subject checklists - mathematics

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Mathematics Textbooks

CHECKLIST

2014

2

Basic CommutativeAlgebraBalwant Singh

This textbook, set for a one or two semester course in commutativealgebra, provides an introduction to commutative algebra at thepostgraduate and research levels. The main prerequisites arefamiliarity with groups, rings and fields. Proofs are self-contained.

The book will be useful to beginners and experienced researchersalike. The material is so arranged that the beginner can learn throughself-study or by attending a course. For the experienced researcher, thebook may serve to present new perspectives on some well-knownresults, or as a reference.

ISBN: 9789382993131 404pp ` 695.00WORLD SCIENTIFICNEW

Popular Problems andPuzzles in MathematicsAsok Kumar Mallik

Innovative thinking backed by logical reasoning is the key to thepuzzles in Popular Problems and Puzzles in Mathematics. Collectedover several years by the author, more than 150 elegant, intriguingnumerical challenges are presented here. The answers are easy toexplain, but one would devilishly find it hard without this book. One’sability to construct a mathematical proof will be rigorously tested inthese problems – even in the case of a mathematics teacher. For truemaths lovers, there is even a section on historically prominentproblems. Designed for high-school students and teachers with aninterest in mathematical problem solving, this stimulating collectionprovides a new twist to familiar topics that introduce unfamiliar topics.

ISBN: 9789382993865 170pp ` 225.00NEW

3

Partial DifferentialEquationsMethods, Applicationsand Theories

Harumi Hattori

This volume is an introductory level textbook for partial differentialequations (PDE’s) and suitable for a one-semester undergraduate levelor two-semester graduate level course in PDE’s or appliedmathematics. Chapters One to Five are organized according to theequations and the basic PDE’s are introduced in an easy to understandmanner. They include the first-order equations and the threefundamental second-order equations, i.e. the heat, wave and Laplaceequations. Through these equations we learn the types of problems,how we pose the problems, and the methods of solutions such as theseparation of variables and the methods of characteristics. Themodeling aspects are explained as well. The methods introduced inearlier chapters are developed further in Chapters Six to Twelve. Theyinclude the Fourier series, the Fourier and the Laplace transforms, andthe Green’s functions. The equations in higher dimensions are alsodiscussed in detail.

This volume is application-oriented and rich in examples. Goingthrough these examples, the reader is able to easily grasp the basics ofPDE’s.

ISBN: 9789382993797 394pp ` 495.00WORLD SCIENTIFIC

NEW

Advanced Topics InApplied MathematicsFor Engineering and thePhysical Sciences

Sudhakar Nair

This book is ideal for engineering, physical science, and appliedmathematics students and professionals who want to enhance theirmathematical knowledge. Advanced Topics in Applied Mathematicscovers four essential applied mathematics topics: Green’s functions,integral equations, Fourier transforms, and Laplace transforms. Alsoincluded is a useful discussion of topics such as the Wiener-Hopfmethod, finite Hilbert transforms, Cagniard-De Hoop method, and theproper orthogonal decomposition. This book reflects Sudhakar Nair’slong classroom experience from engineering and physics to illustratethe solution procedures. The text includes exercise sets at the end ofeach chapter and a solutions manual, which is available for instructors.

ISBN: 9781107685093 232pp ` 325.00

Solutions Manualavailable

4

High AccuracyComputingMethodsFluid Flows and WavePhenomena

Tapan K. Sengupta

This book presents methods necessary for high accuracy computing offluid flow and wave phenomena. These two topics have commonthreads and are presented in the book in single source format usingunified spectral theory of computing.

This book attempts to systematically develop scientific computing fromclassical approaches – describing equations of motion; classifying,discretizing and solving parabolic, elliptic, hyperbolic PDEs; curvilinearco-ordinates and structured meshing techniques; classical FVM andFEM and solving Navier-Stokes equation by FDM – to its present stateof art in high accuracy computing.

New topics discussed in this book are:

• Correct error propagation analysis • Practical compact schemes andglobal analysis tool • Aliasing error and its alleviation • Spuriousupstream propagating q-waves • Explanation of Gibbs phenomenon• New 1D and 2D filters for LES/DNS without SGS modelling• Anisotropic skewed wave propagation • Development and analysis ofdispersion relation preservation (DRP) schemes and • Focus oncapturing flow instabilities and wave propagation phenomena

ISBN: 9781107023635 590pp ` 1295.00

A ComprehensiveCourse in NumberTheoryAlan Baker

Developed from the author’s popular text, A Concise Introduction to theTheory of Numbers, this book provides a comprehensive initiation to allthe major branches of number theory. Beginning with the rudiments ofthe subject, the author proceeds to more advanced topics, includingelements of cryptography and primality testing; an account of numberfields in the classical vein including properties of their units, ideas andideal classes; aspects of analytic number theory including studies of theRiemann zeta-function, the prime-number theorem and primes inarithmetical progressions; a description of the Hardy-Littlewood andsieve methods from respectively additive and multiplicative numbertheory; and an exposition of the arithmetic of elliptic curves.

The book includes many worked examples, exercises and, as with theearlier volume, there is a guide to further reading at the end of eachchapter. Its wide coverage and versatility make this book suitable forcourses extending from the elementary to the graduate level.

ISBN: 9781107619173 266pp ` 395.00

5

Basic ControlVolume FiniteElement Methodsfor Fluids andSolidsVaughan R Voller

The Control Volume Finite Element Method (CVFEM) is a hybridnumerial method, combining the physics of Control Volume Methodswith the geometric flexibility of Finite Element Methods. The concept ofthis monograph is to introduce a common framework for the CVFEMsolution so that it can be applied to both fluid flow and solid mechanicsproblems. To emphasize the essential ingredients, discussion focusseson the application to problems in two-dimensional domains which arediscretized with linear-triangular meshes. This allows for astraightforward provision of the key information required to fullyconstruct working CVFEM solutions of basic fluid flow and solidmechanics problems.


Introduction toAlgebraicGeometry andCommutativeAlgebraDilip P Patil &Uwe Storch

This introductory textbook for a graduate course in pure mathematicsprovides a gateway into the two difficult fields of algebraic geometryand commutative algebra. Algebraic geometry, supportedfundamentally by commutative algebra, is a cornerstone of puremathematics.

Along the lines developed by Grothendieck, this book delves into therich interplay between algebraic geometry and commutative algebra.With concise yet clear definitions and synopses a selection is madefrom the wealth of material in the disciplines including the Riemann-Roch theorem for arbitrary projective curves.


6

Introduction toLinear AlgebraGilbert Strang

This leading textbook for first courses in linear algebra comes from thehugely experienced MIT lecturer and author Gilbert Strang. The book’stried and tested approach is direct, offering practical explanations andexamples, while showing the beauty and variety of the subject. Unlikemost other linear algebra textbooks, the approach is not a repetitivedrill. Instead it inspires an understanding of real mathematics. The bookmoves gradually and naturally from numbers to vectors to the fourfundamental subspaces. This new edition includes challenge problemsat the end of each section. Preview five complete sections atmath.mit.edu/linearalgebra. Readers can also view freely availableonline videos of Gilbert Strang’s 18.06 linear algebra course at MIT, viaOpenCourseWare (ocw.mit.edu), that have been watched by over amillion viewers. Also on the web (http://web.mit.edu/18.06/www/),readers will find years of MIT exam questions, MATLAB help files andproblem sets to practise what they have learned.

ISBN: 9788175968110 574pp ` 595.00

A Guide to MATLABFor Beginners andExperienced UsersSecond Edition

Brian R. Hunt, Ronald L. Lipsman &Jonathan M. Rosenberg

This is a short, focused introduction to MATLAB, a comprehensivesoftware system for mathematical and technical computing. It containsconcise explanations of essential MATLAB commands, as well aseasily understood instructions for using MATLAB’s programmingfeatures, graphical capabilities, simulation models, and rich desktopinterface. Written for MATLAB 7, it can also be used with earlier (andlater) versions of MATLAB. This book teaches how to graph functions,solve equations, manipulate images, and much more. It containsexplicit instructions for using MATLAB’s companion software, Simulink,which allows graphical models to be built for dynamical systems.MATLAB’s new “publish” feature is discussed, which allowsmathematical computations to be combined with text and graphics, toproduce polished, integrated, interactive documents. For the beginner itexplains everything needed to start using MATLAB, while experiencedusers making the switch to MATLAB 7 from an earlier version will alsofind much useful information here.

ISBN: 9781107641129 328pp ` 395.00

7

Statistics ExplainedAn Introductory Guide forLife Scientists

Steve McKillup

Statistics Explained is a reader-friendly introduction to experimentaldesign and statistics for undergraduate students in the life sciences,particularly those who do not have a strong mathematical background.Hypothesis testing and experimental design are discussed first.Statistical tests are then explained using pictorial examples and aminimum of formulae. This class-tested approach, along with a well-structured set of diagnostic tables will give students the confidence tochoose an appropriate test with which to analyse their own data sets.Presented in a lively and straight-forward manner, Statistics Explainedwill give readers the depth and background necessary to proceed tomore advanced texts and applications. It will therefore be essentialreading for all bioscience undergraduates, and will serve as a usefulrefresher course for more advanced students.

ISBN: 9781107673847 280pp ` 445.00

FoundationMathematics for thePhysical SciencesK. F. Riley & M. P. Hobson

This tutorial-style textbook develops the basic mathematical toolsneeded by first and second year undergraduates to solve problems inthe physical sciences. Students gain hands-on experience throughhundreds of worked examples, self-test questions and homeworkproblems. Each chapter includes a summary of the main results,definitions and formulae. Over 270 worked examples show how to putthe tools into practice. Around 170 self-test questions in the footnotesand 300 end-of-section exercises give students an instant check oftheir understanding. More than 450 end-of-chapter problems allowstudents to put what they have just learned into practice. Hints andoutline answers to the odd-numbered problems are given at the end ofeach chapter. Complete solutions to these problems can be found inthe accompanying Student Solutions Manual. Fully-worked solutions toall problems, password-protected for instructors, are available atwww.cambridge.org/foundation.

ISBN: 9781107647671 736pp ` 795.00

Companion Websiteavailable

8

EssentialMathematical Methodsfor the PhysicalSciencesK. F. Riley & M. P. Hobson

The mathematical methods that physical scientists need for solvingsubstantial problems in their fields of study are set out clearly andsimply in this tutorial-style textbook. Students will develop problem-solving skills through hundreds of worked examples, self-test questionsand homework problems. Each chapter concludes with a summary ofthe main procedures and results and all assumed prior knowledge issummarized in one of the appendices. Over 300 worked examplesshow how to use the techniques and around 100 self-test questions inthe footnotes act as checkpoints to build student confidence. Nearly400 end-of-chapter problems combine ideas from the chapter toreinforce the concepts. Hints and outline answers to the odd-numberedproblems are given at the end of each chapter, with fully-workedsolutions to these problems given in the accompanying StudentSolutions Manual. Fully-worked solutions to all problems, password-protected for instructors, are available atwww.cambridge.org/essential.

ISBN: 9781107643529 846pp ` 595.00


Student SolutionManual for EssentialMathematical Methodsfor the PhysicalSciencesK. F. Riley & M. P. Hobson

This Student Solution Manual provides complete solutions to all theodd-numbered problems in Essential Mathematical Methods for thePhysical Sciences. It takes students through each problem step-by-step, so they can clearly see how the solution is reached, andunderstand any mistakes in their own working. Students will learn byexample how to select an appropriate method, improving their problem-solving skills.

ISBN: 9781107675421 250pp ` 445.00

9

Numerical Methodsof StatisticsSecond Edition

John F. Monahan

This book explains how computer software is designed to perform thetasks required for sophisticated statistical analysis. For statisticians, itexamines the nitty-gritty computational problems behind statisticalmethods. For mathematicians and computer scientists, it looks at theapplication of mathematical tools to statistical problems. The first half ofthe book offers a basic background in numerical analysis thatemphasizes issues important to statisticians. The next several chapterscover a broad array of statistical tools, such as maximum likelihood andnonlinear regression. The author also treats the application ofnumerical tools; numerical integration and random number generationare explained in a unified manner reflecting complementary views ofMonte Carlo methods. Each chapter contains exercises that range fromsimple questions to research problems. Most of the examples areaccompanied by demonstration and source code available from theauthor's website. New in this second edition are demonstrations codedin R, as well as new sections on linear programming and the Nelder-Mead search algorithm.

ISBN: 9781107665934 464pp ` 595.00

Elementary DifferentialGeometryChristian Bär

The link between the physical world and its visualization is geometry.This easy-to-read, generously illustrated textbook presents anelementary introduction to differential geometry with emphasis ongeometric results. Avoiding formalism as much as possible, the authorharnesses basic mathematical skills in analysis and linear algebra tosolve interesting geometric problems, which prepare students for moreadvanced study in mathematics and other scientific fields such asphysics and computer science. The wide range of topics includes curvetheory, a detailed study of surfaces, curvature, variation of area andminimal surfaces, geodesics, spherical and hyperbolic geometry, thedivergence theorem, triangulations, and the Gauss–Bonnet theorem.The section on cartography demonstrates the concrete importance ofelementary differential geometry in applications. Clearly developedarguments and proofs, colour illustrations, and over 100 exercises andsolutions make this book ideal for courses and self-study. The onlyprerequisites are one year of undergraduate calculus and linearalgebra.

ISBN: 9781107603967 330pp ` 495.00

10

Complex VariablesPrinciples and ProblemSessions

A. K. Kapoor

This textbook introduces the theory of complex variables atundergraduate level. A good collection of problems is provided in thesecond part of the book. The book is written in a user-friendly style thatpresents important fundamentals a beginner needs to master thetechnical details of the subject. The organization of problems intofocused sets is an important feature of the book and the teachers mayadopt this book for a course on complex variables and for miningproblems.

ISBN: 9788175968981 522pp ` 495.00 WORLD SCIENTIFIC

Risk ManagementValue at Risk and Beyond

M. A. H. Dempster

The use of derivative products in risk management has spread fromcommodities, stocks and fixed income items, to such virtualcommodities as energy, weather and bandwidth. All this can give rise toso-called volatility and there has been a consequent development informal risk management techniques to cover all types of risk: market,credit, liquidity, etc. One of these techniques, Value at Risk, wasdeveloped specifically to help manage market risk over short periods.Its success led, somewhat controversially, to its take up and extensionto credit risk over longer time-scales. This extension, ultimately notsuccessful, led to the collapse of a number of institutions. The presentbook, which was originally published in 2002, by some of the leadingfigures in risk management, examines the complex issues that concernthe stability of the global financial system by presenting a mix of theoryand practice.

ISBN: 9780521263740 290pp ` 350.00

11

An Outline ofErgodic TheorySteven Kalikow &Randall McCutcheon

This informal introduction provides a fresh perspective on isomorphismtheory, which is the branch of ergodic theory that explores theconditions under which two measure preserving systems areessentially equivalent. It contains a primer in basic measure theory,proofs of fundamental ergodic theorems, and material on entropy,martingales, Bernoulli processes, and various varieties of mixing.Original proofs of classic theorems - including the Shannon–McMillan–Breiman theorem, the Krieger finite generator theorem, and theOrnstein isomorphism theorem - are presented by degrees, togetherwith helpful hints that encourage the reader to develop the proofs ontheir own. Hundreds of exercises and open problems are also included,making this an ideal text for graduate courses. Professionals needing aquick review, or seeking a different perspective on the subject, will alsovalue this book.

ISBN: 9780521170314 182pp ` 595.00

The Art ofMathematicsCoffee Time in Memphis

Bela Bollobás

Can a Christian escape from a lion? How quickly can a rumour spread?Can you fool an airline into accepting oversize baggage? Recreationalmathematics is full of frivolous questions where the mathematician’s artcan be brought to bear. But play often has a purpose. In mathematics, itcan sharpen skills, provide amusement, or simply surprise, and booksof problems have been the stock-in-trade of mathematicians forcenturies. This collection is designed to be sipped from, rather thanconsumed in one sitting. The questions range in difficulty: the mostchallenging offer a glimpse of deep results that engage mathematicianstoday; even the easiest prompt readers to think about mathematics. Allcome with solutions, many with hints, and most with illustrations.Whether you are an expert, or a beginner or an amateurmathematician, this book will delight for a lifetime.

ISBN: 9781107601734 376pp ` 250.00

12

Brownian MotionPeter Mörters& Yuval Peres

This eagerly awaited textbook covers everything the graduate studentin probability wants to know about Brownian motion, as well as thelatest research in the area. Starting with the construction of Brownianmotion, the book then proceeds to sample path properties likecontinuity and nowhere differentiability. Notions of fractal dimension areintroduced early and are used throughout the book to describe fineproperties of Brownian paths. The relation of Brownian motion andrandom walk is explored from several viewpoints, including adevelopment of the theory of Brownian local times from random walkembeddings. Stochastic integration is introduced as a tool and anaccessible treatment of the potential theory of Brownian motion clearsthe path for an extensive treatment of intersections of Brownian paths.An investigation of exceptional points on the Brownian path and anappendix on SLE processes, by Oded Schramm and Wendelin Werner,lead directly to recent research themes.

ISBN: 9780521168847 416pp ` 995.00

Central SimpleAlgebras and GaloisCohomologyPhilippe Gille& Tamás Szamuely

This book is the first comprehensive, modern introduction to the theoryof central simple algebras over arbitrary fields. Starting from the basics,it reaches such advanced results as the Merkurjev-Suslin theorem. Thistheorem is both the culmination of work initiated by Brauer, Noether,Hasse and Albert and the starting point of current research in motiviccohomology theory by Voevodsky, Suslin, Rost and others. Assumingonly a solid background in algebra, but no homological algebra, thebook covers the basic theory of central simple algebras, methods ofGalois descent and Galois cohomology, Severi-Brauer varieties,residue maps and, finally, Milnor K-theory and K-cohomology. The lastchapter rounds off the theory by presenting the results in positivecharacteristic, including the theorem of Bloch-Gabber-Kato. The book issuitable as a textbook for graduate students and as a reference forresearchers working in algebra, algebraic geometry or K-theory.

ISBN: 9780521168915 356pp ` 695.00

13

Curved SpacesFrom Classical Geometriesto Elementary DifferentialGeometry

P. M. H. Wilson

This self-contained textbook presents an exposition of the well-knownclassical two-dimensional geometries, such as Euclidean, spherical,hyperbolic, and the locally Euclidean torus, and introduces the basicconcepts of Euler numbers for topological triangulations, andRiemannian metrics. The careful discussion of these classicalexamples provides students with an introduction to the more generaltheory of curved spaces developed later in the book, as represented byembedded surfaces in Euclidean 3-space, and their generalization toabstract surfaces equipped with Riemannian metrics. Themes runningthroughout include those of geodesic curves, polygonal approximationsto triangulations, Gaussian curvature, and the link to topology providedby the Gauss-Bonnet theorem. Numerous diagrams help bring the keypoints to life and helpful examples and exercises are included to aidunderstanding. Throughout the emphasis is placed on explicit proofs,making this text ideal for any student with a basic background inanalysis and algebra.

ISBN: 9780521170062 196pp ` 695.00

An Introduction toInvariants and ModuliShigeru Mukai & W. M. Oxbury

Incorporated in this volume are the first two books in Mukai’s series onmoduli theory. The notion of a moduli space is central to geometry.However, its influence is not confined there; for example the theory ofmoduli spaces is a crucial ingredient in the proof of Fermat’s lasttheorem. Researchers and graduate students working in areas rangingfrom Donaldson or Seiberg-Witten invariants to more concreteproblems such as vector bundles on curves will find this to be avaluable resource. Amongst other things this volume includes animproved presentation of the classical foundations of invarant theorythat, in addition to geometers, would be useful to those studyingrepresentation theory. This translation gives an accurate account ofMukai’s influential Japanese texts.

ISBN: 9780521168885 524pp ` 895.00

14

An Introduction toSieve Methods andTheir ApplicationsAlina Carmen Cojocaru& M. Ram Murty

Sieve theory has a rich and romantic history. The ancient question ofwhether there exist infinitely many twin primes (primes p such that p+2is also prime), and Goldbach’s conjecture that every even number canbe written as the sum of two prime numbers, have been two of theproblems that have inspired the development of the theory. This bookprovides a motivated introduction to sieve theory. Rather than focus ontechnical details which can obscure the beauty of the theory, theauthors focus on examples and applications, developing the theory inparallel. The text can be used for a senior level undergraduate courseor an introductory graduate course in analytic number theory, and non-experts can gain a quick introduction to the techniques of the subject.

ISBN: 9780521170345 236pp ` 595.00

Representations andCohomologyVolume IBasic Representation Theoryof Finite Groups andAssociative Algebras

D. J. Benson

This is the first of two volumes which will provide an introduction tomodern developments in the representation theory of finite groups andassociative algebras. The subject is viewed from the perspective ofhomological algebra and the theory of representations of finitedimensional algebras; the author emphasises modular representationsand the homological algebra associated with their categories. Thisvolume is self-contained and independent of its successor, beingprimarily concerned with the exposition of the necessary backgroundmaterial. The heart of the book is a lengthy introduction to the(Auslander–Reiten) representation theory of finite dimensionalalgebras, in which the techniques of quivers with relations and almostsplit sequences are discussed in detail. Much of the material presentedhere has never appeared in book form. Consequently students andresearch workers studying group theory and indeed algebra in generalwill be grateful to Dr Benson for supplying an exposition of a good dealof the essential results of modern representation theory.

ISBN: 9780521169882 260pp ` 595.00

15

The CambridgeElementaryMathematical TablesSecond Edition

J.C.P. Miller & F.C. Powell

Contents: 1. Notes on the use of the tables 2. Logarithms3. Antilogarithms 4. Logarithms of sines 5. Logarithms of cosines6. Minutes to decimals of a degree 7. Logarithms of tangents 8. Sines9. Cosines 10. Proportional parts for sixths 11. Tangents 12. Secants13. Squares 14. Square roots 15. Reciprocals 16. Powers andfactorials 17. Degrees, minutes and radians 18. Natural logarithms19. Exponential, hyperbolic and circular functions 20. Binomialcoefficients 21. Binomial distribution 22. Normal distribution23. t-distributions 24. Chi-square distributions 25. Correlationcoefficients 26. Proportional parts for tenths 27. International system ofunits (SI) 28. Physical constants

ISBN: 9780521747370 48pp ` 40.00

Real AnalysisN.L. Carothers

This text for a course in Real Analysis addresses advancedundergraduates and beginning graduate students in mathematics andrelated fields. Presupposing only a modest background in real analysisor advanced calculus, the book offers something of value to specialistsand non-specialists alike. It considers three major topics: Metric andnormed linear spaces, function spaces, and Lebesgue measure andintegration on the line.

Written in an informal, down-to-earth style, the book motivates thereader with an intuitive overview of new ideas, while still supplying fulldetails and complete proofs. The author includes historical commentarywith references to original works and alternate presentations,recommends expository and survey articles for non-specialists andtechnical articles for specialists, and provides a great many exercisesand suggestions for further study.

The author has written this text with the consideration of theheterogeneous audiences found at the masters level: studentsinterested in pure and applied mathematics, statistics, education,engineering and economics.

ISBN: 9780521696241 416pp ` 545.00

16

A First Course inProbability andStatisticsB. L. S. Prakasa Rao

Explanation of the basic concepts and methods of statistics requires areasonably good mathematical background, at least at a first-year-levelknowledge of calculus. Most of the statistical software explain how toconduct data analysis, but do not explain when to apply and when notto apply it. Keeping this in view, we try to explain the basic concepts ofprobability and statistics for students with an understanding of a firstcourse in calculus at the undergraduate level.

Designed as a textbook for undergraduate and first-year graduatestudents in statistics, bio-statistics, social sciences and businessadministration programs as well as undergraduates in engineeringsciences and computer science programs, it provides a clear expositionof the theory of probability along with applications in statistics. Thebook contains a large number of solved examples and chapter-endexercises designed to reinforce the probability theory and emphasizestatistical applications.


RemarkableMathematiciansFrom Euler tovon Neumann

Ioan James

Ioan James introduces and profiles sixty mathematicians from an erawhich saw mathematics freed from its classical origins to develop intoits modern form. The characters, all born between 1700 and 1910,come from a wide range of countries, and all made an importantcontribution to mathematics, through their ideas, their teaching, theirinfluence, and so on. The book is organised chronologically into tenchapters each of which contain life stories of six mathematicians. Theplayers James has chosen to portray are sufficiently representative thattheir stories, when read in sequence, convey in human termssomething of the way in which mathematics developed.

ISBN: 9780521670487 448pp ` 395.00

17

An Introduction toFluid DynamicsG.K. Batchelor

First published in 1967, Professor Batchelor’s classic text on fluiddynamics is still one of the foremost texts in the subject. The carefulpresentation of the underlying theories of fluids is still timely andapplicable, even in these days of almost limitless computer power. Thisre-issue should ensure that a new generation of graduate students seethe elegance of Professor Batchelor’s presentation.

ISBN: 9788185618241 633pp ` 445.00

Introduction toLattices and OrderSecond Edition

B. A Davey & H. A. Priestly

This new edition of Introduction to Lattices and Order presents a radicalreorganization and updating, though its primary aim is unchanged. Theexplosive development of theoretical computer science in recent yearshas, in particular, influenced the book's evolution: a fresh treatment offixpoints testifies to this and Galois connections now featureprominently. An early presentation of concept analysis gives both aconcrete foundation for the subsequent theory of complete lattices anda glimpse of a methodology for data analysis that is of commercialvalue in social science. Classroom experience has led to numerouspedagogical improvements and many new exercises have been added.As before, exposure to elementary abstract algebra and the notation ofset theory are the only prerequisites, making the book suitable foradvanced undergraduates and beginning graduate students. It will alsobe a valuable resource for anyone who meets ordered structures.

ISBN: 9780521134514 310pp ` 395.00

18

Classical MechanicsR. Douglas Gregory

Gregory's Classical Mechanics is a major new textbook forundergraduates in mathematics and physics. It is a thorough, self-contained and highly readable account of a subject many students finddifficult. The author's clear and systematic style promotes a goodunderstanding of the subject: each concept is motivated and illustratedby worked examples, while problem sets provide plenty of practice forunderstanding and technique. Computer assisted problems, somesuitable for projects, are also included. The book is structured to makelearning the subject easy; there is a natural progression from coretopics to more advanced ones and hard topics are treated withparticular care. A theme of the book is the importance of conservationprinciples. These appear first in vectorial mechanics where they areproved and applied to problem solving. They reappear in analyticalmechanics, where they are shown to be related to symmetries of theLagrangian, culminating in Noether's theorem.

ISBN: 9780521733120 608pp ` 545.00

ComputationalDiscrete MathematicsCombinatorics and GraphTheory with Mathematica

Sriram Pemmaraju &Steven Skiena

Combinatorica, an extension to the popular computer algebra systemMathematica®, is the most comprehensive software available forteaching and research applications of discrete mathematics, particularlycombinatorics and graph theory. This book is the definitive reference/user’s guide to Combinatorica, with examples of all 450 Combinatoricafunctions in action, along with the associated mathematical andalgorithmic theory. The authors cover classical and advanced topics onthe most important combinatorial objects: permutations, subsets,partitions, and Young tableaux, as well as all important areas of graphtheory: graph construction operations, invariants, embeddings, andalgorithmic graph theory.

In addition to being a research tool, Combinatorica makes discretemathematics accessible in new and exciting ways, by encouragingcomputational experimentation and visualization. The book is suitablefor self-study and as a primary or supplementary textbook for discretemathematics courses.

ISBN: 9780521733113 494pp ` 545.00

19

All the MathematicsYou MissedThomas A. Garrity

This book will help students to see the broad outline of mathematicsand to fill in the gaps in their knowledge. The author explains the basicpoints and a few key results of all the most important undergraduatetopics in mathematics, emphasizing the intuitions behind the subject.The topics include linear algebra, vector calculus, differential geometry,real analysis, point-set topology, probability, complex analysis, abstractalgebra, and more. An annotated bibliography then offers a guide tofurther reading and to more rigorous foundations. This book will be anessential resource for advanced undergraduate and beginninggraduate students in mathematics, the physical sciences, engineering,computer science, statistics, and economics who need to quickly learnsome serious mathematics.

ISBN: 9780521670340 372pp ` 445.00

Basic AbstractAlgebraSecond Edition

P.B. Bhattacharya,S.K. Jain & S.R. Nagpaul

This book provides a complete abstract algebra course, enablinginstructors to select the topics for use in individual classes. Completeproofs are given throughout for all theorems. This revised editionincludes an introduction to lattices, a new chapter on tensor productsand a discussion of the new (1993) approach to the Lasker-Noethertheorem.

ISBN: 9780521545488 507pp ` 345.00

20

Complex VariablesIntroduction and Applications

Mark J. Ablowitz &Athanassios S. Fokas

Complex variables provide powerful methods for attacking manydifficult problems, and it is the aim of this book to provide a thoroughgrounding in these methods and their application. This new edition hasbeen improved throughout and is ideal for use in undergraduate andintroductory graduate courses in complex variables.

ISBN: 9780521682152 647pp ` 550.00

Differential EquationsA.C. King, J. Billingham& S.R. Otto

Finding and interpreting the solutions of differential equations is acentral and essential part of applied mathematics. This book aims toenable the reader to develop the required skills needed for a thoroughunderstanding of the subject. The authors focus on the business ofconstructing solutions analytically, and interpreting their meaning, usingrigorous analysis where needed. MATLAB is used extensively toillustrate the material. There are many worked examples based oninteresting and unusual real world problems. A large selection ofexercises is provided, including several lengthier projects, some ofwhich involve the use of MATLAB. The coverage is broad, ranging frombasic second-order ODEs and PDEs, through to techniques fornonlinear differential equations, chaos, asymptotics and control theory.

ISBN: 9780521670456 552pp ` 545.00

21

A Course inCombinatoricsJ.H. Van Lint & R.M. Wilson

This is the second edition of a popular book on combinatorics, asubject dealing with ways of arranging and distributing objects, andwhich involves ideas from geometry, algebra and analysis. Thebreadth of the theory is matched by that of its applications, whichinclude topics as diverse as codes, circuit design and algorithmcomplexity. It has thus become essential for workers in many scientificfields to have some familiarity with the subject. The authors have triedto be as comprehensive as possible, dealing in a unified manner with,for example, graph theory, extremal problems, designs, colorings andcodes. The depth and breadth of the coverage make the book aunique guide to the whole of the subject.

ISBN: 9780521718172 616pp ` 545.00

MathsA Self-Study GuideSecond Edition(CLPE)

Jenny Olive

The book contains more than 800 exercises, with detailed solutionsgiven in the back to allow students who get stuck to see exactly wherethey have gone wrong. Topics covered include trigonometry andhyperbolic functions, sequences and series (with detailed coverage ofbinomial series), differentiation and integration, complex numbers andvectors.

ISBN: 9780521612951 578pp ` 595.00

22

Mathematics forEconomics andFinanceMartin Anthony& Norman Biggs

An introduction to mathematical modelling in economics and finance forstudents of both economics and mathematics. Throughout, the stress isfirmly on how mathematics relates to economics, illustrated withcopious examples and exercises that will foster depth of understanding.

ISBN: 9780521683197 394pp ` 395.00

Mathematical Modelsin BiologyAn Introduction

Elizabeth S. Allman& John A. Rhodes

This introductory textbook on mathematical biology focuses on discretemodels across a variety of biological subdisciplines. Biological topicstreated include linear and nonlinear models of populations, Markovmodels of molecular evolution, phylogenetic tree construction, genetics,and infectious disease models. The coverage of models of molecularevolution and phylogenetic tree construction from DNA sequence datais unique among books at this level.

Computer investigations with MATLAB are incorporated throughout, inboth exercises and more extensive projects, to give readers hands-onexperience with the mathematical models developed. MATLABprograms accompany the text.

ISBN: 9780521615556 370pp ` 445.00

23

RandomizedAlgorithmsRajeev Motwani &Prabhakar Raghavan

For many applications a randomized algorithm is the simplest algorithmavailable, or the fastest, or both. This text by two well-known experts inthe field presents the basic concepts in the design and analysis ofrandomized algorithms at a level accessible to beginning graduatestudents.

The first part of the book presents basic tools from probability theoryand probabilistic analysis that are recurrent in algorithmic applications.Algorithmic examples are given to illustrate the use of each tool in aconcrete setting. In the second part of the book each of the sevenchapters focuses on one important area of application of randomizedalgorithms: data structures, geometric algorithms, graph algorithms,giving a comprehensive and representative selection of the algorithmsin these areas.

ISBN: 9780521613903 492pp ` 595.00

First Course inMetric SpacesB. K. Tyagi

First Course in Metric Spaces provides a foundation for modern puremathematics. The book is completely rigorous in its approach andcovers all the standard topics. It provides ample solved examples andtheorems to assist the students in self-study. The book contains manyexercises to test understanding of the concepts learnt. The book isexpected to meet the requirement of the undergraduate and graduatestudents, teachers and researchers in terms of sufficiently advancedmaterial covered in the book.

Key Features• Contents explained in simple and lucid style• Detailed derivations of theorems with mathematical rigour• Course book for B.A/B.Sc (Hons) Mathematics

ISBN: 9788175967281 364pp ` 350.00

24

GeometrySecond Edition

David A. Brannan,Matthew F. Esplen& Jeremy J. Gray

This richly illustrated and clearly written undergraduate textbookcaptures the excitement and beauty of geometry. The approach is thatof Klein in his Erlangen programme: a geometry is a space togetherwith a set of transformations of the space. The authors explore variousgeometries: affine, projective, inversive, hyperbolic and elliptic. In eachcase they carefully explain the key results and discuss the relationshipsbetween the geometries. New features in this second edition includeconcise end-of-chapter summaries to aid student revision, a list offurther reading and a list of special symbols. The authors have alsorevised many of the end-of-chapter exercises to make them morechallenging and to include some interesting new results. Full solutionsto the 200 problems are included in the text, while complete solutions toall of the end-of-chapter exercises are available in a new Instructors'Manual, which can be downloaded fromwww.cambridge.org/ 9781107647831.

ISBN: 9781107627888 540pp ` 495.00

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26

A

A Comprehensive Course in Number Theory ..... 4

A Course in Combinatorics ............................... 21

A First Course in Probability and Statistics ....... 16

A Guide to MATLAB ............................................ 6

Ablowitz, Mark J. ............................................... 20

Advanced Topics In Applied Mathematics ........... 3

All the Mathematics You Missed ....................... 19

Allman, Elizabeth S. .......................................... 22

An Introduction to Fluid Dynamics .................... 17

An Introduction to Invariants and Moduli ........... 13

An Introduction to Sieve Methods and TheirApplications ....................................................... 14

An Outline of Ergodic Theory ............................ 11

Anthony, Martin ................................................. 22

B

Baker, Alan .......................................................... 4

Bär, Christian ...................................................... 9

Basic Abstract Algebra ...................................... 19

Basic Commutative Algebra ................................ 2

Basic Control Volume FiniteElement Methods for Fluids and Solids .............. 5

Batchelor, G.K. .................................................. 17

Benson, D. J. .................................................... 14

Bhattacharya, P.B. ............................................ 19

Biggs, Norman .................................................. 22

Billingham, J ...................................................... 20

Bollobás, Bela ................................................... 11

Brannan, David A .............................................. 24

Brownian Motion ............................................... 12

C

Carothers, N.L. .................................................. 15

Central Simple Algebras andGalois Cohomology ........................................... 12

Classical Mechanics ......................................... 18

Cojocaru, Alina Carmen .................................... 14

Complex Variables ...................................... 10, 20

Computational Discrete Mathematics ............... 18

Curved Spaces ................................................. 13

D

Davey, B. A ........................................................ 17

Dempster, M. A. H. ............................................ 10

Differential Equations ........................................ 20

E

Elementary Differential Geometry ....................... 9

Esplen, Matthew F. ............................................ 24

Essential Mathematical Methods forthe Physical Sciences ......................................... 8

F

First Course in Metric Spaces ........................... 23

Fokas, Athanassios S. ...................................... 20

Foundation Mathematics for thePhysical Sciences ............................................... 7

G

Garrity, Thomas A. ............................................ 19

Geometry .......................................................... 24

Gille, Philippe .................................................... 12

Gray, Jeremy J. ................................................. 24

Gregory, R. Douglas ......................................... 18

H

Hattori, Harumi .................................................... 3

High Accuracy Computing Methods .................... 4

Hobson, M. P. .................................................. 7, 8

Hunt, Brian R. ..................................................... 6

INDEX

27

I

Introduction to Algebraic Geometry andCommutative Algebra .......................................... 5

Introduction to Lattices and Order ..................... 17

Introduction to Linear Algebra ............................. 6

J

Jain, S.K. ........................................................... 19

James, Ioan ...................................................... 16

K

Kalikow, Steven ................................................. 11

Kapoor, A. K. ..................................................... 10

King, A.C. .......................................................... 20

L

Lipsman, Ronald L. ............................................. 6

M

Mallik, Asok Kumar ............................................. 2

Mathematical Models in Biology ....................... 22

Mathematics for Economics and Finance ......... 22

Maths ................................................................ 21

McCutcheon, Randall ........................................ 11

McKillup, Steve ................................................... 7

Metric Spaces ................................................... 23

Miller, J.C.P. ...................................................... 15

Monahan, John F. ............................................... 9

Mörters, Peter ................................................... 12

Motwani, Rajeev ............................................... 23

Mukai, Shigeru .................................................. 13

Murty, M. Ram ................................................... 14

N

Nagpaul, S.R. .................................................... 19

Nair, Sudhakar .................................................... 3

Numerical Methods of Statistics .......................... 9

O

Olive, Jenny ...................................................... 21

Otto, S.R. .......................................................... 20

Oxbury, W. M. ................................................... 13

P

Partial Differential Equations ............................... 3

Patil, Dilip P ......................................................... 5

Pemmaraju, Sriram ........................................... 18

Peres, Yuval ...................................................... 12

Popular Problems and Puzzlesin Mathematics .................................................... 2

Powell, F.C. ....................................................... 15

Priestly, H. A. ..................................................... 17

R

Raghavan, Prabhakar ....................................... 23

Randomized Algorithms .................................... 23

Rao, B. L. S. Prakasa ....................................... 16

Real Analysis .................................................... 15

Remarkable Mathematicians ............................ 16

Representations and Cohomology .................... 14

Rhodes, John A. ................................................ 22

Riley, K. F. ....................................................... 7, 8

Risk Management ............................................. 10

Rosenberg, Jonathan M. ..................................... 6

S

Sengupta, Tapan K. ............................................ 4

Singh, Balwant ................................................... 2

Skiena, Steven .................................................. 18

Statistics Explained ............................................. 7

Storch, Uwe ........................................................ 5

Strang, Gilbert ..................................................... 6

Student Solution Manual for EssentialMathematical Methods for thePhysical Sciences ............................................... 8

Szamuely, Tamás .............................................. 12

28

India Private Limitedwww.cambridgeindia.org

Follow us on: www.facebook.com/cambridgeindia www.twitter.com/cambridgeindia

T

The Art of Mathematics ..................................... 11

The Cambridge ElementaryMathematical Tables ......................................... 15

Tyagi, B. K. ........................................................ 23

V

Van Lint, J.H. ..................................................... 21

Voller, Vaughan R ............................................... 5

W

Wilson, P. M. H. ................................................. 13

Wilson, R.M. ...................................................... 21

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