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Introduction to Integration and Measure Theory
This book describes integration and measure theory for readers interested in analysis, engineering, and economics. It gives a systematic account of Riemann-Stieltjes integration and deduces the Lebesgue-Stieltjes measure from the Lebesgue-Stieltjes integral.
R 7,716.00
Introduction to the Theory of Complex Systems
This book is a comprehensive introduction to quantitative approaches to complex adaptive systems. Practically all areas of life on this planet are constantly confronted with complex systems, be it ecosystems, societies, traffic, financial markets, opinion formation and spreading, or the internet and social media. Complex systems are systems composed of many elements that interact strongly with each other, which makes them extremely rich dynamical systems showing ahuge range of phenomena. Properties of complex systems that are of particular importance are their efficiency, robustness, resilience, and proneness to collapse.The quantitative tools and concepts needed to understand the co-evolutionary nature of networked systems and their properties are challenging. The book gives a self-contained introduction to these concepts, so that the reader will be equipped with a toolset that allows them to engage in the science of complex systems. Topics covered include random processes of path-dependent processes, co-evolutionary dynamics, dynamics of networks, the theory of scaling, and approaches from statisticalmechanics and information theory. The book extends beyond the early classical literature in the field of complex systems and summarizes the methodological progress made over the past 20 years in a clear, structured, and comprehensive way.
R 3,867.00
Introduction to the Mathematical Theory of the Navier-Stokes Equations
The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of boundary-value problems related to the Navier-Stokes equations. These properties include existence, uniqueness and regularity of solutions in bounded as well as unbounded domains. Whenever the domain is unbounded, the asymptotic behavior of solutions is also investigated. This book is the new edition of the original two volume book, under the same title, published in 1994.In this new edition, the two volumes have merged into one and two more chapters on steady generalized oseen flow in exterior domains and steady Navier–Stokes flow in three-dimensional exterior domains have been added. Most of the proofs given in the previous edition were also updated.An introductory first chapter describes all relevant questions treated in the book and lists and motivates a number of significant and still open questions. It is written in an expository style so as to be accessible also to non-specialists.Each chapter is preceded by a substantial, preliminary discussion of the problems treated, along with their motivation and the strategy used to solve them. Also, each chapter ends with a section dedicated to alternative approaches and procedures, as well as historical notes. The book contains more than 400 stimulating exercises, at different levels of difficulty, that will help the junior researcher and the graduate student to gradually become accustomed with the subject. Finally, the book is endowed with a vast bibliography that includes more than 500 items. Each item brings a reference to the section of the book where it is cited. The book will be useful to researchers and graduate students in mathematics in particular mathematical fluid mechanics and differential equations.Review of First Edition, First Volume:“The emphasis of this book is on an introduction to the mathematical theory of the stationary Navier-Stokes equations. It is written in the style of a textbook and is essentially self-contained. The problems are presented clearly and in an accessible manner. Every chapter begins with a good introductory discussion of the problems considered, and ends with interesting notes on different approaches developed in the literature. Further, stimulating exercises are proposed. (Mathematical Reviews, 1995)
R 3,156.65
Introduction to the Theory of Knowledge
Now revised and containing three new chapters, this book provides a clear and accessible introduction to epistemology, or the theory of knowledge. It discusses some of the main theories of justification, including foundationalism, coherentism, reliabilism, and virtue epistemology. Other topics include the Gettier problem, internalism and externalism, skepticism, the problem of epistemic circularity, a priori knowledge, naturalized epistemology, and the epistemic significance of testimony and disagreement. Intended primarily for students taking their first classes in epistemology, this lucid and well-written text will provide an excellent introduction to anyone interested in knowing more about this important area of philosophy.
R 4,806.98
Introduction to the Mathematical Theory of the Navier-Stokes Equations
The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of boundary-value problems related to the Navier-Stokes equations. These properties include existence, uniqueness and regularity of solutions in bounded as well as unbounded domains. Whenever the domain is unbounded, the asymptotic behavior of solutions is also investigated. This book is the new edition of the original two volume book, under the same title, published in 1994.In this new edition, the two volumes have merged into one and two more chapters on steady generalized oseen flow in exterior domains and steady Navier–Stokes flow in three-dimensional exterior domains have been added. Most of the proofs given in the previous edition were also updated.An introductory first chapter describes all relevant questions treated in the book and lists and motivates a number of significant and still open questions. It is written in an expository style so as to be accessible also to non-specialists.Each chapter is preceded by a substantial, preliminary discussion of the problems treated, along with their motivation and the strategy used to solve them. Also, each chapter ends with a section dedicated to alternative approaches and procedures, as well as historical notes. The book contains more than 400 stimulating exercises, at different levels of difficulty, that will help the junior researcher and the graduate student to gradually become accustomed with the subject. Finally, the book is endowed with a vast bibliography that includes more than 500 items. Each item brings a reference to the section of the book where it is cited. The book will be useful to researchers and graduate students in mathematics in particular mathematical fluid mechanics and differential equations.Review of First Edition, First Volume:“The emphasis of this book is on an introduction to the mathematical theory of the stationary Navier-Stokes equations. It is written in the style of a textbook and is essentially self-contained. The problems are presented clearly and in an accessible manner. Every chapter begins with a good introductory discussion of the problems considered, and ends with interesting notes on different approaches developed in the literature. Further, stimulating exercises are proposed. (Mathematical Reviews, 1995)
R 4,772.14
Introduction to Quantum Field Theory
Quantum Field Theory provides a theoretical framework for understanding fields and the particles associated with them, and is the basis of particle physics and condensed matter research. This graduate level textbook provides a comprehensive introduction to quantum field theory, giving equal emphasis to operator and path integral formalisms. It covers modern research such as helicity spinors, BCFW construction and generalized unitarity cuts; as well as treating advanced topics including BRST quantization, loop equations, and finite temperature field theory. Various quantum fields are described, including scalar and fermionic fields, Abelian vector fields and Quantum ElectroDynamics (QED), and finally non-Abelian vector fields and Quantum ChromoDynamics (QCD). Applications to scattering cross sections in QED and QCD are also described. Each chapter ends with exercises and an important concepts section, allowing students to identify the key aspects of the chapter and test their understanding.
R 3,525.77
R 4,951.14
Abstract Algebra: Introduction To Groups, Rings And Fields With Applications
This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata.This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced — via congruence classes — to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless.In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.
R 4,812.74
Introduction to Dynamic Systems
Integrates the traditional approach to differential equations with the modern systems and control theoretic approach to dynamic systems, emphasizing theoretical principles and classic models in a wide variety of areas. Provides a particularly comprehensive theoretical development that includes chapters on positive dynamic systems and optimal control theory. Contains numerous problems.
R 8,326.00
Introduction to the Theory of Stability
Many books on stability theory of motion have been published in various lan guages, including English. Most of these are comprehensive monographs, with each one devoted to a separate complicated issue of the theory. Generally, the examples included in such books are very interesting from the point of view of mathematics, without necessarily having much practical value. Usually, they are written using complicated mathematical language, so that except in rare cases, their content becomes incomprehensible to engineers, researchers, students, and sometimes even to professors at technical universities. The present book deals only with those issues of stability of motion that most often are encountered in the solution of scientific and technical problems. This allows the author to explain the theory in a simple but rigorous manner without going into minute details that would be of interest only to specialists. Also, using appropriate examples, he demonstrates the process of investigating the stability of motion from the formulation of a problem and obtaining the differential equations of perturbed motion to complete analysis and recommendations. About one fourth of the examples are from various areas of science and technology. Moreover, some of the examples and the problems have an independent value in that they could be applicable to the design of various mechanisms and devices. The present translation is based on the third Russian edition of 1987.
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Introduction to the Theory of Piezoelectricity
This textbook introduces theoretical piezoelectricity. The second edition updates a classical, seminal reference on a fundamental topic that is addressed in every materials science curriculum. It presents a concise treatment of the basic theoretical aspects of continuum modeling of electroelastic interactions in solids. The general nonlinear theory for large deformations and strong fields is established and specialized to the linear theory for small deformations and weak fields, i.e., the theory of piezoelectricity. Relatively simple and useful solutions of many static and dynamic problems of piezoelectricity that are useful in device applications are given. Emphasis is on the formulation of solutions to problems rather than advanced mathematical solution techniques. This book includes many examples to assist and enhance students’ understanding of piezoelectricity and piezoelastics.
R 3,403.40
Introduction to the Theory of Solid Surfaces
First published in 1979, this is a self-contained account of the theory of surface physics. In drawing together many results only previously reported in research papers, the authors emphasise basic disciplines such as electrodynamics and electron gas theory and demonstrate their application to simple models. Connections between intuitive derivations and more rigourous formulations are explained and there is an extensive treatment of the general problem of matching at a surface as a mathematical formalism with a physical meaning. Commonly recurring concepts such as surface modes, Green functions and phase shifts link different parts of the book, so giving coherence to the theory as a whole. A good background in physics is assumed but no previous acquaintance with surface physics. Starting from first principles, the reader is led from elementary analysis to the level of current research literature. The book is thus suitable for postgraduate students, post-doctoral workers or anyone wanting a systematic introduction to the field.
R 2,972.96
Introduction to Microcontroller Programming for Power Electronics Control Applications
Microcontroller programming is not a trivial task. Indeed, it is necessary to set correctly the required peripherals by using programming languages like C/C++ or directly machine code. Nevertheless, MathWorks® developed a model-based workflow linked with an automatic code generation tool able to translate Simulink® schemes into executable files. This represents a rapid prototyping procedure, and it can be applied to many microcontroller boards available on the market. Among them, this introductory book focuses on the C2000 LaunchPadTM family from Texas InstrumentsTM to provide the reader basic programming strategies, implementation guidelines and hardware considerations for some power electronics-based control applications. Starting from simple examples such as turning on/off on-board LEDs, Analog-to-Digital conversion, waveform generation, or how a Pulse-Width-Modulation peripheral should be managed, the reader is guided through the settings of the specific MCU-related Simulink® blocks enabled for code translation. Then, the book proposes several control problems in terms of power management of RL and RLC loads (e.g., involving DC-DC converters) and closed-loop control of DC motors. The control schemes are investigated as well as the working principles of power converter topologies needed to drive the systems under investigation. Finally, a couple of exercises are proposed to check the reader’s understanding while presenting a processor-in-the loop (PIL) technique to either emulate the dynamics of complex systems or testing computational performance.Thus, this book is oriented to graduate students of electrical and automation and control engineering pursuing a curriculum in power electronics and drives, as well as to engineers and researchers who want to deepen their knowledge and acquire new competences in the design and implementations of control schemes aimed to the aforementioned application fields. Indeed, it is assumed that the reader is well acquainted with fundamentals of electrical machines and power electronics, as well as with continuous-time modeling strategies and linear control techniques. In addition, familiarity with sampled-data, discrete-time system analysis and embedded design topics is a plus. However, even if these competences are helpful, they are not essential, since this book provides some basic knowledge even to whom is approaching these topics for the first time. Key concepts are developed from scratch, including a brief review of control theory and modeling strategies for power electronic-based systems.
R 2,904.26
Introduction to Financial Mathematics
Introduction to Financial Mathematics: Option Valuation, Second Edition is a well-rounded primer to the mathematics and models used in the valuation of financial derivatives. The book consists of fifteen chapters, the first ten of which develop option valuation techniques in discrete time, the last five describing the theory in continuous time. The first half of the textbook develops basic finance and probability. The author then treats the binomial model as the primary example of discrete-time option valuation. The final part of the textbook examines the Black-Scholes model. The book is written to provide a straightforward account of the principles of option pricing and examines these principles in detail using standard discrete and stochastic calculus models. Additionally, the second edition has new exercises and examples, and includes many tables and graphs generated by over 30 MS Excel VBA modules available on the author’s webpage https://home.gwu.edu/~hdj/.
R 7,584.09
Introduction to Nursing for First Year Students
The perfect handbook for first year nursing students! Whether you are just starting your course, preparing for your first placement, writing an assignment, or revising for your end-of-year exams, this book will support you through it all, with interactive activities, real-life scenarios and interesting case studies. Covering all the skills, theory and knowledge that you will need to know in order to succeed, this book is packed full of information relating to the core modules taught in the first year of your nursing degree, including: Person centred care, effective communication and ethical valuesResearch, academic and study skillsCore clinical skills for effective practiceAnatomy and PhysiologyPharmacology and medicines management Written specifically for first year Nursing Students in all specialisms and students on the first year of their Nursing Associate or Nursing Apprenticeship programmes.
R 1,928.61
Introduction to Modern Analysis
This textbook provides an introduction to modern analysis aimed at advanced undergraduate and graduate-level students of mathematics. Professional academics will also find this to be a useful reference work. It covers measure theory, basic functional analysis, single operator theory, spectral theory of bounded and unbounded operators, semigroups of operators, and Banach algebras. Further, this new edition of the textbook also delves deeper into C*-algebras and theirstandard constructions, von Neumann algebras, probability and mathematical statistics, and partial differential equations. Most chapters contain relatively advanced topics alongside simpler ones, starting from the very basics of modern analysis and slowly advancing to more involved topics. The text is supplemented by many exercises, to allow readers to test their understanding and practical analysis skills.
R 5,607.00
Introduction to Linear Programming and Game Theory
Praise for the Second Edition: "This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications." —Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems. This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications. Additional features of the Third Edition include: A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy models Revised proofs and a discussion on the relevance and solution of the dual problem A section on developing an example in Data Envelopment Analysis An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science.
R 4,883.00
Introduction to the Theory of Distributions
The theory of distributions is an extension of classical analysis which has acquired a particular importance in the field of linear partial differential equations, as well as having many other applications, for example in harmonic analysis. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without presupposing a knowledge, or using more than a bare minimum, of this. This book, first published in 1999, adopts this course and is based on graduate lectures given over a number of years. The prerequisites are few, but a reasonable degree of mathematical maturity is expected of the reader, as the treatment is rigorous throughout. From the outset the theory is developed in several variables, unlike most elementary texts; it is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces.
R 6,651.95
Introduction to the Perturbation Theory of Hamiltonian Systems
This book is an extended version of lectures given by the ?rst author in 1995–1996 at the Department of Mechanics and Mathematics of Moscow State University. We believe that a major part of the book can be regarded as an additional material to the standard course of Hamiltonian mechanics. In comparison with the original Russian 1 version we have included new material, simpli?ed some proofs and corrected m- prints. Hamiltonian equations ?rst appeared in connection with problems of geometric optics and celestial mechanics. Later it became clear that these equations describe a large classof systemsin classical mechanics,physics,chemistry,and otherdomains. Hamiltonian systems and their discrete analogs play a basic role in such problems as rigid body dynamics, geodesics on Riemann surfaces, quasi-classic approximation in quantum mechanics, cosmological models, dynamics of particles in an accel- ator, billiards and other systems with elastic re?ections, many in?nite-dimensional models in mathematical physics, etc. In this book we study Hamiltonian systems assuming that they depend on some parameter (usually?), where for?= 0 the dynamics is in a sense simple (as a rule, integrable). Frequently such a parameter appears naturally. For example, in celestial mechanics it is accepted to take? equal to the ratio: the mass of Jupiter over the mass of the Sun. In other cases it is possible to introduce the small parameter ar- ?cially.
R 4,103.32
Group Theory In Physics: An Introduction To Symmetry Principles, Group Representations, And Special Functions In Classical And Quantum Physics
An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems.Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry.Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained.A set of problems and solutions has been published in a separate booklet.
R 2,269.08
Introduction to Arithmetical Functions
The theory of arithmetical functions has always been one of the more active parts of the theory of numbers. The large number of papers in the bibliography, most of which were written in the last forty years, attests to its popularity. Most textbooks on the theory of numbers contain some information on arithmetical functions, usually results which are classical. My purpose is to carry the reader beyond the point at which the textbooks abandon the subject. In each chapter there are some results which can be described as contemporary, and in some chapters this is true of almost all the material. This is an introduction to the subject, not a treatise. It should not be expected that it covers every topic in the theory of arithmetical functions. The bibliography is a list of papers related to the topics that are covered, and it is at least a good approximation to a complete list within the limits I have set for myself. In the case of some of the topics omitted from or slighted in the book, I cite expository papers on those topics.
R 1,568.42
Introduction to Smooth Manifolds
This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer.This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sard’s theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures.Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.
R 2,297.58
Introduction to Manifolds
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory.In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems.This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
R 2,198.00
Interpretive Introduction to Quantum Field Theory
Quantum mechanics is a subject that has captured the imagination of a surprisingly broad range of thinkers, including many philosophers of science. Quantum field theory, however, is a subject that has been discussed mostly by physicists. This is the first book to present quantum field theory in a manner that makes it accessible to philosophers. Because it presents a lucid view of the theory and debates that surround the theory, An Interpretive Introduction to Quantum Field Theory will interest students of physics as well as students of philosophy. Paul Teller presents the basic ideas of quantum field theory in a way that is understandable to readers who are familiar with non-relativistic quantum mechanics. He provides information about the physics of the theory without calculational detail, and he enlightens readers on how to think about the theory physically. Along the way, he dismantles some popular myths and clarifies the novel ways in which quantum field theory is both a theory about fields and about particles. His goal is to raise questions about the philosophical implications of the theory and to offer some tentative interpretive views of his own.This provocative and thoughtful book challenges philosophers to extend their thinking beyond the realm of quantum mechanics and it challenges physicists to consider the philosophical issues that their explorations have encouraged.
R 2,140.41
Introduction to Ergodic Theory
The first part of this introduction to ergodic theory addresses measure-preserving transformations of probability spaces and covers such topics as recurrence properties and the Birkhoff ergodic theorem. The second part focuses on the ergodic theory of continuous transformations of compact metrizable spaces. Several examples are detailed, and the final chapter outlines results and applications of ergodic theory to other branches of mathematics.
R 2,088.39
Mathematical Introduction To Control Theory, A
Striking a nice balance between mathematical rigor and engineering-oriented applications, this second edition covers the bedrock parts of classical control theory — the Routh-Hurwitz theorem and applications, Nyquist diagrams, Bode plots, root locus plots, and the design of controllers (phase-lag, phase-lead, lag-lead, and PID). It also covers three more advanced topics — non-linear control, modern control, and discrete-time control.This invaluable book makes effective use of MATLAB® as a tool in design and analysis. Containing 75 solved problems and 200 figures, this edition will be useful for junior and senior level university students in engineering who have a good knowledge of complex variables and linear algebra.
R 3,190.40
Introduction to Quantum Theory
Since its emergence in the early twentieth century, quantum theory has become the fundamental physical paradigm, and is essential to our understanding of the world. Providing a deeper understanding of the microscopic world through quantum theory, this supplementary text reviews a wider range of topics than conventional textbooks. Emphasis is given to modern entanglement, quantum teleportation, and Bose-Einstein condensation. Macroscopic quantum effects of practical relevance, for example superconductivity and the quantum Hall effect, are also described. Looking to the future, the author discusses the exciting prospects for quantum computing. Physical, rather than formal, explanations are given, and mathematical formalism is kept to a minimum so readers can understand the concepts more easily. Theoretical discussions are combined with a description of the corresponding experimental results. This book is ideal for undergraduate and graduate students in quantum theory and quantum optics.
R 2,318.00
Introduction to the Mechanics of Deformable Solids
Introduction to the Mechanics of Deformable Solids: Bars and Beams introduces the theory of beams and bars, including axial, torsion, and bending loading and analysis of bars that are subjected to combined loadings, including resulting complex stress states using Mohr’s circle. The book provides failure analysis based on maximum stress criteria and introduces design using models developed in the text. Throughout the book, the author emphasizes fundamentals, including consistent mathematical notation. The author also presents the fundamentals of the mechanics of solids in such a way that the beginning student is able to progress directly to a follow-up course that utilizes two- and three-dimensional finite element codes imbedded within modern software packages for structural design purposes. As such, excessive details included in the previous generation of textbooks on the subject are obviated due to their obsolescence with the availability of today’s finite element software packages.
R 2,054.24
String Theory: Volume 1, An Introduction to the Bosonic String
String Theory comprises two volumes which give a comprehensive and pedagogic account of the subject. Volume 1, first published in 1998, provides a thorough introduction to the bosonic string. The first four chapters introduce the central ideas of string theory, the tools of conformal field theory and of the Polyakov path integral, and the covariant quantization of the string. The next three chapters treat string interactions: the general formalism, and detailed treatments of the tree level and one loop amplitudes. Chapter eight covers toroidal compactification and many important aspects of string physics, such as T-duality and D-branes. Chapter nine treats higher-order amplitudes, including an analysis of their finiteness and unitarity, and various nonperturbative ideas. An appendix giving a short course on path integral methods is included. This is an essential text and reference for graduate students and researchers interested in modern superstring theory.
R 3,653.86
Introduction to Communication Theory and Systems
This book was written as a first treatment of statistical com munication theory and communication systems at a senior graduate level. The only formal prerequisite is a knowledge of ele mentary calculus; however, some familiarity with linear systems and transform theory will be helpful. Chapter 1 is introductory and contains no substantial techni cal material. Chapter 2 is an elementary introduction to probability theory at a nonrigorous and non abstract level. It is essential to the remainder of the book but may be skipped (or reviewed has tily) by any student who has taken a one-semester undergraduate course in probability. Chapter 3 is a brief treatment of random processes and spec tral analysis. It includes an introduction to shot noise (Sections 3.14-3.17) which is not subsequently used explicitly. Chapter 4 considers linear systems with random inputs. It includes a considerable amount of material on narrow-band sys tems and on the representation of random processes. Chapter 5 treats the matched filter and the linear least mean-squared-error filter at an elementary level but in some detail. Numerous examples are provided throughout the book. Many of these are of an elementary nature and are intended merely to illustrate textual material. A reasonable number of problems of varying difficulty are provided. Instructors who adopt the text for classroom use may obtain a Solutions Manual for most of the problems by writing to the author.
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Introduction to Arakelov Theory
Arakelov introduced a component at infinity in arithmetic considerations, thus giving rise to global theorems similar to those of the theory of surfaces, but in an arithmetic context over the ring of integers of a number field. The book gives an introduction to this theory, including the analogues of the Hodge Index Theorem, the Arakelov adjunction formula, and the Faltings Riemann-Roch theorem. The book is intended for second year graduate students and researchers in the field who want a systematic introduction to the subject. The residue theorem, which forms the basis for the adjunction formula, is proved by a direct method due to Kunz and Waldi. The Faltings Riemann-Roch theorem is proved without assumptions of semistability. An effort has been made to include all necessary details, and as complete references as possible, especially to needed facts of analysis for Green's functions and the Faltings metrics.
R 3,021.58
Introduction to Banach Space Theory
Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.
R 2,282.32
Concise Guide to Computation Theory
This textbook presents a thorough foundation to the theory of computation. Combining intuitive descriptions and illustrations with rigorous arguments and detailed proofs for key topics, the logically structured discussion guides the reader through the core concepts of automata and languages, computability, and complexity of computation. Topics and features: presents a detailed introduction to the theory of computation, complete with concise explanations of the mathematical prerequisites; provides end-of-chapter problems with solutions, in addition to chapter-opening summaries and numerous examples and definitions throughout the text; draws upon the author’s extensive teaching experience and broad research interests; discusses finite automata, context-free languages, and pushdown automata; examines the concept, universality and limitations of the Turing machine; investigates computational complexity based on Turing machines and Boolean circuits, as well as the notion of NP-completeness.
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Critical Introduction to Syntax
This book introduces, analyzes and critiques the main areas of debate within the field of syntax. This book introduces the main areas of debate within the field of syntax. Jim Miller analyzes the major themes in syntactic research, paying attention to overlooked non-generative theories and the adoption of the same concepts across different models of grammar. The book analyzes the difference between spoken and written syntax, standard and non-standard syntax, grammar and usage, and addresses concerns such as grammatical prescription. Examples are drawn from a range of everyday examples extracted from corpus data, to present an analysis of how syntax is used in the real world. Comprehensive, accessible and challenging, this book is essential reading for students taking introductory courses in syntax and syntactic theory, both at undergraduate and postgraduate level. "Continuum Critical Introductions to Linguistics" are comprehensive introductions to core areas in linguistics. The introductions are original and approach the subject from unique and different perspectives. Using contemporary examples and analogies, these books seek to explain complicated issues in an accessible way.The books prompt critical thinking about each core area, and are a radical departure from traditional, staid introductions to the subject. Written by key academics in each field who are not afraid to be controversial, each book will be essential reading for undergraduate students.
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Introduction to Quantum Groups
The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.
R 2,508.96
R 1,529.00
Introduction to Abstract Algebra
The second volume continues the course of study started in Volume 1, but may be used independently by those already possessing an elementary knowledge of the subject. A summary of basic group theory is followed by accounts of group homomorphisms, rings, fields and integral domains. The related concepts of an invariant subgroup and an ideal in a ring are brought in and the reader introduced to vector spaces and Boolean algebra. The theorems behind the abstract work and the reasons for their importance are discussed in greater detail than is usual at this level. The book is intended both for those who, educated in traditional mathematics, wish to know something about modern algebra and also for those already familiar with the elements of the subject who wish to study further. Fresh ideas and structures are introduced gradually and in a simpler manner, with concrete examples and much more informal discussion. There are many graded exercises, including some worked examples. This book is thus suitable both for the student working by himself without the aid of the teacher and for those taking formal courses in universities or colleges of education.
R 2,821.77
Ordinal Analysis with an Introduction to Proof Theory
This book provides readers with a guide to both ordinal analysis, and to proof theory. It mainly focuses on ordinal analysis, a research topic in proof theory that is concerned with the ordinal theoretic content of formal theories. However, the book also addresses ordinal analysis and basic materials in proof theory of first-order or omega logic, presenting some new results and new proofs of known ones.Primarily intended for graduate students and researchers in mathematics, especially in mathematical logic, the book also includes numerous exercises and answers for selected exercises, designed to help readers grasp and apply the main results and techniques discussed.
R 1,830.62
Introduction to Mathematical Relativity
This concise textbook introduces the reader to advanced mathematical aspects of general relativity, covering topics like Penrose diagrams, causality theory, singularity theorems, the Cauchy problem for the Einstein equations, the positive mass theorem, and the laws of black hole thermodynamics. It emerged from lecture notes originally conceived for a one-semester course in Mathematical Relativity which has been taught at the Instituto Superior Técnico (University of Lisbon, Portugal) since 2010 to Masters and Doctorate students in Mathematics and Physics. Mostly self-contained, and mathematically rigorous, this book can be appealing to graduate students in Mathematics or Physics seeking specialization in general relativity, geometry or partial differential equations. Prerequisites include proficiency in differential geometry and the basic principles of relativity. Readers who are familiar with special relativity and have taken a course either in Riemannian geometry (for students of Mathematics) or in general relativity (for those in Physics) can benefit from this book.
R 2,357.98
Number Theory: An Elementary Introduction Through Diophantine Problems
This textbook presents an elementary introduction to number theory and its different aspects: approximation of real numbers, irrationality and transcendence problems, continued fractions, diophantine equations, quadratic forms, arithmetical functions and algebraic number theory.These topics are covered in 12 chapters and more than 200 solved exercises.Clear, concise, and self-contained, this textbook may be used by undergraduate and graduate students, as well as highschool mathematics teachers. More generally, it will be suitable for all those who are interested in number theory, this fascinating branch of mathematics.
R 1,037.03
Introduction to Nonlinear Analysis: Theory
An Introduction to Nonlinear Analysis: Theory is an overview of some basic, important aspects of Nonlinear Analysis, with an emphasis on those not included in the classical treatment of the field. Today Nonlinear Analysis is a very prolific part of modern mathematical analysis, with fascinating theory and many different applications ranging from mathematical physics and engineering to social sciences and economics. Topics covered in this book include the necessary background material from topology, measure theory and functional analysis (Banach space theory). The text also deals with multivalued analysis and basic features of nonsmooth analysis, providing a solid background for the more applications-oriented material of the book An Introduction to Nonlinear Analysis: Applications by the same authors. The book is self-contained and accessible to the newcomer, complete with numerous examples, exercises and solutions. It is a valuable tool, not only for specialists in the field interested in technical details, but also for scientists entering Nonlinear Analysis in search of promising directions for research.
R 6,132.53
Abstract Algebra: Introduction To Groups, Rings And Fields With Applications
This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata.This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced — via congruence classes — to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless.In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.
R 2,256.59
Introduction to Singularities
This book is an introduction to singularities for graduate students and researchers.Algebraic geometry is said to have originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. First, mostly non-singular varieties were studied. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dimensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied. In the second edition, brief descriptions about recent remarkable developments of the researches are added as the last chapter.
R 1,817.39
