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Books > Science & Mathematics > Mathematics > Geometry

A Functorial Model Theory - Newer Applications to Algebraic Topology, Descriptive Sets, and Computing Categories Topos... A Functorial Model Theory - Newer Applications to Algebraic Topology, Descriptive Sets, and Computing Categories Topos (Paperback)
Cyrus F Nourani
R2,514 Discovery Miles 25 140 Ships in 12 - 17 working days

This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.

Algebraic Computability and Enumeration Models - Recursion Theory and Descriptive Complexity (Paperback): Cyrus F Nourani Algebraic Computability and Enumeration Models - Recursion Theory and Descriptive Complexity (Paperback)
Cyrus F Nourani
R2,515 Discovery Miles 25 150 Ships in 12 - 17 working days

This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements. Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic types of models. New homotopy techniques are applied to Marin Lof types of computations with model categories. Functorial computability, induction, and recursion are examined in view of the above, presenting new computability techniques with monad transformations and projective sets. This informative volume will give readers a complete new feel for models, computability, recursion sets, complexity, and realizability. This book pulls together functorial thoughts, models, computability, sets, recursion, arithmetic hierarchy, filters, with real tree computing areas, presented in a very intuitive manner for university teaching, with exercises for every chapter. The book will also prove valuable for faculty in computer science and mathematics.

Solving Problems In Geometry: Insights And Strategies For Mathematical Olympiad And Competitions (Hardcover): Kim Hoo Hang,... Solving Problems In Geometry: Insights And Strategies For Mathematical Olympiad And Competitions (Hardcover)
Kim Hoo Hang, Haibin Wang
R1,512 Discovery Miles 15 120 Ships in 12 - 17 working days

'This book is a useful reference for faculty members involved in contest preparation or teaching Euclidean geometry at the college level.'MAA ReviewsThis new volume of the Mathematical Olympiad Series focuses on the topic of geometry. Basic and advanced theorems commonly seen in Mathematical Olympiad are introduced and illustrated with plenty of examples. Special techniques in solving various types of geometrical problems are also introduced, while the authors elaborate extensively on how to acquire an insight and develop strategies in tackling difficult geometrical problems.This book is suitable for any reader with elementary geometrical knowledge at the lower secondary level. Each chapter includes sufficient scaffolding and is comprehensive enough for the purpose of self-study. Readers who complete the chapters on the basic theorems and techniques would acquire a good foundation in geometry and may attempt to solve many geometrical problems in various mathematical competitions. Meanwhile, experienced contestants in Mathematical Olympiad competitions will find a large collection of problems pitched at competitions at the international level, with opportunities to practise and sharpen their problem-solving skills in geometry.

Theory of Spinors and Its Application in Physics and Mechanics (Hardcover, 1st ed. 2019): Vladimir A. Zhelnorovich Theory of Spinors and Its Application in Physics and Mechanics (Hardcover, 1st ed. 2019)
Vladimir A. Zhelnorovich
R4,091 Discovery Miles 40 910 Ships in 12 - 17 working days

This book contains a systematic exposition of the theory of spinors in finite-dimensional Euclidean and Riemannian spaces. The applications of spinors in field theory and relativistic mechanics of continuous media are considered. The main mathematical part is connected with the study of invariant algebraic and geometric relations between spinors and tensors. The theory of spinors and the methods of the tensor representation of spinors and spinor equations are thoroughly expounded in four-dimensional and three-dimensional spaces. Very useful and important relations are derived that express the derivatives of the spinor fields in terms of the derivatives of various tensor fields. The problems associated with an invariant description of spinors as objects that do not depend on the choice of a coordinate system are addressed in detail. As an application, the author considers an invariant tensor formulation of certain classes of differential spinor equations containing, in particular, the most important spinor equations of field theory and quantum mechanics. Exact solutions of the Einstein-Dirac equations, nonlinear Heisenberg's spinor equations, and equations for relativistic spin fluids are given. The book presents a large body of factual material and is suited for use as a handbook. It is intended for specialists in theoretical physics, as well as for students and post-graduate students of physical and mathematical specialties.

Beauville Surfaces and Groups (Hardcover, 2015 ed.): Ingrid Bauer, Shelly Garion, Alina Vdovina Beauville Surfaces and Groups (Hardcover, 2015 ed.)
Ingrid Bauer, Shelly Garion, Alina Vdovina
R3,652 R3,384 Discovery Miles 33 840 Save R268 (7%) Ships in 12 - 17 working days

This collection of surveys and research articles explores a fascinating class of varieties: Beauville surfaces. It is the first time that these objects are discussed from the points of view of algebraic geometry as well as group theory. The book also includes various open problems and conjectures related to these surfaces. Beauville surfaces are a class of rigid regular surfaces of general type, which can be described in a purely algebraic combinatoric way. They play an important role in different fields of mathematics like algebraic geometry, group theory and number theory. The notion of Beauville surface was introduced by Fabrizio Catanese in 2000 and after the first systematic study of these surfaces by Ingrid Bauer, Fabrizio Catanese and Fritz Grunewald, there has been an increasing interest in the subject. These proceedings reflect the topics of the lectures presented during the workshop 'Beauville surfaces and groups 2012', held at Newcastle University, UK in June 2012. This conference brought together, for the first time, experts of different fields of mathematics interested in Beauville surfaces.

Complex Analysis and Algebraic Geometry - A Volume in Memory of Michael Schneider (Hardcover, Reprint 2016): Thomas Peternell,... Complex Analysis and Algebraic Geometry - A Volume in Memory of Michael Schneider (Hardcover, Reprint 2016)
Thomas Peternell, Frank-Olaf Schreyer
R6,137 Discovery Miles 61 370 Ships in 12 - 17 working days

Without an introduction, this volume of 19 papers plunges right into the subject matter presented at the June 1998 symposium held at Bayreuth U. in Bayreuth, Germany. A sampling of topics: almost-lines and quasi-lines on projective manifolds, the classification of K3 surfaces with nine cusps, simply connected Godeaux surfaces, Kahlerian structures on symplectic reductions, and A geometric proof of Ax' theorem. One paper is in untranslated French. Includes an essay on Michael Schneider's scientific work with a publications list (including his still standard reference on vector bundles on projective spaces); a photograph and "alpine" vita of Schneider (who died while sports-climbing in 1997); a list of the eight symposium lectures; and a listing of the authors and participants with contact information. Lacks an index.

Normally Hyperbolic Invariant Manifolds in Dynamical Systems (Hardcover, 1994 ed.): Stephen Wiggins Normally Hyperbolic Invariant Manifolds in Dynamical Systems (Hardcover, 1994 ed.)
Stephen Wiggins; Assisted by G. Haller, I. Mezic
R1,637 Discovery Miles 16 370 Ships in 10 - 15 working days

In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications.

Introduction To The Geometrical Analysis Of Vector Fields, An: With Applications To Maximum Principles And Lie Groups... Introduction To The Geometrical Analysis Of Vector Fields, An: With Applications To Maximum Principles And Lie Groups (Hardcover)
Stefano Biagi, Andrea Bonfiglioli
R4,293 Discovery Miles 42 930 Ships in 10 - 15 working days

This book provides the reader with a gentle path through the multifaceted theory of vector fields, starting from the definitions and the basic properties of vector fields and flows, and ending with some of their countless applications, in the framework of what is nowadays called Geometrical Analysis. Once the background material is established, the applications mainly deal with the following meaningful settings:

Elementary Topology And Applications (Hardcover, Second Edition): Carlos R Borges Elementary Topology And Applications (Hardcover, Second Edition)
Carlos R Borges
R1,564 Discovery Miles 15 640 Ships in 10 - 15 working days

The textbook is a very good start into the mathematical field of topology. A variety of topological concepts with some elementary applications are introduced. It is organized in such a way that the reader gets to significant applications quickly.This revised version corrects the many discrepancies in the earlier edition. The emphasis is on the geometric understanding and the use of new concepts, indicating that topology is really the language of modern mathematics.

From Classical Field Theory to Perturbative Quantum Field Theory (Hardcover, 1st ed. 2019): Michael Dutsch From Classical Field Theory to Perturbative Quantum Field Theory (Hardcover, 1st ed. 2019)
Michael Dutsch
R3,718 Discovery Miles 37 180 Ships in 10 - 15 working days

This book develops a novel approach to perturbative quantum field theory: starting with a perturbative formulation of classical field theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying the principle that as much of the classical structure as possible should be maintained. The resulting formulation of perturbative quantum field theory is a version of the Epstein-Glaser renormalization that is conceptually clear, mathematically rigorous and pragmatically useful for physicists. The connection to traditional formulations of perturbative quantum field theory is also elaborated on, and the formalism is illustrated in a wealth of examples and exercises.

Buildings and Schubert Schemes (Paperback): Carlos Contou-Carrere Buildings and Schubert Schemes (Paperback)
Carlos Contou-Carrere
R1,528 Discovery Miles 15 280 Ships in 12 - 17 working days

The first part of this book introduces the Schubert Cells and varieties of the general linear group Gl (k^(r+1)) over a field k according to Ehresmann geometric way. Smooth resolutions for these varieties are constructed in terms of Flag Configurations in k^(r+1) given by linear graphs called Minimal Galleries. In the second part, Schubert Schemes, the Universal Schubert Scheme and their Canonical Smooth Resolution, in terms of the incidence relation in a Tits relative building are constructed for a Reductive Group Scheme as in Grothendieck's SGAIII. This is a topic where algebra and algebraic geometry, combinatorics, and group theory interact in unusual and deep ways.

Theory of Convex Structures, Volume 50 (Hardcover): M.L.J.Van De Vel Theory of Convex Structures, Volume 50 (Hardcover)
M.L.J.Van De Vel
R2,008 Discovery Miles 20 080 Ships in 12 - 17 working days

Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. A wide variety of results has been included (ranging for instance from the area of partition calculus to that of continuous selection). The tools involved are borrowed from areas ranging from discrete mathematics to infinite-dimensional topology.

Although addressed primarily to the researcher, parts of this monograph can be used as a basis for a well-balanced, one-semester graduate course.

Current Developments In Differential Geometry And Its Related Fields - Proceedings Of The 4th International Colloquium On... Current Developments In Differential Geometry And Its Related Fields - Proceedings Of The 4th International Colloquium On Differential Geometry And Its Related Fields (Hardcover)
Toshiaki Adachi, Hideya Hashimoto, Milen J. Hristov
R3,526 Discovery Miles 35 260 Ships in 12 - 17 working days

This volume contains contributions by the main participants of the 4th International Colloquium on Differential Geometry and its Related Fields (ICDG2014). These articles cover recent developments and are devoted mainly to the study of some geometric structures on manifolds and graphs. Readers will find a broad overview of differential geometry and its relationship to other fields in mathematics and physics.

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
R2,748 Discovery Miles 27 480 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.

Homological Algebra: In Strongly Non-abelian Settings (Hardcover): Marco Grandis Homological Algebra: In Strongly Non-abelian Settings (Hardcover)
Marco Grandis
R3,183 Discovery Miles 31 830 Ships in 12 - 17 working days

We propose here a study of 'semiexact' and 'homological' categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, where satellites and spectral sequences can still be studied.This is a sequel of a book on 'Homological Algebra, The interplay of homology with distributive lattices and orthodox semigroups', published by the same Editor, but can be read independently of the latter.The previous book develops homological algebra in p-exact categories, i.e. exact categories in the sense of Puppe and Mitchell - a moderate generalisation of abelian categories that is nevertheless crucial for a theory of 'coherence' and 'universal models' of (even abelian) homological algebra. The main motivation of the present, much wider extension is that the exact sequences or spectral sequences produced by unstable homotopy theory cannot be dealt with in the previous framework.According to the present definitions, a semiexact category is a category equipped with an ideal of 'null' morphisms and provided with kernels and cokernels with respect to this ideal. A homological category satisfies some further conditions that allow the construction of subquotients and induced morphisms, in particular the homology of a chain complex or the spectral sequence of an exact couple.Extending abelian categories, and also the p-exact ones, these notions include the usual domains of homology and homotopy theories, e.g. the category of 'pairs' of topological spaces or groups; they also include their codomains, since the sequences of homotopy 'objects' for a pair of pointed spaces or a fibration can be viewed as exact sequences in a homological category, whose objects are actions of groups on pointed sets.

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
R3,763 Discovery Miles 37 630 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.

Degree Theory of Immersed Hypersurfaces (Paperback): Harold Rosenberg, Graham Smith Degree Theory of Immersed Hypersurfaces (Paperback)
Harold Rosenberg, Graham Smith
R2,210 Discovery Miles 22 100 Ships in 12 - 17 working days

The authors develop a degree theory for compact immersed hypersurfaces of prescribed $K$-curvature immersed in a compact, orientable Riemannian manifold, where $K$ is any elliptic curvature function. They apply this theory to count the (algebraic) number of immersed hyperspheres in various cases: where $K$ is mean curvature, extrinsic curvature and special Lagrangian curvature and show that in all these cases, this number is equal to $-\chi(M)$, where $\chi(M)$ is the Euler characteristic of the ambient manifold $M$.

Tools for Infinite Dimensional Analysis (Hardcover): Jeremy J. Becnel Tools for Infinite Dimensional Analysis (Hardcover)
Jeremy J. Becnel
R4,743 Discovery Miles 47 430 Ships in 12 - 17 working days

Over the past six decades, several extremely important fields in mathematics have been developed. Among these are Ito calculus, Gaussian measures on Banach spaces, Malliavan calculus, and white noise distribution theory. These subjects have many applications, ranging from finance and economics to physics and biology. Unfortunately, the background information required to conduct research in these subjects presents a tremendous roadblock. The background material primarily stems from an abstract subject known as infinite dimensional topological vector spaces. While this information forms the backdrop for these subjects, the books and papers written about topological vector spaces were never truly written for researchers studying infinite dimensional analysis. Thus, the literature for topological vector spaces is dense and difficult to digest, much of it being written prior to the 1960s. Tools for Infinite Dimensional Analysis aims to address these problems by providing an introduction to the background material for infinite dimensional analysis that is friendly in style and accessible to graduate students and researchers studying the above-mentioned subjects. It will save current and future researchers countless hours and promote research in these areas by removing an obstacle in the path to beginning study in areas of infinite dimensional analysis. Features Focused approach to the subject matter Suitable for graduate students as well as researchers Detailed proofs of primary results

Fractals in Chemistry (Hardcover, New): WG Rothschild Fractals in Chemistry (Hardcover, New)
WG Rothschild
R5,360 Discovery Miles 53 600 Ships in 10 - 15 working days

A practical guide to solving problems in chemistry with fractal geometry.
It has been two decades since Mandelbrot formulated his revolutionary theories of fractal geometry. Yet, in that brief time, fractals -those strangely beautiful infinite geometric patterns -and the computational processes that give rise to them have become a valued research tool in a broad array of scientific, social-scientific, and commercial fields. While inroads also have been made in applying fractals to theoretical and applied chemistry, there continues to be a dearth of texts and references on the subject. This book helps fill that gap in the literature.
Fractals in Chemistry provides chemists with a concise, practical introduction to fractal theory and its applications to a wide range of "bread and butter" issues in chemistry. Drawing upon his considerable experience as a researcher who helped pioneer some of the methods he describes, Walter Rothschild critically appraises the power and limitations of the fractal approach and shows how it can provide more predictive classification schemes and explain phenomena difficult to handle by classical means. Then, with the help of nearly 100 illustrations, he demonstrates how to apply fractals to model chemical phenomena such as adsorption, aggregation, catalysis, chemical reactivity, degradation, and turbulent flames, and how to understand dynamics on fractals in terms of fractons in diffusion-limited reactions, dispersive spectroscopies, and energy transfer.
Fractals in Chemistry is both a valuable working resource for professionals in physical chemistry, chemical physics, and computer modeling and an excellent graduate-level text for coursescovering the use of fractals in chemistry.

Foliations 2012 - Proceedings Of The International Conference (Hardcover): Jesus A. Alvarez Lopez, Steven Hurder, Remi... Foliations 2012 - Proceedings Of The International Conference (Hardcover)
Jesus A. Alvarez Lopez, Steven Hurder, Remi Langevin, Takashi Tsuboi, Pawel Walczak
R3,434 Discovery Miles 34 340 Ships in 12 - 17 working days

This volume is a compilation of new results and surveys on the current state of some aspects of the foliation theory presented during the conference "FOLIATIONS 2012". It contains recent materials on foliation theory which is related to differential geometry, the theory of dynamical systems and differential topology. Both the original research and survey articles found in here should inspire students and researchers interested in foliation theory and the related fields to plan his/her further research.

An Introduction to Tensor Analysis (Hardcover): Bipin Singh Koranga, Sanjay Kumar Padaliya An Introduction to Tensor Analysis (Hardcover)
Bipin Singh Koranga, Sanjay Kumar Padaliya
R2,322 Discovery Miles 23 220 Ships in 12 - 17 working days

The subject of Tensor Analysis deals with the problem of the formulation of the relation between various entities in forms which remain invariant when we pass from one system of coordinates to another. The invariant form of equation is necessarily related to the possible system of coordinates with reference to which the equation remains invariant. The primary purpose of this book is the study of the invariance form of equation relative to the totally of the rectangular co-ordinate system in the three-dimensional Euclidean space. We start with the consideration of the way the sets representing various entities are transformed when we pass from one system of rectangular co-ordinates to another. A Tensor may be a physical entity that can be described as a Tensor only with respect to the manner of its representation by means of multi-sux sets associated with different system of axes such that the sets associated with different system of co-ordinate obey the transformation law for Tensor. We have employed sux notation for tensors of any order, we could also employ single letter such A,B to denote Tensors.

Recent Advancements in Graph Theory (Hardcover): N. P. Shrimali, Nita H. Shah Recent Advancements in Graph Theory (Hardcover)
N. P. Shrimali, Nita H. Shah
R4,616 Discovery Miles 46 160 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.

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
R1,900 Discovery Miles 19 000 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
R2,873 Discovery Miles 28 730 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.

Lie Groups (Hardcover, 1st ed. 2021): Luiz A. B. San Martin Lie Groups (Hardcover, 1st ed. 2021)
Luiz A. B. San Martin
R1,322 Discovery Miles 13 220 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.

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