, setting the work in its intellectual context for a new generation of students and readers.