Complex Numbers And Geometry

Author : Liang-shin Hahn
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 55,9 Mb
Release : 2019-12-26
Category : Education
ISBN : 9781470451820

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Complex Numbers and Geometry by Liang-shin Hahn Pdf

The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem. The book is self-contained—no background in complex numbers is assumed—and can be covered at a leisurely pace in a one-semester course. Many of the chapters can be read independently. Over 100 exercises are included. The book would be suitable as a text for a geometry course, or for a problem solving seminar, or as enrichment for the student who wants to know more.

Author : I. M. Yaglom
Publisher : Academic Press
Page : 256 pages
File Size : 41,7 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483266633

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Complex Numbers in Geometry by I. M. Yaglom Pdf

Complex Numbers in Geometry focuses on the principles, interrelations, and applications of geometry and algebra. The book first offers information on the types and geometrical interpretation of complex numbers. Topics include interpretation of ordinary complex numbers in the Lobachevskii plane; double numbers as oriented lines of the Lobachevskii plane; dual numbers as oriented lines of a plane; most general complex numbers; and double, hypercomplex, and dual numbers. The text then takes a look at circular transformations and circular geometry, including ordinary circular transformations, axial circular transformations of the Lobachevskii plane, circular transformations of the Lobachevskii plane, axial circular transformations, and ordinary circular transformations. The manuscript is intended for pupils in high schools and students in the mathematics departments of universities and teachers' colleges. The publication is also useful in the work of mathematical societies and teachers of mathematics in junior high and high schools.

Author : Hans Schwerdtfeger
Publisher : Courier Corporation
Page : 224 pages
File Size : 48,8 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486135861

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Geometry of Complex Numbers by Hans Schwerdtfeger Pdf

Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Author : Donu Arapura
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 47,7 Mb
Release : 2012-02-15
Category : Mathematics
ISBN : 9781461418092

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Algebraic Geometry over the Complex Numbers by Donu Arapura Pdf

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 well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.

Author : Titu Andreescu,Dorin Andrica
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 54,9 Mb
Release : 2007-10-08
Category : Mathematics
ISBN : 9780817644499

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Complex Numbers from A to ...Z by Titu Andreescu,Dorin Andrica Pdf

* 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 difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory

Author : Roland Deaux
Publisher : Courier Corporation
Page : 208 pages
File Size : 50,5 Mb
Release : 2013-01-23
Category : Mathematics
ISBN : 9780486158044

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Introduction to the Geometry of Complex Numbers by Roland Deaux Pdf

Geared toward readers unfamiliar with complex numbers, this text explains how to solve problems that frequently arise in the applied sciences and emphasizes constructions related to algebraic operations. 1956 edition.

Author : Isaak Moiseevič Jaglom
Publisher : Unknown
Page : 0 pages
File Size : 40,5 Mb
Release : 1968
Category : Geometry, Modern
ISBN : 1483256634

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Complex Numbers in Geometry by Isaak Moiseevič Jaglom Pdf

Author : H. Schwerdtfeger
Publisher : Unknown
Page : 128 pages
File Size : 41,7 Mb
Release : 1965
Category : Electronic
ISBN : OCLC:1114823033

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Geometry of Complex Numbers by H. Schwerdtfeger Pdf

Author : John P. D'Angelo
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 46,8 Mb
Release : 2010
Category : Functions of complex variables
ISBN : 9780821852743

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An Introduction to Complex Analysis and Geometry by John P. D'Angelo Pdf

Provides the reader with a deep appreciation of complex analysis and how this subject fits into mathematics. The first four chapters provide an introduction to complex analysis with many elementary and unusual applications. Chapters 5 to 7 develop the Cauchy theory and include some striking applications to calculus. Chapter 8 glimpses several appealing topics, simultaneously unifying the book and opening the door to further study.

Author : Roland 1893- Deaux
Publisher : Hassell Street Press
Page : 220 pages
File Size : 43,8 Mb
Release : 2021-09-09
Category : Electronic
ISBN : 1014862523

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Introduction to the Geometry of Complex Numbers by Roland 1893- Deaux Pdf

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206873

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Numbers and Geometry by John Stillwell Pdf

A beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis and geometry - meet. The book provides a broad view of these subjects at the level of calculus, without being a calculus book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. Stillwell has chosen an array of exciting and worthwhile topics and elegantly combines mathematical history with mathematics. He covers the main ideas of Euclid, but with 2000 years of extra insights attached. Presupposing only high school algebra, it can be read by any well prepared student entering university. Moreover, this book will be popular with graduate students and researchers in mathematics due to its attractive and unusual treatment of fundamental topics. A set of well-written exercises at the end of each section allows new ideas to be instantly tested and reinforced.

Author : Daniel Huybrechts
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 41,5 Mb
Release : 2005
Category : Computers
ISBN : 3540212906

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Complex Geometry by Daniel Huybrechts Pdf

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

Author : Anonim
Publisher : Unknown
Page : 344 pages
File Size : 45,5 Mb
Release : 2012-02-16
Category : Electronic
ISBN : 1461418100

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Algebraic Geometry Over the Complex Numbers by Anonim Pdf

Author : Tristan Needham
Publisher : Oxford University Press
Page : 620 pages
File Size : 46,9 Mb
Release : 1997
Category : Mathematics
ISBN : 0198534469

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Visual Complex Analysis by Tristan Needham Pdf

This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

Author : Nolan R. Wallach
Publisher : Springer
Page : 190 pages
File Size : 53,8 Mb
Release : 2017-09-08
Category : Mathematics
ISBN : 9783319659077

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Geometric Invariant Theory by Nolan R. Wallach Pdf

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 background theory included to make the text accessible to advanced graduate students in mathematics and physics with diverse backgrounds in algebraic and differential geometry. Throughout the book, examples are emphasized. Exercises add to the reader’s understanding of the material; most are enhanced with hints. The exposition is divided into two parts. The first part, ‘Background Theory’, is organized as a reference for the rest of the book. It contains two chapters developing material in complex and real algebraic geometry and algebraic groups that are difficult to find in the literature. Chapter 1 emphasizes the relationship between the Zariski topology and the canonical Hausdorff topology of an algebraic variety over the complex numbers. Chapter 2 develops the interaction between Lie groups and algebraic groups. Part 2, ‘Geometric Invariant Theory’ consists of three chapters (3–5). Chapter 3 centers on the Hilbert–Mumford theorem and contains a complete development of the Kempf–Ness theorem and Vindberg’s theory. Chapter 4 studies the orbit structure of a reductive algebraic group on a projective variety emphasizing Kostant’s theory. The final chapter studies the extension of classical invariant theory to products of classical groups emphasizing recent applications of the theory to physics.