The 10 best complex numbers and geometry for 2019
Finding the best complex numbers and geometry suitable for your needs isnt easy. With hundreds of choices can distract you. Knowing whats bad and whats good can be something of a minefield. In this article, weve done the hard work for you.
Finding the best complex numbers and geometry suitable for your needs isnt easy. With hundreds of choices can distract you. Knowing whats bad and whats good can be something of a minefield. In this article, weve done the hard work for you.
Best complex numbers and geometry
1. Complex Numbers and Geometry (Mathematical Association of America Textbooks)
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Used Book in Good ConditionDescription
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.2. Geometry of Complex Numbers (Dover Books on Mathematics)
Description
"This book should be in every library, and every expert in classical function theory should be familiar with this material. The author has performed a distinct service by making this material so conveniently accessible in a single book." Mathematical Review
Since its initial publication in 1962, Professor Schwerdtfeger's illuminating book has been widely praised for generating a deeper understanding of the geometrical theory of analytic functions as well as of the connections between different branches of geometry. Its focus lies in the intersection of geometry, analysis, and algebra, with the exposition generally taking place on a moderately advanced level. Much emphasis, however, has been given to the careful exposition of details and to the development of an adequate algebraic technique.
In three broad chapters, the author clearly and elegantly approaches his subject. The first chapter, Analytic Geometry of Circles, treats such topics as representation of circles by Hermitian matrices, inversion, stereographic projection, and the cross ratio. The second chapter considers in depth the Moebius transformation: its elementary properties, real one-dimensional projectivities, similarity and classification of various kinds, anti-homographies, iteration, and geometrical characterization. The final chapter, Two-Dimensional Non-Euclidean Geometries, discusses subgroups of Moebius transformations, the geometry of a transformation group, hyperbolic geometry, and spherical and elliptic geometry. For this Dover edition, Professor Schwerdtfeger has added four new appendices and a supplementary bibliography.
Advanced undergraduates who possess a working knowledge of the algebra of complex numbers and of the elements of analytical geometry and linear algebra will greatly profit from reading this book. It will also prove a stimulating and thought-provoking book to mathematics professors and teachers.
3. Complex Variables with Applications
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Used Book in Good ConditionDescription
Explores the interrelations betweenrealandcomplex numbers byadopting both generalization and specialization methods to move between them, while simultaneously examining their analytic and geometric characteristics
Engaging expositionwith discussions, remarks, questions, and exercises to motivateunderstandingand critical thinking skills
Encludes numerous examples and applications relevant to science and engineering students
4. Complex Numbers from A to ... Z
Description
This book shows how complex numbers can be used to solve algebraic equations, and to understand the geometric interpretation of complex numbers and the operations involving them. Includes exercises of varying difficulty, many added for this second edition.5. Introduction to the Geometry of Complex Numbers (Dover Books on Mathematics)
Description
The three-part treatment begins with geometric representations of complex numbers and proceeds to an in-depth survey of elements of analytic geometry. Readers are assured of a variety of perspectives, which include references to algebra, to the classical notions of analytic geometry, to modern plane geometry, and to results furnished by kinematics. The third chapter, on circular transformations, revives in a slightly modified form the essentials of the projective geometry of real binary forms. Numerous exercises appear throughout the text.
6. Algebraic Geometry over the Complex Numbers (Universitext)
Description
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.7. Complex Numbers in Geometry
8. Complex Numbers and Geometry (Mathematical Association of America Textbooks) by Hahn, Liang-shin (1996) Paperback
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Will be shipped from US. Used books may not include companion materials, may have some shelf wear, may contain highlighting/notes, may not include CDs or access codes. 100% money back guarantee.9. Representation Theory and Complex Geometry (Modern Birkhuser Classics)
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Used Book in Good ConditionDescription
This volume provides an overview of modern advances in representation theory from a geometric standpoint. The techniques developed are quite general and can be applied to other areas such as quantum groups, affine Lie groups, and quantum field theory.
10. Bicomplex Holomorphic Functions: The Algebra, Geometry and Analysis of Bicomplex Numbers (Frontiers in Mathematics)
Description
The purpose of this book is to develop the foundations of the theory of holomorphicity on the ring of bicomplex numbers. Accordingly, the main focus is on expressing the similarities with, and differences from, the classical theory of one complex variable. The result is an elementary yet comprehensive introduction to the algebra, geometry and analysis of bicomplex numbers.
Around the middle of the nineteenth century, several mathematicians (the best known being Sir William Hamilton and Arthur Cayley) became interested in studying number systems that extended the field of complex numbers. Hamilton famously introduced the quaternions, a skew field in real-dimension four, while almost simultaneously James Cockle introduced a commutative four-dimensional real algebra, which was rediscovered in 1892 by Corrado Segre, who referred to his elements as bicomplex numbers. The advantages of commutativity were accompanied by the introduction of zero divisors, something that for a while dampened interest in this subject. In recent years, due largely to the work of G.B. Price, there has been a resurgence of interest in the study of these numbers and, more importantly, in the study of functions defined on the ring of bicomplex numbers, which mimic the behavior of holomorphic functions of a complex variable.
While the algebra of bicomplex numbers is a four-dimensional real algebra, it is useful to think of it as a complexification of the field of complex
numbers; from this perspective, the bicomplex algebra possesses the properties of a one-dimensional theory inside four real dimensions. Its rich analysis and innovative geometry provide new ideas and potential applications in relativity and quantum mechanics alike.
The book will appeal to researchers in the fields of complex, hypercomplex and functional analysis, as well as undergraduate and graduate students with an interest in one- or multidimensional complex analysis.