Geometry of Complex Numbers

Geared toward readers unfamiliar with complex numbers, this text explains how to solve the kinds of problems that frequently arise in the applied sciences, especially electrical studies. To assure an

Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries. "This book should be in every library, and every expert in cl

Geometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. This sophisticated topic is elegantly presented with enough backg

"Complex geometry studies (compact) complex manifolds. It discusses algebraic as well as metric aspects. The subject is on the crossroad of algebraic and differential geometry. Recent developments in

This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as wel

This book focuses on complex geometry and covers highly active topics centered around geometric problems in several complex variables and complex dynamics, written by some of the world’s leading exper

Complex Analytic Geometry is one of the most important fields of Mathematics. It has a long history that culminated in the Cauchy integral formula in the 19th century. The theory was vastly developed

Presents a survey of some aspects of extension problems in Complex Analysis and Geometry. Recalling the preliminary and necessary notions of complex analysis, this title presents a survey that focuses

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.

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.

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.

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.

This major survey features the work of 18 outstanding mathematicians. Primary subjects include analytic geometry, algebra, ordinary and partial differential equations, the calculus of variations, functions of a complex variable, prime numbers, and theories of probability and functions. Other topics include linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.

This is an introduction to non-commutative geometry, with special emphasis on those cases where the structure algebra, which defines the geometry, is an algebra of matrices over the complex numbers. Applications to elementary particle physics are also discussed. This second edition is thoroughly revised and includes new material on reality conditions and linear connections plus examples from Jordanian deformations and quantum Euclidean spaces. Only some familiarity with ordinary differential geometry and the theory of fibre bundles is assumed, making this book accessible to graduate students and newcomers to this field.

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

The objective of this book is to provide tools for solving problems which involve cubic number fields. Many such problems can be considered geometrically; both in terms of the geometry of numbers and

Differential and complex geometry are two central areas of mathematics with a long and intertwined history. This book, the first to provide a unified historical perspective of both subjects, explores

Trigonometric Functions and Complex Numbers covers the followings areas in the International Mathematical Olympiad (IMO) and other mathematical competitions. Trigonometric identity, graphs and propert

Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book gives for the first time a comprehensive collection of their properties and applications to combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas. Following an introduction to the basic properties of Catalan numbers, the book presents 214 different kinds of objects counted by them in the form of exercises with solutions. The reader can try solving the exercises or simply browse through them. Some 68 additional exercises with prescribed difficulty levels present various properties of Catalan numbers and related numbers, such as Fuss-Catalan numbers, Motzkin numbers, Schröder numbers, Narayana numbers, super Catalan numbers, q-Catalan numbers and (q,t)-Catalan numbers. The book ends with a history of Catalan numbers by Igor Pak and a glossary of key terms. Whether your interest in mathematics is recreation or research, you will find plenty of f

Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book gives for the first time a comprehensive collection of their properties and applications to combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas. Following an introduction to the basic properties of Catalan numbers, the book presents 214 different kinds of objects counted by them in the form of exercises with solutions. The reader can try solving the exercises or simply browse through them. Some 68 additional exercises with prescribed difficulty levels present various properties of Catalan numbers and related numbers, such as Fuss-Catalan numbers, Motzkin numbers, Schröder numbers, Narayana numbers, super Catalan numbers, q-Catalan numbers and (q,t)-Catalan numbers. The book ends with a history of Catalan numbers by Igor Pak and a glossary of key terms. Whether your interest in mathematics is recreation or research, you will find plenty of f

Several important aspects of moduli spaces and irreducible holomorphic symplectic manifolds were highlighted at the conference “Algebraic and Complex Geometry” held September 2012 in Hannover, Germany

* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation* Theoretical aspects are augmented with rich exercises and problems at various levels of

Basic Algebraic Geometry II is a revised edition of Shafarevich's well-known introductory book on algebraic varieties and complex manifolds. It can be read independently of Volume I and is suitable f

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.

This is a reference book for academics working in the fields of several complex variables, PDE theory and geometry. The book collects articles on most recent developments in these fields with special

Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers

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 extraordinary work takes the reader on a long and fascinating journey--from the dual invention of numbers and language, through the major realms of arithmetic, algebra, geometry, trigonometry, a

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.

Why do NBA players only have 24 seconds to score a basket? What’s the geometry behind making the perfect shot? Become a basketball pro and learn all about the numbers and math behind this popular spor

Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theo

Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theo

This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypers

This book is designed as a textbook for a first course on functions of a complex variable. It introduces the fundamental idea of complex numbers and complex variables leading to different tools of com

This book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting. In its classical form, web geometry consists in the study of webs up to local diffeomorph

Contemporary research in algebraic geometry is the focus of this collection, which presents articles on modern aspects of the subject. The list of topics covered is a roll-call of some of the most important and active themes in this thriving area of mathematics: the reader will find articles on birational geometry, vanishing theorems, complex geometry and Hodge theory, free resolutions and syzygies, derived categories, invariant theory, moduli spaces, and related topics, all written by leading experts. The articles, which have an expository flavour, present an overall picture of current research in algebraic geometry, making this book essential for researchers and graduate students. This volume is the outcome of the conference Recent Advances in Algebraic Geometry, held in Ann Arbor, Michigan, to honour Rob Lazarsfeld's many contributions to the subject on the occasion of his 60th birthday.

This book deals with various systems of "numbers" that can be constructed by adding "imaginary units" to the real numbers. The complex numbers are a classical example of such a system. One of the most

This volume contains the Proceedings of the conference "Complex and Differential Geometry 2009", held at Leibniz Universitat Hannover, September 14 - 18, 2009. It was the aim of this conference to bri