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Books > Science & Mathematics > Mathematics > Geometry

From Differential Geometry to Non-commutative Geometry and Topology (Hardcover, 1st ed. 2019): Neculai S. Teleman From Differential Geometry to Non-commutative Geometry and Topology (Hardcover, 1st ed. 2019)
Neculai S. Teleman
R3,993 Discovery Miles 39 930 Ships in 12 - 17 working days

This book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.

Brief Introduction To Symplectic And Contact Manifolds, A (Hardcover): Augustin Banyaga, Djideme F. Houenou Brief Introduction To Symplectic And Contact Manifolds, A (Hardcover)
Augustin Banyaga, Djideme F. Houenou
R2,013 Discovery Miles 20 130 Ships in 12 - 17 working days

The book introduces the basic notions in Symplectic and Contact Geometry at the level of the second year graduate student. It also contains many exercises, some of which are solved only in the last chapter.We begin with the linear theory, then give the definition of symplectic manifolds and some basic examples, review advanced calculus, discuss Hamiltonian systems, tour rapidly group and the basics of contact geometry, and solve problems in chapter 8. The material just described can be used as a one semester course on Symplectic and Contact Geometry.The book contains also more advanced material, suitable to advanced graduate students and researchers.

Geometry of the Fundamental Interactions - On Riemann's Legacy to High Energy Physics and Cosmology (Hardcover, 2011 ed.):... Geometry of the Fundamental Interactions - On Riemann's Legacy to High Energy Physics and Cosmology (Hardcover, 2011 ed.)
M. D. Maia
R3,020 Discovery Miles 30 200 Ships in 10 - 15 working days

The Yang-Mills theory of gauge interactions is a prime example of interdisciplinary mathematics and advanced physics. Its historical development is a fascinating window into the ongoing struggle of mankind to understand nature. The discovery of gauge fields and their properties is the most formidable landmark of modern physics. The expression of the gauge field strength as the curvature associated to a given connection, places quantum field theory in the same geometrical footing as the gravitational field of general relativity which is naturally written in geometrical terms. The understanding of such geometrical property may help one day to write a unified field theory starting from symmetry principles.

Of course, there are remarkable differences between the standard gauge fields and the gravitational field, which must be understood by mathematicians and physicists before attempting such unification. In particular, it is important to understand why gravitation is not a standard gauge field.

This book presents an account of the geometrical properties of gauge field theory, while trying to keep the equilibrium between mathematics and physics. At the end we will introduce a similar approach to the gravitational field.

Centenary of the Borel Conjecture (Paperback): Marion Scheepers, Ond?Ej Zindulka Centenary of the Borel Conjecture (Paperback)
Marion Scheepers, Ond?Ej Zindulka
R3,274 Discovery Miles 32 740 Ships in 12 - 17 working days

Borel’s Conjecture entered the mathematics arena in 1919 as an innocuous remark about sets of real numbers in the context of a new covering property introduced by Émile Borel. In the 100 years since, this conjecture has led to a remarkably rich adventure of discovery in mathematics, producing independent results and the discovery of countable support iterated forcing, developments in infinitary game theory, deep connections with infinitary Ramsey Theory, and significant impact on the study of topological groups and topological covering properties. The papers in this volume present a broad introduction to the frontiers of research that has been spurred on by Borel’s 1919 conjecture and identify fundamental unanswered research problems in the field. Philosophers of science and historians of mathematics can glean from this collection some of the typical trends in the discovery, innovation, and development of mathematical theories.

Quantum Field Theory on Curved Spacetimes - Concepts and Mathematical Foundations (Hardcover, 2009 ed.): Christian Bar, Klaus... Quantum Field Theory on Curved Spacetimes - Concepts and Mathematical Foundations (Hardcover, 2009 ed.)
Christian Bar, Klaus Fredenhagen
R2,501 R2,039 Discovery Miles 20 390 Save R462 (18%) Ships in 12 - 17 working days

After some decades of work a satisfactory theory of quantum gravity is still not available; moreover, there are indications that the original field theoretical approach may be better suited than originally expected. There, to first approximation, one is left with the problem of quantum field theory on Lorentzian manifolds. Surprisingly, this seemingly modest approach leads to far reaching conceptual and mathematical problems and to spectacular predictions, the most famous one being the Hawking radiation of black holes. Ingredients of this approach are the formulation of quantum physics in terms of C*-algebras, the geometry of Lorentzian manifolds, in particular their causal structure, and linear hyperbolic differential equations where the well-posedness of the Cauchy problem plays a distinguished role, as well as more recently the insights from suitable concepts such as microlocal analysis. This primer is an outgrowth of a compact course given by the editors and contributing authors to an audience of advanced graduate students and young researchers in the field, and assumes working knowledge of differential geometry and functional analysis on the part of the reader.

Polyhedra and Beyond - Contributions from Geometrias'19, Porto, Portugal, September 05-07 (Hardcover, 1st ed. 2022): Vera... Polyhedra and Beyond - Contributions from Geometrias'19, Porto, Portugal, September 05-07 (Hardcover, 1st ed. 2022)
Vera Viana, Helena Mena Matos, Joao Pedro Xavier
R2,915 Discovery Miles 29 150 Ships in 12 - 17 working days

This volume collects papers based on talks given at the conference "Geometrias'19: Polyhedra and Beyond", held in the Faculty of Sciences of the University of Porto between September 5-7, 2019 in Portugal. These papers explore the conference's theme from an interdisciplinary standpoint, all the while emphasizing the relevance of polyhedral geometry in contemporary academic research and professional practice. They also investigate how this topic connects to mathematics, art, architecture, computer science, and the science of representation. Polyhedra and Beyond will help inspire scholars, researchers, professionals, and students of any of these disciplines to develop a more thorough understanding of polyhedra.

Complex Tori (Hardcover, 1999 ed.): Herbert Lange, Christina Birkenhake Complex Tori (Hardcover, 1999 ed.)
Herbert Lange, Christina Birkenhake
R3,185 Discovery Miles 31 850 Ships in 10 - 15 working days

This work is at the crossroads of a number of mathematical areas, including algebraic geometry, several complex variables, differential geometry, and representation theory. It is the first book to cover complex tori, among the simplest of complex manifolds, which are important to research in the above areas. The book gives a systematic approach to the theory, presents new results, and includes an up-to-date bibliography.

Comparison Theorems in Riemannian Geometry (Hardcover, UK ed.): Jeffrey Cheeger Comparison Theorems in Riemannian Geometry (Hardcover, UK ed.)
Jeffrey Cheeger
R1,938 Discovery Miles 19 380 Ships in 12 - 17 working days

The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry.

Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics (Paperback): Steinar Johannesen Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics (Paperback)
Steinar Johannesen
R1,652 Discovery Miles 16 520 Ships in 12 - 17 working days

This book provides a systematic presentation of the mathematical foundation of modern physics with applications particularly within classical mechanics and the theory of relativity. Written to be self-contained, this book provides complete and rigorous proofs of all the results presented within. Among the themes illustrated in the book are differentiable manifolds, differential forms, fiber bundles and differential geometry with non-trivial applications especially within the general theory of relativity. The emphasis is upon a systematic and logical construction of the mathematical foundations. It can be used as a textbook for a pure mathematics course in differential geometry, assuming the reader has a good understanding of basic analysis, linear algebra and point set topology. The book will also appeal to students of theoretical physics interested in the mathematical foundation of the theories.

Knot Theory - Second Edition (Paperback, 2nd edition): Vassily Olegovich Manturov Knot Theory - Second Edition (Paperback, 2nd edition)
Vassily Olegovich Manturov
R1,696 Discovery Miles 16 960 Ships in 12 - 17 working days

Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to this Edition is a discussion of Heegaard-Floer homology theory and A-polynomial of classical links, as well as updates throughout the text. Knot Theory, Second Edition is notable not only for its expert presentation of knot theory's state of the art but also for its accessibility. It is valuable as a profes-sional reference and will serve equally well as a text for a course on knot theory.

Recent Advancements in Graph Theory (Hardcover): N. P. Shrimali, Nita H. Shah Recent Advancements in Graph Theory (Hardcover)
N. P. Shrimali, Nita H. Shah
R5,206 Discovery Miles 52 060 Ships in 12 - 17 working days

Focuses on the latest research in Graph Theory Provides recent research findings that are occurring in this field Discusses the advanced developments and gives insights on an international and transnational level Identifies the gaps in the results Presents forthcoming international studies and researches, long with applications in Networking, Computer Science, Chemistry, Biological Sciences, etc.

A Concise Introduction to Hypercomplex Fractals (Paperback): Andrzej Katunin A Concise Introduction to Hypercomplex Fractals (Paperback)
Andrzej Katunin
R1,474 Discovery Miles 14 740 Ships in 12 - 17 working days

This book presents concisely the full story on complex and hypercomplex fractals, starting from the very first steps in complex dynamics and resulting complex fractal sets, through the generalizations of Julia and Mandelbrot sets on a complex plane and the Holy Grail of the fractal geometry - a 3D Mandelbrot set, and ending with hypercomplex, multicomplex and multihypercomplex fractal sets which are still under consideration of scientists. I tried to write this book in a possibly simple way in order to make it understandable to most people whose math knowledge covers the fundamentals of complex numbers only. Moreover, the book is full of illustrations of generated fractals and stories concerned with great mathematicians, number spaces and related fractals. In the most cases only information required for proper understanding of a nature of a given vector space or a construction of a given fractal set is provided, nevertheless a more advanced reader may treat this book as a fundamental compendium on hypercomplex fractals with references to purely scientific issues like dynamics and stability of hypercomplex systems.

Morse Index of Solutions of Nonlinear Elliptic Equations (Hardcover): Lucio Damascelli, Filomena Pacella Morse Index of Solutions of Nonlinear Elliptic Equations (Hardcover)
Lucio Damascelli, Filomena Pacella
R3,943 Discovery Miles 39 430 Ships in 12 - 17 working days

This monograph presents in a unified manner the use of the Morse index, and especially its connections to the maximum principle, in the study of nonlinear elliptic equations. The knowledge or a bound on the Morse index of a solution is a very important qualitative information which can be used in several ways for different problems, in order to derive uniqueness, existence or nonexistence, symmetry, and other properties of solutions.

Architecture of Mathematics (Hardcover): Simon Serovajsky Architecture of Mathematics (Hardcover)
Simon Serovajsky
R4,119 Discovery Miles 41 190 Ships in 12 - 17 working days

Architecture of Mathematics describes the logical structure of Mathematics from its foundations to its real-world applications. It describes the many interweaving relationships between different areas of mathematics and its practical applications, and as such provides unique reading for professional mathematicians and nonmathematicians alike. This book can be a very important resource both for the teaching of mathematics and as a means to outline the research links between different subjects within and beyond the subject. Features All notions and properties are introduced logically and sequentially, to help the reader gradually build understanding. Focusses on illustrative examples that explain the meaning of mathematical objects and their properties. Suitable as a supplementary resource for teaching undergraduate mathematics, and as an aid to interdisciplinary research. Forming the reader's understanding of Mathematics as a unified science, the book helps to increase his general mathematical culture.

Number Theory III - Diophantine Geometry (Hardcover, 1991 ed.): Serge Lang Number Theory III - Diophantine Geometry (Hardcover, 1991 ed.)
Serge Lang; Serge Lang
R3,210 Discovery Miles 32 100 Ships in 10 - 15 working days

In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the volume. By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q. The word Geometry is tacked on to suggest geometric methods. This means that the present volume is not elementary. For a survey of some basic problems with a much more elementary approach, see La 9Oc]. The field of diophantine geometry is now moving quite rapidly. Out standing conjectures ranging from decades back are being proved. I have tried to give the book some sort of coherence and permanence by em phasizing structural conjectures as much as results, so that one has a clear picture of the field. On the whole, I omit proofs, according to the boundary conditions of the encyclopedia. On some occasions I do give some ideas for the proofs when these are especially important. In any case, a lengthy bibliography refers to papers and books where proofs may be found. I have also followed Shafarevich's suggestion to give examples, and I have especially chosen these examples which show how some classical problems do or do not get solved by contemporary in sights. Fermat's last theorem occupies an intermediate position. Al though it is not proved, it is not an isolated problem any more."

Lie Groups (Hardcover, 1st ed. 2021): Luiz A. B. San Martin Lie Groups (Hardcover, 1st ed. 2021)
Luiz A. B. San Martin
R1,399 Discovery Miles 13 990 Ships in 12 - 17 working days

This textbook provides an essential introduction to Lie groups, presenting the theory from its fundamental principles. Lie groups are a special class of groups that are studied using differential and integral calculus methods. As a mathematical structure, a Lie group combines the algebraic group structure and the differentiable variety structure. Studies of such groups began around 1870 as groups of symmetries of differential equations and the various geometries that had emerged. Since that time, there have been major advances in Lie theory, with ramifications for diverse areas of mathematics and its applications. Each chapter of the book begins with a general, straightforward introduction to the concepts covered; then the formal definitions are presented; and end-of-chapter exercises help to check and reinforce comprehension. Graduate and advanced undergraduate students alike will find in this book a solid yet approachable guide that will help them continue their studies with confidence.

Apercu Historique Sur L'origine Et Le Developpement Des Methodes En Geometrie - Particulierement De Celles Qui Se... Apercu Historique Sur L'origine Et Le Developpement Des Methodes En Geometrie - Particulierement De Celles Qui Se Rapportent A La Geometrie Moderne, Suivi D'un Memoire De Geometrie Sur Deux Principes Generaux De La Science, La Dualite Et L'homographie (French, Paperback)
Michel Chasles
R957 Discovery Miles 9 570 Ships in 12 - 17 working days
Traite Des Proprietes Projectives Des Figures (French, Paperback): Jean Victor Poncelet Traite Des Proprietes Projectives Des Figures (French, Paperback)
Jean Victor Poncelet
R689 Discovery Miles 6 890 Ships in 12 - 17 working days
Introduction to Recognition and Deciphering of Patterns (Hardcover): Michael A. Radin Introduction to Recognition and Deciphering of Patterns (Hardcover)
Michael A. Radin
R4,105 Discovery Miles 41 050 Ships in 12 - 17 working days

Introduction to Recognition and Deciphering of Patterns is meant to acquaint STEM and non-STEM students with different patterns, as well as to where and when specific patterns arise. In addition, the book teaches students how to recognize patterns and distinguish the similarities and differences between them. Patterns, such as weather patterns, traffic patterns, behavioral patterns, geometric patterns, linguistic patterns, structural patterns, digital patterns, and the like, emerge on an everyday basis, . Recognizing patterns and studying their unique traits are essential for the development and enhancement of our intuitive skills and for strengthening our analytical skills. Mathematicians often apply patterns to get acquainted with new concepts--a technique that can be applied across many disciplines. Throughout this book we explore assorted patterns that emerge from various geometrical configurations of squares, circles, right triangles, and equilateral triangles that either repeat at the same scale or at different scales. The book also analytically examines linear patterns, geometric patterns, alternating patterns, piecewise patterns, summation-type patterns and factorial-type patterns. Deciphering the details of these distinct patterns leads to the proof by induction method, and the book will also render properties of Pascal's triangle and provide supplemental practice in deciphering specific patterns and verifying them. This book concludes with first-order recursive relations: describing sequences as recursive relations, obtaining the general solution by solving an initial value problem, and determining the periodic traits. Features * Readily accessible to a broad audience, including those with limited mathematical background * Especially useful for students in non-STEM disciplines, such as psychology, sociology, economics and business, as well as for liberal arts disciplines and art students.

Introduction to Recognition and Deciphering of Patterns (Paperback): Michael A. Radin Introduction to Recognition and Deciphering of Patterns (Paperback)
Michael A. Radin
R1,546 Discovery Miles 15 460 Ships in 12 - 17 working days

Introduction to Recognition and Deciphering of Patterns is meant to acquaint STEM and non-STEM students with different patterns, as well as to where and when specific patterns arise. In addition, the book teaches students how to recognize patterns and distinguish the similarities and differences between them. Patterns, such as weather patterns, traffic patterns, behavioral patterns, geometric patterns, linguistic patterns, structural patterns, digital patterns, and the like, emerge on an everyday basis, . Recognizing patterns and studying their unique traits are essential for the development and enhancement of our intuitive skills and for strengthening our analytical skills. Mathematicians often apply patterns to get acquainted with new concepts--a technique that can be applied across many disciplines. Throughout this book we explore assorted patterns that emerge from various geometrical configurations of squares, circles, right triangles, and equilateral triangles that either repeat at the same scale or at different scales. The book also analytically examines linear patterns, geometric patterns, alternating patterns, piecewise patterns, summation-type patterns and factorial-type patterns. Deciphering the details of these distinct patterns leads to the proof by induction method, and the book will also render properties of Pascal's triangle and provide supplemental practice in deciphering specific patterns and verifying them. This book concludes with first-order recursive relations: describing sequences as recursive relations, obtaining the general solution by solving an initial value problem, and determining the periodic traits. Features * Readily accessible to a broad audience, including those with limited mathematical background * Especially useful for students in non-STEM disciplines, such as psychology, sociology, economics and business, as well as for liberal arts disciplines and art students.

Prospects Of Differential Geometry And Its Related Fields - Proceedings Of The 3rd International Colloquium On Differential... Prospects Of Differential Geometry And Its Related Fields - Proceedings Of The 3rd International Colloquium On Differential Geometry And Its Related Fields (Hardcover)
Toshiaki Adachi, Hideya Hashimoto, Milen J. Hristov
R3,035 Discovery Miles 30 350 Ships in 12 - 17 working days

This volume consists of contributions by the main participants of the 3rd International Colloquium on Differential Geometry and its Related Fields (ICDG2012), which was held in Veliko Tarnovo, Bulgaria. Readers will find original papers by specialists and well-organized reports of recent developments in the fields of differential geometry, complex analysis, information geometry, mathematical physics and coding theory. This volume provides significant information that will be useful to researchers and serves as a good guide for young scientists. It is also for those who wish to start investigating these topics and interested in their interdisciplinary areas.

Barycentric Calculus In Euclidean And Hyperbolic Geometry: A Comparative Introduction (Hardcover): Abraham Albert Ungar Barycentric Calculus In Euclidean And Hyperbolic Geometry: A Comparative Introduction (Hardcover)
Abraham Albert Ungar
R3,438 Discovery Miles 34 380 Ships in 12 - 17 working days

The word barycentric is derived from the Greek word barys (heavy), and refers to center of gravity. Barycentric calculus is a method of treating geometry by considering a point as the center of gravity of certain other points to which weights are ascribed. Hence, in particular, barycentric calculus provides excellent insight into triangle centers. This unique book on barycentric calculus in Euclidean and hyperbolic geometry provides an introduction to the fascinating and beautiful subject of novel triangle centers in hyperbolic geometry along with analogies they share with familiar triangle centers in Euclidean geometry. As such, the book uncovers magnificent unifying notions that Euclidean and hyperbolic triangle centers share. In his earlier books the author adopted Cartesian coordinates, trigonometry and vector algebra for use in hyperbolic geometry that is fully analogous to the common use of Cartesian coordinates, trigonometry and vector algebra in Euclidean geometry. As a result, powerful tools that are commonly available in Euclidean geometry became available in hyperbolic geometry as well, enabling one to explore hyperbolic geometry in novel ways. In particular, this new book establishes hyperbolic barycentric coordinates that are used to determine various hyperbolic triangle centers just as Euclidean barycentric coordinates are commonly used to determine various Euclidean triangle centers. The hunt for Euclidean triangle centers is an old tradition in Euclidean geometry, resulting in a repertoire of more than three thousand triangle centers that are known by their barycentric coordinate representations. The aim of this book is to initiate a fully analogous hunt for hyperbolic triangle centers that will broaden the repertoire of hyperbolic triangle centers provided here.

The Restricted 3-Body Problem: Plane Periodic Orbits (Hardcover, Reprint 2011): Alexander D. Bruno The Restricted 3-Body Problem: Plane Periodic Orbits (Hardcover, Reprint 2011)
Alexander D. Bruno
R6,512 Discovery Miles 65 120 Ships in 12 - 17 working days

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

An Introduction to Metric Spaces (Hardcover): Dhananjay Gopal, Aniruddha Deshmukh, Abhay S Ranadive, Shubham Yadav An Introduction to Metric Spaces (Hardcover)
Dhananjay Gopal, Aniruddha Deshmukh, Abhay S Ranadive, Shubham Yadav
R3,658 Discovery Miles 36 580 Ships in 12 - 17 working days

This book serves as a textbook for an introductory course in metric spaces for undergraduate or graduate students. The goal is to present the basics of metric spaces in a natural and intuitive way and encourage students to think geometrically while actively participating in the learning of this subject. In this book, the authors illustrated the strategy of the proofs of various theorems that motivate readers to complete them on their own. Bits of pertinent history are infused in the text, including brief biographies of some of the central players in the development of metric spaces. The textbook is divided into seven chapters that contain the main materials on metric spaces; namely, introductory concepts, completeness, compactness, connectedness, continuous functions and metric fixed point theorems with applications. Some of the noteworthy features of this book include * Diagrammatic illustrations that encourage readers to think geometrically * Focus on systematic strategy to generate ideas for the proofs of theorems * A wealth of remarks, observations along with a variety of exercises * Historical notes and brief biographies appearing throughout the text

Algebraic Function Fields and Codes (Hardcover, 2nd ed. 2008): Henning Stichtenoth Algebraic Function Fields and Codes (Hardcover, 2nd ed. 2008)
Henning Stichtenoth
R2,828 Discovery Miles 28 280 Ships in 12 - 17 working days

This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.

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