mathematics - october 2010

http://www.crcpress.com/product/isbn/9781439800409










Contents

Algebra ..................................................................3

Discrete Mathematics and Combinatorics ............5

Differential Equations and Nonlinearity ................9

General and Introductory Mathematics ..............11

Geometry and Topology......................................14

Mathematical Modeling ......................................15

Mathematics for Finance......................................16

Numerical Analysis and Scientific Computing ....20

Real, Complex, and Functional Analysis ..............22

Number Theory ..................................................24

Mathematics for Engineering ..............................25

Mathematics for Biology and Medicine ..............27

Operations Research ............................................29

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Algebra

For more information and complete contents, visit www.crcpress.com

New!Textbook

Advanced LinearAlgebraBruce CoopersteinUniversity of California, Santa Cruz, USA

Starting with familiar con-cepts and slowly building todeeper results, this text focuses on vector spacesand the maps between them that preserve theirstructure (linear transformations). It introducesvector spaces and linear transformations, beforediscussing the algebra of polynomials with coef-ficients in a field. The author then develops thewhole structure theory of a linear operator on afinite dimensional vector space from a collectionof some simple results. He also explores theentire range of topics associated with innerproduct spaces and describes the trace anddeterminant of linear operators and squarematrices. The final two chapters focus on bilin-ear forms and tensor products.Features • Discusses the structure theory of an opera-tor, various topics on inner product spaces,and the trace and determinant functions ofa linear operator

• Covers bilinear forms with a full treatmentof symplectic spaces and orthogonal spaces

• Explains the construction of tensor, symmetric, and exterior algebras

• Takes a gentle approach that graduallybuilds from simple concepts to complexideas and results

• Begins each section with an outline of previously introduced concepts and resultsnecessary for mastering the new material

• Includes a wide variety of exercises andproblems, with selected solutions in theappendices

Solutions manual available for qualifying instructors

Catalog no. K11457, June 2010, 364 pp.ISBN: 978-1-4398-2966-0, $79.95 / £49.99

New!Textbook

Finite-DimensionalLinear AlgebraMark S. GockenbachMichigan Technological University,Houghton, USA

Drawing on material fromthe author’s own course, this book gives readersa strong theoretical understanding of linearalgebra. It offers many illustrations of how linearalgebra is used throughout mathematics in suchdiverse areas as combinatorics, differential equa-tions, optimization, and approximation. Theauthor takes students through an axiomaticdevelopment of vector spaces, linear operators,eigenvalues, norms, and inner products. In addi-tion to discussing the special properties of sym-metric matrices, he covers the Jordan canonicalform, an important theoretical tool, and the sin-gular value decomposition, a powerful tool forcomputation. The final chapters present intro-ductions to numerical linear algebra and analy-sis in vector spaces.Features • Provides a thorough foundation for thestudy of advanced mathematics

• Contains a range of exercises in each section, including some that can be solvedusing MATLAB® or other software

• Incorporates mini-projects that encouragereaders to develop topics not covered inthe text

• Explores various applications of linear alge-bra, including polynomial interpolation,graph and coding theory, linear and integerprogramming, linear ordinary differentialequations, Lagrange multipliers, and more

• Presents important concepts and methodsfrom numerical linear algebra


Catalog no. K10803, May 2010, 672 pp.ISBN: 978-1-4398-1563-2, $99.95 / £48.99



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Algebra

Theory andApplications of Higher-DimensionalHadamardMatricesSecond EditionYi Xian Yang, Xin Xin Niu,and Cheng Qing XuBeijing University of Posts and Telecommunication, People’s Republic of China

Drawing on the authors’ use of the Hadamard-related theory in several successful engineeringprojects, this book presents the applications anddimensions of Hadamard matrices. It covers classi-cal two-dimensional Walsh and Hadamard matri-ces as well as new Hadamard designs based ondyadic addition sets. In a new section of the book,the authors explore the applications of higher-dimensional Hadamard matrices to the areas oftelecommunications and information security.

Catalog no. K10942, March 2010, 437 pp.ISBN: 978-1-4398-1807-7, $99.95 / £63.99

Textbook

AbstractAlgebraAn InteractiveApproachWilliam PaulsenArkansas State University,Jonesboro, USA

By integrating the use ofGAP and Mathematica®, this work presents ahands-on approach to learning about groups,rings, and fields. The author discusses topics notcovered in similar texts, such as semi-directproducts and skew fields, and includes manydiagrams produced by Mathematica to helpreaders visualize difficult concepts. The accom-panying CD-ROM contains GAP packages andMathematica notebooks.Solutions manual available for qualifying instructors

Catalog no. C4521, January 2010, 560 pp.ISBN: 978-1-4200-9452-7, $99.95 / £46.99

Textbook

Applied AlgebraCodes, Ciphers andDiscrete Algorithms,Second EditionDarel W. HardyColorado State University, Fort Collins, USA

Fred RichmanFlorida Atlantic University, Boca Raton, USA

Carol L. WalkerNew Mexico State University, Las Cruces, USA

Using mathematical tools from number theoryand finite fields, this text presents practicalmethods for solving problems in data securityand data integrity. This edition doubles thenumber of exercises and includes a new appendix that reviews prerequisite topics inalgebra and number theory. The accompanyingCD-ROM contains an interactive version of thebook that is powered by Scientific Notebook®. Solutions manual available for qualifying instructors

Catalog no. C7142, 2009, 424 pp.ISBN: 978-1-4200-7142-9, $99.95 / £44.99

Textbook

A ModernIntroduction toLinear AlgebraHenry RicardoMedgar Evers College, Brooklyn,New York, USA

“This work is a sound pres-entation of linear algebra.… Each topic is carefully and thoroughly covered via the pedagogy … The volumeincludes more than 1,200 exercises, some to becompleted manually and others intended to besolved using a computer algebra system. … The generality of approach makes this workappropriate for students in virtually any disci-pline. Summing Up: Recommended.”

—CHOICE, June 2010Solutions manual available for qualifying instructors

Catalog no. K10040, January 2010, 670 pp.ISBN: 978-1-4398-0040-9, $99.95 / £49.99





5

Discrete Mathematics and Combinatorics


New!Textbook

Graphs &DigraphsFifth EditionGary ChartrandWestern Michigan University,Kalamazoo, USA

Linda LesniakDrew University, Madison, New Jersey, USA

Ping ZhangWestern Michigan University, Kalamazoo, USA

Praise for the Fourth Edition

“… emphasizes clear exposition, well-writtenproofs, and many original and innovative exer-cises of varying difficulty and challenge … For25 years, Graphs & Digraphs, in its variouseditions, has served as an exemplary introduc-tion to the emerging mathematical disciplinesof graph theories for advanced undergraduateand graduate students. It has also servedestablished graph theorists, combinatorialists,and other discrete mathematicians, as well ascomputer scientists and chemists, as a usefulreference work. The fourth edition continuesthese fine traditions.”

—Zentralblatt MATH

New to the Fifth Edition• New or expanded coverage of graphminors, perfect graphs, chromatic polyno-mials, nowhere-zero flows, flows in networks, degree sequences, toughness, list colorings, and list edge colorings

• New examples, figures, and applications toillustrate concepts and theorems

• Expanded historical discussions of well-known mathematicians and problems

• More than 300 new exercises, along withhints and solutions to odd-numbered exercises at the back of the book

• Reorganization of sections into subsectionsto make the material easier to read

• Bolded definitions of terms, making themeasier to locate


Catalog no. K11263, October 2010, 600 pp.ISBN: 978-1-4398-2627-0, $89.95 / £49.99

New!Textbook

Introduction toCryptographywithMathematicalFoundations andComputerImplementationsAlexander StanoyevitchCalifornia State University–Dominguez Hills, Carson, USA

“…it is the little thoughtful touches that makethe book truly shine … judicious use of accessi-ble examples plus step-by-step worked out mathto illustrate concepts … the text layout [has]breathing room to offset the inevitable tersenessof mathematical cryptology. … [it] makes lifeeasier for the instructor. In addition, the book’scompanion site features short MATLAB m-filesand applets for quick demos. … a very welldone, thoughtful introduction to cryptography.”

—Daniel Bilar, University of New Orleans, Louisiana, USA

From the exciting history of its development inancient times to the present day, this self-con-tained introduction provides a focused tour ofthe central concepts of cryptography. It delin-eates cryptographic concepts in chronologicalorder, developing the mathematics as needed. Italso guides readers through the process of writ-ing their own programs. Features • Covers elliptic curve cryptography• Offers complete coverage of all the neededmaterial on number theory and abstractalgebra

• Presents algorithms in pseudo-code• Contains background material and exten-sive exercise solutions in the appendices

• Includes both standard and computer exer-cises as well as numerous worked examples

• Incorporates sample programs and plat-form-independent applets on the author’swebsite


Catalog no. K10916, August 2010, 669 pp.ISBN: 978-1-4398-1763-6, $89.95 / £44.99





New!Textbook

How to CountAn Introduction toCombinatorics,Second EditionR.B.J.T. Allenby and Alan Slomson University of Leeds, UK

“… the best one-volume book on combina-torics for undergraduates. It begins slowly andgently, but does not avoid subtleties or difficul-ties. It includes the right mixture of topics without bloat, and always with an eye to good mathematical taste and coherence.Enumerative combinatorics is developed ratherfully … before generating functions are intro-duced. … partitions are introduced in theabsence of generating functions, and thenlater generating functions are applied to them:again, a wise pedagogical move. The orderingof chapters is nicely set up for two different sin-gle-semester courses: one that uses more algebra, culminating in Polya’s counting theo-rem; the other concentrating on graph theory,ending with a variety of Ramsey theory topics.… I was very much impressed with the first edition when I encountered it in 1994. I like thesecond edition even more. …”

—Paul Zeitz, University of San Francisco, California, USA

Completely revised, this text shows how to solvenumerous classic and other interesting combi-natorial problems. This second edition includesseven new chapters that cover occupancy problems, Stirling and Catalan numbers, graphtheory, trees, Dirichlet’s pigeonhole principle,Ramsey theory, and rook polynomials. It alsocontains 450 paired exercises, along with a fullsolution to one of the exercises in each pair. Solutions manual available for qualifying instructors

Catalog no. C8260, August 2010, 444 pp.ISBN: 978-1-4200-8260-9, $79.95 / £34.99

New!Textbook

DiscreteStructures withContemporaryApplicationsAlexander StanoyevitchCalifornia StateUniversity–Dominguez Hills,Carson, USA

Reflecting many of the recent advances andtrends in this area, this classroom-tested textcovers the core topics in discrete structures asoutlined by the ACM and explores an assort-ment of novel applications, including simula-tions, genetic algorithms, network flows, probabilistic primality tests, public key cryptog-raphy, and coding theory. With clear definitionsand theorems and carefully explained proofs, itpresents an accessible yet rigorous treatment ofthe material.

Although the book highly encourages the use ofcomputing platforms, it can be used withoutcomputers. The author explains algorithms inordinary English and, when appropriate, in anatural and easy-to-understand pseudo codethat can be readily translated into any computerlanguage.

Features • Covers many recent applications of discretemathematics, including simulations, geneticalgorithms, and public key cryptography

• Presents algorithms in pseudo code• Offers sample programs via the author’swebsite

• Illustrates difficult concepts with over 300figures

• Follows the recommendations of the ACM• Introduces several supplementary topicsthat can form an excellent basis for projects

• Includes a wide variety of examples andexercises, with solutions in the appendices

• Incorporates computer exercises that teachreaders how to write their own programs


Catalog no. K10918, December 2010, c. 933 pp.ISBN: 978-1-4398-1768-1, $99.95 / £44.99



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New!Textbook

Introduction toCombinatoricsW.D. WallisSouthern Illinois University,Carbondale, USA

J.C. GeorgeGordon College, Barnesville, Georgia, USA

With many modern examples, this introductionpresents approaches for solving counting andstructural questions. It provides basic informa-tion on sets, proof techniques, enumeration,and graph theory. It covers important families offunctions as well as coding theory and designtheory. The authors also explore the interactionbetween linear algebra and combinatorics.Maple™, Mathematica®, and other tools are dis-cussed where appropriate.

Catalog no. K10310, September 2010, 397 pp.ISBN: 978-1-4398-0622-7, $79.95 / £49.99

Combinatoricsof Compositionsand WordsSilvia HeubachCalifornia State University, Los Angeles, USA

Toufik MansourUniversity of Haifa, Israel

Highlighting both estab-lished and new results, this book provides anintroduction to the methods used in the combi-natorics of pattern avoidance and pattern enu-meration in compositions and words. It illus-trates new methods and definitions with workedexamples and describes the strengths and weak-nesses of a wide variety of solution techniquesand approaches. It also incorporates the use ofMaple™, Mathematica®, and C++ to performcomputations. Solutions manual available for qualifying instructors


Pearls ofDiscreteMathematicsMartin EricksonTruman State University, Kirksville,Missouri, USA

“… a friendly volume indiscrete mathematics,which covers various classi-cal topics, such as counting, probability andnumber theory, and more recent topics, such asinformation theory, game theory and algo-rithms. As far as I know, this book is one of onlya few at this level that covers such recent top-ics. … the book may be interesting for studentsinterested in computer programming. …”

—Mehdi Hassani, MAA Reviews, December 2009

Catalog no. K10831, January 2010, 280 pp.Soft CoverISBN: 978-1-4398-1616-5, $59.95 / £38.99

Textbook

DiscreteMathematicsProofs, Structures and Applications,Third EditionRowan GarnierSurrey, UK

John TaylorUniversity of Brighton, UK

“… The style of exposition is very clear, step bystep and the level is well adapted to under-graduates in computer science. The treatmentis mathematically rigorous; therefore it is alsosuitable for mathematics students. … there aremany concrete examples and exercises (withsolutions!) … . I can recommend warmly thisbook as a textbook for a course. …”

—H.G.J. Pijls, University of Amsterdam, TheNetherlands









Textbook

AppliedCombinatoricsSecond EditionFred RobertsRutgers University, Piscataway,New Jersey, USA

Barry TesmanDickinson College, Carlisle,Pennsylvania, USA

“This is an overwhelmingly complete introduc-tory textbook in combinatorics. It not only cov-ers nearly every topic in the subject, but givesseveral realistic applications for each topic. …much more breadth than its competitors. …”

—MAA Reviews, December 2009

“… what really sets it apart is its impressive useof applications. I know of no other text whichcomes close. …”

—Thomas Quint, University of Nevada, Reno, USA

Catalog no. K10016, 2009, 848 pp.ISBN: 978-1-4200-9982-9, $99.95 / £60.99

AlgorithmicCryptanalysisAntoine JouxUniversité de Versailles Saint-Quentin-en-Yvelines, France

“…a complete panoramicof the different methodsand techniques used inmodern cryptanalysis …emphasis is in the algo-rithms, in fact one of the main attractions ofthe book is the great quantity of algorithmsthat it presents: some described in pseudocode(listed as algorithms) and others as programsin C language (listed as programs). AdditionalC implementations can be downloaded fromthe website www.joux.biz/algcrypt …”

—Zentralblatt MATH 1172


Cryptanalysis of RSA and Its VariantsM. Jason HinekiCORE Information Security Lab,Calgary, Canada

Focusing on mathematicalattacks that exploit thestructure of RSA and specif-ic parameter choices, this book provides an up-to-date collection of the most well-knownattacks on RSA and its main variants, includingCRT-RSA, multi-prime RSA, and multi-powerRSA. It includes recent results for lattice tech-niques based on Coppersmith’s methods anddifferentiates between provable attacks andthose based on assumptions.


CombinatorialPattern MatchingAlgorithms inComputationalBiology UsingPerl and RGabriel ValienteTechnical University of Catalonia,Barcelona, Spain

“… this book will be part of my fundamentallibrary for me and my group from the momentit is published. There are so many good thingsto say that I do not know where to start. …The Perl is beautifully clear and the exampleshave already taught me how to improve myown code.”

—Michael Levitt, Professor and Chair, Departmentof Structural Biology, Stanford University,

California, USAPerl and R source code available on author’s website






9

Differential Equations and Nonlinearity


New!

Applications ofLie Groups toDifferenceEquationsVladimir DorodnitsynKeldysh Institute of AppliedMathematics, Moscow, Russia

This book presents methods and results in a newapplication area of Lie groups to differenceequations and difference meshes (lattices). Itfocuses on the formulation and mathematicalsubstantiation of exact symmetry preservation indifference models, such as difference equationsand meshes. Methods are illustrated withnumerous examples and applications in heatand mass transfer, hydrodynamics, physics, andmechanics.

To highlight the numerical aspect of the book,the author provides a short survey of methodsand theory of finite difference schemes andmeshes. He also explains other approaches toquality features of difference schemes, includingvariational and moving frames methods.Features• Outlines methods to construct differenceequations and meshes, which preserve allsymmetries of original differential equations

• Contains hundreds of nonlinear invariantschemes and meshes, along with theirexact solutions and conservation laws (first integrals)

• Illustrates the application of the methodswith numerous examples

• Explores equations that arise in heat andmass transfer, hydrodynamics, physics, and mechanics

• Includes numerical aspects such as discretization schemes

Catalog no. C3090, December 2010, c. 344 pp.ISBN: 978-1-4200-8309-5, $89.95 / £57.99

Coming soon!

Green’s Functionsand LinearDifferentialEquationsTheory, Applications,and ComputationPrem K. KytheUniversity of New Orleans, Louisiana, USA

This work provides complete coverage ofGreen’s functions, which have become animportant topic of interest in recent years. Alongwith Mathematica® and MATLAB® code, it sup-plies the necessary background material andpresents a large number of examples and exer-cises from different areas of mathematics,applied science, and engineering.

The book discusses boundary value problemsinvolving ordinary differential equations, partialdifferential equations, and stochastic differentialequations. The author describes various meth-ods for solving these problems, including classi-cal methods, Bernoulli’s separation method,integral transform, conformal mapping, andwavelet transform.Contents

CONCEPT AND THEORY: Concept of a Green’sFunction. Sturm–Louiville Systems. ParabolicEquations. Hyperbolic Equations. EllipticEquations. APPLICATIONS: Green’s Functionsand Conformal Mapping. Green’s Functions andBoundary Integral Methods. Green’s Functionsand Integral Equations. Appendix A: Adjoint andSelf-Adjoint Operators. Appendix B: SomeIntegral Transforms and Tables. Appendix C:Inequalities and Some Useful Results. AppendixD: Green’s Identities. Appendix E: FractionalDerivatives. Appendix F: Computer Codes inMathematica and MATLAB. Bibliography.Notation and Definitions. Index.

Catalog no. K11855, January 2011, c. 384 pp.ISBN: 978-1-4398-4008-5, $119.95 / £76.99




Differential Equations and Nonlinearity

New!

DiscoveringEvolutionEquations withApplicationsVolume 1-Deterministic EquationsMark A. McKibbenGoucher College, Baltimore, Maryland, USA

With many concrete examples and questions,this book provides an engaging, accessibleaccount of core theoretical results of evolutionequations in a way that gradually builds intuitionand culminates in exploring active research. Itgives nonspecialists the foundation to under-stand what evolution equations are and how towork with them in various areas of practice. The book covers 35 different models spanningpharmacokinetics, neural networks, mathemati-cal physics, infectious disease epidemiology,environmental issues, and more.

Catalog no. C9207, July 2010, 466 pp.ISBN: 978-1-4200-9207-3, $99.95 / £63.99

New!Textbook

SolutionTechniques forElementaryPartial DifferentialEquationsSecond EditionChristian ConstandaUniversity of Tulsa, Oklahoma, USA

“This concise, well-written book, which includesa profusion of worked examples and exercises,serves both as an excellent text in undergradu-ate and graduate learning and as a useful pres-entation of solution techniques for researchersand engineers interested in applying partial differential equations to real-life problems.”

—Barbara Zubik-Kowal, Boise State University,Idaho, USA


Catalog no. K10569, June 2010, 343 pp.Soft CoverISBN: 978-1-4398-1139-9, $69.95 / £24.99

New!

MultiparameterEigenvalueProblemsSturm-Liouville TheoryF.V. AtkinsonAngelo B. MingarelliCarleton University, Ottawa,Ontario, Canada

One of the masters in the differential equationscommunity, the late F.V. Atkinson contributedseminal research to multiparameter spectral theory and Sturm-Liouville theory for more than 40 years. His ideas and techniques havelong inspired researchers and continue to stimulate discussion. With the help of co-authorAngelo B. Mingarelli, this book reflects much ofDr. Atkinson’s final work. Examples are illustratedusing Maple™.

Catalog no. K10834, November 2010, c. 320 pp.ISBN: 978-1-4398-1622-6, $99.95 / £63.99

Textbook

OrdinaryDifferentialEquationsApplications, Models,and ComputingCharles E. Roberts, Jr.Indiana State University, Terre Haute, USA

With software programs on the accompanyingCD-ROM, this text emphasizes the use of com-puter software in solving linear and nonlineardifferential equations and systems. It includesnumerical case studies that highlight possiblepitfalls when computing a numerical solutionwithout first considering the appropriate theory.The text shows how to solve various mathemat-ical models, such as population growth, epi-demic, and predator-prey models.Solutions manual available for qualifying instructors

Catalog no. K11006, April 2010, 600 pp.ISBN: 978-1-4398-1908-1, $99.95 / £48.99





11

General and Introductory Mathematics


New!Textbook

A ConciseIntroduction toPure MathematicsThird EditionMartin LiebeckImperial College, London, UK

“This book displays a unique combination oflightness and rigor, leavened with the rightdose of humor. When I used it for a course, stu-dents could not get enough, and I have beenrecommending independent study from it tostudents wishing to take a core course in analy-sis without having taken the prerequisitecourse. The material is very well chosen andarranged, and teaching from Liebeck’s bookhas in many different ways been among mymost rewarding teaching experiences duringthe last decades.”

—Boris Hasselblatt, Tufts University, Medford, Massachusetts, USA

“… This book will give a student the under-standing to go on in further courses in abstractalgebra and analysis. The notion of a proofwill no longer be foreign, but also mathemat-ics will not be viewed as some abstract blackbox. At the very least, the student will have anappreciation of mathematics.

As usual, Liebeck’s writing style is clear andeasy to read. This is a book that could be readby a student on his or her own. There is a wideselection of problems ranging from routine toquite challenging.”

—From the Foreword by Robert Guralnick,University of Southern California, Los Angeles, USA


Catalog no. K11624, August 2010, 268 pp.Soft CoverISBN: 978-1-4398-3598-2, $59.95 / £25.99

New!

A ConciseHandbook ofMathematics,Physics, andEngineeringSciencesEdited byAndrei D. PolyaninRussian Academy of Sciences, Moscow, Russia

Alexei I. ChernoutsanGubkin Russian State University of Oil and Gas, Moscow, Russia

This handbook takes a practical approach to thebasic notions, formulas, equations, problems, theo-rems, methods, and laws that most frequentlyoccur in scientific and engineering applications anduniversity education. The authors pay special atten-tion to issues that many engineers and studentsfind difficult to understand.

Each chapter includes a list of literature sourcescontaining more detailed information about topicsof interest. Additional issues of importance can befound in the remarks. For ease of reading, the sup-plement at the back of the book provides severallong mathematical tables, including indefinite anddefinite integrals, direct and inverse integral trans-forms, and exact solutions of differential equations.Features • Covers important formulas, equations,problems, theorems, methods, and laws inmathematics, physics, applied sciences, andengineering

• Includes numerous examples, figures,graphs, and diagrams

• Presents many results in tabular form• Avoids special terminology and excessivelycomplicated details whenever possible

• Offers an extensive table of contents, adetailed index, special font highlighting inthe text, and cross-references that helpreaders find the desired information






New!

A Student’sGuide to theStudy, Practice,and Tools ofModernMathematicsDonald Bindner andMartin EricksonTruman State University, Kirksville, Missouri, USA

This guide offers a thorough reference to keytopics in modern mathematics. With an intro-duction to MATLAB®, Mathematica®, Maple™,Maxima, and R, the text explains how to studymathematics, how to write proofs, how to con-duct mathematical research, how to give pre-sentations on mathematics, and how to getstarted with various programming languages. Italso discusses how Geometer’s sketchpad is auseful tool for drawing illustrations.

Catalog no. K12061, November 2010, c. 280 pp.Soft CoverISBN: 978-1-4398-4606-3, $39.95 / £25.99

Mathematics inGames, Sports,and GamblingThe Games PeoplePlayRonald J. GouldEmory University, Atlanta, Georgia, USA

“… a wonderful referencefor studying probability or statistics … Thoughthis book might serve as the seed for the devel-opment of a new mathematics course at someinstitutions, this reviewer sees its greater valueas a reference for mathematicians who areunfamiliar with the probabilities associatedwith gambling or applying statistics in sports.”

—J.T. Noonan, CHOICE, Vol. 47, No. 9, May 2010


New!

Handbook ofMathematicalInductionTheory andApplicationsDavid S. GundersonUniversity of Manitoba, Winnipeg, Canada

This comprehensive handbook presents hun-dreds of classical theorems and proofs that spanmany areas, including combinatorics, linearalgebra, calculus, trigonometry, geometry, settheory, game theory, recursion, and algorithms.It derives many forms of mathematical induc-tion, such as infinite descent and the axiom ofchoice, from basic principles. The book containsnearly 600 bibliographic references and morethan 750 exercises—with complete solutions toat least 500.

Catalog no. C3649, September 2010, 921 pp.ISBN: 978-1-4200-9364-3, $109.95 / £69.99

New!Textbook

A MathematicalLook at PoliticsE. Arthur Robinson, Jr.and Daniel UllmanGeorge Washington University,Washington, DC, USA

This book is based on apopular mathematics and politics course thatthe authors have taught at George WashingtonUniversity for the past six years. The authorsexplore the mathematics of politics, showinghow mathematical reasoning is connected tothe pressing issues of contemporary politics andin the liberal arts. Focusing on voting, appor-tionment, conflict, and the Electoral College,each part of the text examines a type of decisionproblem and a way to solve it.






13



Coming soon!Textbook

Mathematics forthe EnvironmentMartin WalterUniversity of Colorado, USA

Suitable for a general stud-ies course on mathematics,this text presents the math-ematics by building patterns in numbers, arithmetic, and algebra and by using axioms asbuilding blocks. It explores examples in popula-tion models, DNA computing, epidemics, financial mathematics, and more. It also encour-ages the use of Excel spreadsheets to solve many of the open-ended problems. Solutionsare provided in an appendix.


Introduction toMathematics ofSatisfiabilityVictor W. MarekUniversity of Kentucky, Lexington, USA

“… an invaluable referencefor anyone who is interest-ed in issues ranging fromtheoretical mathematical logic to computa-tional logic. The book maintains a nice trade-off between formalism and clarity. … Theauthor excels at relating his expositions to thecurrent state of the art … its most significantcontribution is its accessible explanations ofhow and why algorithms and ideas exposework.”

—Carlos Linares Lopez, Computing Reviews,March 2010


Textbook

Introduction toMathematicalLogicFifth EditionElliott MendelsonQueens College, Flushing, New York, USA

“…This book rightfullybelongs in the small, elite set of superb booksthat every computer science graduate, gradu-ate student, scientist, and teacher should befamiliar with.”

—Computing Reviews, May 2010

“…Mendelson’s textbook remains a sure choicefor a first course for its clear explanations andorganization: definitions, examples and resultsfit together in a harmonic way, making thebook a pleasure to read. … a wealth of exer-cises test the reader’s understanding.”

—MAA Reviews, December 2009

Catalog no. C8768, January 2010, 469 pp. ISBN: 978-1-58488-876-5, $89.95 / £39.99

Textbook

Introduction toMathematicalProofsA TransitionCharles E. Roberts, Jr.Indiana State University, Terre Haute, USA

Written in a conversationalstyle, yet maintaining the proper level of mathe-matical rigor, this accessible book teaches howto reason logically, read proofs critically, andwrite valid mathematical proofs. It facilitates asmooth transition from courses designed todevelop computational skills and problem solv-ing abilities to courses that emphasize theoremproving.Solutions manual available for qualifying instructors







Geometry and Topology

New!

Combinatoricsof Spreads andParallelismsNorman L. JohnsonUniversity of Iowa, Iowa City, USA

This book covers all knownfinite and infinite paral-lelisms, including many new examples, as wellas the planes comprising them. It also presents acomplete analysis of general spreads and parti-tions of vector spaces that provide groupsenabling the construction of subgeometry partitions of projective spaces. More than 70open problems listed in the book encompassmany new areas of research. More informationon the author’s related books can be found atwww.crcpress.com


New!

WaveletSubdivisionMethodsGEMS for RenderingCurves and SurfacesCharles ChuiStanford University, California,and University of Missouri, St. Louis, USA

Johan de VilliersStellenbosch University, South Africa

“This book is the first writing that introducesand incorporates the wavelet component of thebottom-up subdivision scheme. … The bookcontains a large collection of carefully preparedexercises … . The authors have been in the fore-front for advances in wavelets and wavelet subdivision methods and I congratulate themfor writing such a comprehensive text.”

—From the Foreword by Tom Lyche, University of Oslo, Norway


New!

SobolevInequalities,Heat Kernelsunder Ricci Flow,and the PoincareConjectureQi S. ZhangUniversity of California, Riverside, USA

Focusing on Sobolev inequalities and their appli-cations to analysis on manifolds and Ricci flow,this book introduces the field of analysis onRiemann manifolds and uses the tools ofSobolev imbedding and heat kernel estimates tostudy Ricci flows with surgeries. The authorexplains key ideas, difficult proofs, and impor-tant applications in a succinct, accessible, andunified manner.

Catalog no. K11558, July 2010, 432 pp.ISBN: 978-1-4398-3459-6, $79.95 / £49.99

Textbook

Essentials ofTopology withApplicationsSteven G. KrantzWashington University, St. Louis, Missouri, USA

Supported by many exam-ples in mathematics, physics,economics, engineering, and other disciplines,this text provides a clear, insightful, and thor-ough introduction to the basics of moderntopology. It presents the traditional concepts oftopological space, open and closed sets, separa-tion axioms, and more, along with applicationsof the ideas in Morse, manifold, homotopy, andhomology theories.






15

Mathematical Modeling


Textbook

MathematicalandExperimentalModeling ofPhysical andBiologicalProcessesH.T. Banks and H.T. TranNorth Carolina State University, Raleigh, USA

“…would I buy this textbook? absolutely yes!The concise and clear style in which the back-ground is written for each chapter will beinvaluable as a quick, ‘before the lecture isgiven’ refresher. … Most of the topics coveredare those which have arisen out of the researchprojects that the authors have conductedthemselves. This is the kind of hands-on experi-ence that a lecturer would need in order tomake the laboratory experiences for the stu-dents enjoyable and rewarding. … the truevalue of this textbook, namely, [is that] it pro-vides a stimulus package to provoke the readerto adopt a similar teaching philosophy.”

—Mathematical Reviews, Issue 2010

Exploring how mathematics is applied to prob-lems in science and engineering, this book dis-cusses mathematical modeling in the context ofcase study problems that arise in industry andgovernment laboratories. It covers thermalimaging and detection, dynamic properties ofbeams, acoustics and fluid transport, and size-structured population dynamics for marinepopulations. The text explains physical and bio-logical relationships and mechanisms through afirst principles-based fundamental modelingapproach. It also emphasizes model validationthrough specific laboratory experiments as well as data collection and analysis. Downloadreal experimental data for projects at www.crcpress.com


New!Textbook

ComputerGraphicsThrough OpenGLFrom Theory toExperimentsSumanta GuhaAsian Institute of Technology,Thailand

From geometric primitives to animation to 3Dmodeling to lighting and shading, this compre-hensive introduction uses an active learning styleto teach key concepts. Equally emphasizing theory and practice, the text provides an understanding not only of the principles of 3Dcomputer graphics, but also the use of theOpenGL API to program 3D applications.

Forming the core of the book, the first fourteenchapters cover the concepts fundamental to 3Dcomputer graphics and illustrate how to codefairly sophisticated 3D scenes and animation,including games and movies. The remainingchapters explore more advanced topics, such asthe structure of curves and surfaces and applica-tions of projective spaces and transformations.

Features • Covers the foundations of 3D computergraphics, including animation, visual techniques, and 3D modeling

• Introduces classical and programmablepipelines in OpenGL

• Integrates code with the theory to givereaders a hands-on appreciation of the subject

• Includes 140 programs with 200 experimentsbased on them

• Contains 600 exercises, 100 worked examples, and nearly 600 color illustrations

• Requires no previous knowledge of computer graphics

• Offers downloadable multiplatformprograms in C++ and OpenGL, installationguides, and an interactive discussion forumat www.sumantaguha.com

Solutions manual and test bank available for qualifyinginstructors

Catalog no. K12068, September 2010, 888 pp.,ISBN: 978-1-4398-4620-9, $99.95 / £49.99




Mathematics for Finance

New!

Introduction toCredit RiskModelingSecond EditionChristian BluhmMunich, Germany

Ludger OverbeckUniversity of Giessen, Germany

Christoph WagnerMunich, Germany

Praise for the First Edition

“This is an outstanding book on the defaultmodels that are used internally by financialinstitutions. This practical book delves into themathematics, the assumptions and theapproximations that practitioners apply tomake these models work.”

—Glyn A. Holton, Contingency Analysis

“… a well-rounded introduction.”—Journal of the Operational Research Society

While continuing to focus on common mathe-matical approaches to model credit portfolios,this second edition presents updates on modeldevelopments that have occurred since the pub-lication of the bestselling first edition. It recom-mends using a variety of models to shed light ondifferent aspects of the true nature of a credit riskproblem, thereby allowing the problem to beviewed from different angles. It also includesmany worked out examples and numericalresults. New to the Second Edition• An expanded section on techniques for the generation of loss distributions

• Introductory sections on new topics, suchas spectral risk measures, an axiomaticapproach to capital allocation, and nonhomogeneous Markov chains

• Updated sections on the probability ofdefault, exposure-at-default, loss-given-default, and regulatory capital

• A new section on multi-period models• Recent developments in structured credit

Catalog no. C8992, June 2010, 384 pp.ISBN: 978-1-58488-992-2, $79.95 / £49.99

Textbook

StochasticFinancial ModelsDouglas KennedyTrinity College, Cambridge, UK

“This book is a superbbeginning level text for sen-ior undergraduate/gradu-ate mathematicians, whichis based on lectures delivered by its author tomany generations of appreciative Cambridgemathematicians. Many of my own Ph.D. andmasters students have taken Dr. Kennedy’scourse to uniformly good reviews; this readablebook will make its material available to aworldwide audience. … the book contains 40pages of fully worked out solutions … .”

—M.A.H. Dempster, Centre for Financial Research,Statistical Laboratory, University of Cambridge, UK

Developed from the esteemed author’sadvanced undergraduate and graduate coursesat the University of Cambridge, this text pro-vides a hands-on, sound introduction to mathe-matical finance, enabling readers to derive theprices of many common financial products. Theauthor includes the relevant mathematical back-ground, assuming no prior knowledge of sto-chastic calculus or measure-theoretic probability.

The book first presents the classical topics of utility and the mean-variance approach to port-folio choice. Focusing on derivative pricing, thetext then covers the binomial model, the gener-al discrete-time model, Brownian motion, theBlack–Scholes model, and various interest-ratemodels. Each chapter contains many exercisesand solutions can be found in an appendix.




17



New! Utility-BasedLearning fromDataCraig FriedmanStandard & Poor’s, New York, New York, USASven SandowMorgan Stanley, New York, New York, USA

“…Friedman and Sandow lucidly describe theconnections between different branches of sta-tistics and econometrics … . A must-read forserious statisticians!”

—Marco Avellaneda, Professor of Mathematics, New York University, and Risk Magazine Quant

of the Year 2010

“…a much-needed and comprehensive book,which should help put model-building for useby decision makers on more solid ground.”

—Gregory Piatetsky-Shapiro, editor ofKDnuggets.com, co-founder and past Chair of

SIGKDD, and founder of the Knowledge Discoveryand Data Mining (KDD) conferences

Catalog no. C6226, August 2010, 417 pp.ISBN: 978-1-58488-622-8, $79.95 / £49.99

Applied GameTheory andStrategicBehaviorIlhan Kubilay GeckilAnderson Economic Group,Chicago, Illinois, USA

Patrick L. AndersonAnderson Economic Group, EastLansing, Michigan, USA

Along with many case studies, this book usesgame theory techniques to address practicalbusiness, economic, and public policy issues. Italso illustrates the benefits of employing strate-gic thinking that incorporates the uncertaintysurrounding the behavior of other parties. Theauthors show how to build a model to analyzereal-world problems and find strategically sounddecisions in uncertain environments.

Catalog no. C843X, January 2010, 230 pp.ISBN: 978-1-58488-843-7, $79.95 / £48.99

Decision OptionsThe Art and Scienceof Making DecisionsGill EapenDecision Options, LLC, Groton, Connecticut, USA

This book details howuncertainty and flexibilitycan be evaluated to assist inmaking better investmentdecisions in companies. It demonstrates howfinancial and real options are related and presents case studies from diverse industries,including life sciences, pharmaceuticals, com-modities, energy, technology, manufacturing,and financial services. The author looks at howorganizations can become successful using aholistic framework that integrates uncertaintyand flexibility.


StochasticDominance andApplications toFinance, Riskand EconomicsSongsak Sriboonchita,Wing-Keung Wong,Sompong Dhompongsa,and Hung T. Nguyen

“The book helps readers in building a usefulrepertoire of mathematical tools in decisionmaking under uncertainty, especially in invest-ment science, and provides thorough coverageon the theory of SD, along with many applications to economics and other fieldswhere risk is crucial. … a solid reference bookfor researchers, especially in the field of eco-nomics.”

—Zentralblatt MATH 1180








New!

Handbook ofSolvency forActuaries andRisk ManagersTheory and PracticeArne SandstromSwedish Insurance Federation,Stockholm, Sweden

A one-stop shop for actuaries and risk managers,this handbook presents a complete overview ofsolvency and the European Solvency II standardformula. It discusses the development of solven-cy and risk management as well as the modelingand calibration of the specific standard formuladeveloped for Solvency II. The book also coversthe modeling of capital charges in a general set-ting and highlights key concepts in enterpriserisk management.


Textbook

Interest RateModelingTheory and PracticeLixin WuUniversity of Science &Technology, Kowloon, Hong Kong

Containing many resultsthat are new or exist only inrecent research articles, this text portrays thetheory of interest rate modeling as a three-dimensional object of finance, mathematics, andcomputation. It introduces all models withfinancial-economical justifications, developsoptions along the martingale approach, andhandles option evaluations with precise numeri-cal methods. The author also shows readers howto build and use models. Code, tables, and fig-ures are accessible on the author’s website. Solutions manual available for qualifying instructors


Textbook

PortfolioOptimizationMichael J. BestUniversity of Waterloo, Ontario, Canada

Eschewing a more theoreti-cal approach, PortfolioOptimization shows howthe mathematical tools of linear algebra andoptimization can quickly and clearly formulateimportant ideas on the subject. This practicalbook extends the concepts of the Markowitz“budget constraint only” model to a linearlyconstrained model. It uses MATLAB® to helpwith problem solving and offers the programson a CD-ROM.Solutions manual available for qualifying instructors

Catalog no. C5840, March 2010, 236 pp.ISBN: 978-1-4200-8584-6, $79.95 / £49.99

Pension Fund RiskManagementFinancial andActuarial ModelingEdited by

Marco MicocciUniversity of Cagliari, Italy

Greg N. GregoriouState University of New York, Plattsburgh, USA

Giovanni Batista MasalaUniversity of Cagliari, Italy

With contributions from well-known, interna-tional academics and professionals, this booksheds new light on the current state of pensionfund risk management and provides new tech-nical tools for addressing pension risk from anintegrated point of view. It will assist pensionfund executives, risk managers, consultants, andacademic researchers in attaining a clear pictureof the integration of risks in the pension world.






19



New!

Operational RiskModelling andManagementClaudio FranzettiSERV, Zurich, Switzerland

Helping you navigate thetricky world of risk calcula-tion and management, this book employs the loss distribution approach as a model for calculating the risk capital figure and explainsrisk mitigation through management and man-agement’s actuations. While R scripts are usedfor some examples, a prototypical software program for calculating the loss distribution and economic capital in the more detailed run-through example can be downloaded fromwww.garrulus.com


Monte CarloMethods andModels in Financeand InsuranceRalf KornUniversity of Kaiserslautern,Germany

Elke KornIndependent MathematicalConsultant, Stelzenberg, Germany

Gerald KroisandtFraunhofer ITWM, Kaiserslautern, Germany

Offering a unique balance between applicationsand calculations, this book incorporates theapplication background of finance and insur-ance with the theory and applications of MonteCarlo methods. It presents recent methods andalgorithms, including the multilevel MonteCarlo method, the statistical Romberg method,and the Heath–Platen estimator, as well asrecent financial and actuarial models, such asthe Cheyette and dynamic mortality models.

Catalog no. C7618, February 2010, 484 pp.ISBN: 978-1-4200-7618-9, $89.95 / £57.99

Coming soon!Textbook

StochasticFinanceA NumeraireApproachJan VecerColumbia University, New York, New York, USA

This text is based on quantitative finance cours-es taught at Columbia University to graduatestudents and Wall Street professionals. Focusingon fundamental finance principles instead ofmathematical theory, the author considers theprice of an asset as an exchange ratio betweengoods that pay for each other, rather thanexpressing prices in currency terms. This novelapproach leads to simple derivations of pricingformulas that are model independent.


New!

Handbook ofEmpiricalEconomics andFinanceEdited by

Aman UllahUniversity of California, Riverside, USA

David E. A. GilesUniversity of Victoria, British Columbia, Canada

This handbook explores cutting-edge develop-ments in applied econometrics and the modelingof special types of economic and financial data. The book covers major themes in the areas ofmicroeconometrics, macroeconometrics, financialeconometrics, panel and spatial data, time-seriesanalysis, semiparametric and nonparametric meth-ods, and treatment effects. It also discusses compu-tation with reference to Bayesian methods as wellas information-theoretic approaches to inference.







Numerical Analysis and Scientific Computing

DecompositionMethods forDifferentialEquationsTheory andApplicationsJuergen GeiserHumboldt University of Berlin,Germany

Exploring iterative operator-splitting methods,this work describes the analysis of numericalmethods for evolution equations based on tem-poral and spatial decomposition methods. Itcovers real-life problems, the underlying decom-position and discretization, the stability and con-sistency analysis of the decomposition methods,and numerical results. Software tools are listed inan appendix.


MathematicalObjects in C++Computational Toolsin a Unified Object-Oriented ApproachYair ShapiraTechnion, Haifa, Israel

“This is an exciting bookon mathematics on onehand and computer programming on theother, and the reader can concentrate on oneof the topics or both. …The programming partof the book serves as a very good introductionto C and C++, using meaningful and motivat-ing examples from mathematics. The book isfull of useful exercises of various difficulty. …”

—Hans Petter Langtangen, Simula ResearchLaboratory and University of Oslo, Norway

Download code at www.crcpress.com


NumericalTechniques forDirect andLarge-EddySimulationsXi JiangBrunel University, Uxbridge, UK

Choi-Hong LaiUniversity of Greenwich, London, UK

This text covers basic techniques for DNS andLES that can be applied to practical problems offlow, turbulence, and combustion. It presentsnumerical methods for compressible and incom-pressible three-dimensional flows, such as high-order discretization schemes, high-fidelityboundary conditions, and coupling aspects. Thebook gives sample numerical simulation resultsthat exemplify the practical application of themethods and includes sample FORTRAN pro-grams in the appendix.


New!

DiscreteVariationalDerivative MethodA Structure-PreservingNumerical Method forPartial DifferentialEquationsDaisuke FurihataOsaka University, Toyonaka, Japan

Takayasu MatsuoUniversity of Tokyo, Bunkyo, Japan

This book first introduces the key factors andbasic ideas of the discrete variational derivativemethod and target problems that are solvable bythe method. The second section describes therigorous mathematics in detail along with rele-vant applications, which are illustrated by workedexamples. The book concludes with a compre-hensive of listing of essential references on struc-ture-preserving algorithms for advanced readers.






21

Numerical Analysis and Scientific Computing


New!

Handbook ofSinc NumericalMethodsFrank StengerUniversity of Utah, Salt Lake City, USA

Reflecting the author'sadvances with Sinc since1995, this handbook provides a package ofmethods based on Sinc approximation. It con-tains roughly 450 MATLAB® programs forapproximating almost every type of operationstemming from calculus. The book also presentsnew and powerful methods for solving ordinarydifferential equations, partial differential equa-tions, and integral equations. Sinc-Pack pro-grams are available on a companion CD-ROM.

Catalog no. K11144, November 2010, 496 pp.ISBN: 978-1-4398-2158-9, $99.95 / £63.99

New!

Introduction toHigh PerformanceComputing forScientists andEngineersGeorg Hager andGerhard WelleinUniversity of Erlangen Nuremberg, Germany

“…easy to read and follow … This book presents a balanced treatment of the theory,technology, architecture, and software formodern high performance computers and the use of high performance computing systems.… I highly recommend this timely book for scientists and engineers. …”

—From the Foreword by Jack Dongarra, University of Tennessee, Knoxville, USA

Download code and more on the book’s website

Catalog no. K10600, July 2010, 356 pp., Soft CoverISBN: 978-1-4398-1192-4, $69.95 / £42.99

New!

PerformanceTuning ofScientificApplicationsEdited byDavid H. BaileyLawrence Berkeley NationalLaboratory, California, USARobert F. LucasUniversity of Southern California, Los Angeles, USASamuel WilliamsLawrence Berkeley National Laboratory, California, USA

This book presents an overview of recent researchand applications in computer system perform-ance for scientific and high performance comput-ing. After a brief introduction to the field of scien-tific computer performance, the text providescomprehensive coverage of performance meas-urement and tools, performance modeling, andautomatic performance tuning. It also includesperformance tools and techniques for real-worldscientific applications, such as climate modeling.

Catalog no. K10806, November 2010, c. 392 pp.ISBN: 978-1-4398-1569-4, $89.95 / £57.99

GeneticAlgorithms and GeneticProgrammingModern Concepts andPractical ApplicationsMichael AffenzellerUpper Austria University of Applied Sciences, Hagenberg, andJohannes Kepler University of Linz, Austria

Stefan Wagner, Stephan Winkler, andAndreas BehamUpper Austria University of Applied Sciences, Hagenberg

This book describes several generic algorithmicconcepts that can be used in any kind of GA orwith evolutionary optimization techniques. It pro-vides a better understanding of the basic workflowof GAs and GP, encouraging readers to establishnew bionic, problem-independent theoretical con-cepts. It also documents the beneficial effects ofenhanced algorithmic concepts. Software, dynam-ical presentations of representative test runs, andmore are available on a supplementary website.







Real, Complex, and Functional Analysis

Fundamentals ofGrid ComputingTheory, Algorithmsand TechnologiesEdited by

Frédéric Magoulès École Centrale Paris, Châtenay-Malabry, France

“This book shows, in somesense, the way to the future, where next gener-ation middleware such as those described herewill replace in the production infrastructure themore rudimentary ones in use today. Therefore,I am sure that the readers will greatly benefitfrom this insightful journey in the heart of thegrids … .”

—From the Foreword by Guy Wormser, Institut des Grilles, CNRS, Orsay, France


Textbook

Classical andModern NumericalAnalysisTheory, Methods andPracticeAzmy S. Ackleh, Edward James Allen,Ralph Baker Kearfott,and Padmanabhan Seshaiyer

Helping readers prepare for doctoral examina-tions in numerical analysis, this text provides asound introduction to the theory and applicationof computational methods for applied mathe-matics problems. It presents advanced aspects ofnumerical linear algebra, finite element theory,approximation theory, optimization, and integralequations. The authors also cover interval com-putation methods in numerical analysis.Solutions manual available for qualifying instructors


New!Textbook

Introduction tothe Simulationof DynamicsUsing Simulink®

Michael A. GrayAmerican University, Washington, DC, USA

Requiring no prior programming experience,this book shows how to use the powerful tool ofSimulink® to investigate and form intuitionsabout the behavior of dynamical systems. Step by step, the author presents the basics ofbuilding a simulation in Simulink. He also offersoverviews of some advanced topics, includingthe simulation of chaotic dynamics and partialdifferential equations. Ancillary materials areavailable on the author’s website.

Catalog no. K11000, July 2010, 332 pp.ISBN: 978-1-4398-1897-8, $89.95 / £49.99

Real, Complex,and FunctionalAnalysis Localization andPerturbation of Zerosof Entire FunctionsMichael Gil’Ben Gurion University of theNegev, Israel

This is the first book to provide a systematicexposition of the bounds for the zeros of entire functions and variations of zeros under per-turbations. It also offers a new approach forinvestigating entire functions based on recentestimates for the resolvents of compact opera-tors. The author describes applications to differ-ential, functional differential, and difference equa-tions.






23

Real, Complex, and Functional Analysis


New!

TopologicalVector SpacesSecond EditionLawrence Narici andEdward BeckensteinSt. John’s University, New York, New York, USA

With many new concreteexamples and historical notes, this second edition provides one of the most thorough andup-to-date treatments of the Hahn–Banach theorem. This edition explores the theorem’sconnection with the axiom of choice, discussesthe uniqueness of Hahn–Banach extensions, andincludes an entirely new chapter on vector-valued Hahn–Banach theorems. It also considersdifferent approaches to the Banach–Stone theorem as well as variations of the theorem.

Catalog no. C866X, July 2010, 628 pp.ISBN: 978-1-58488-866-6, $89.95 / £57.99

Textbook

Real andComplexAnalysisChristopher Apelian and Steve SuraceDrew University, Madison, New Jersey, USA

Unlike other undergradu-ate-level texts, this book develops both the realand complex theory together, illustrating theconnections and differences between these twobranches of analysis right from the beginning.The text takes a unified, elegant approach to thetheory that is consistent with the recommenda-tions of the MAA’s 2004 Curriculum Guide.Ancillary materials are available on the book’swebsite.


New!

MathematicalInequalitiesA PerspectivePietro Cerone andSilvestru S. DragomirVictoria University, Melbourne, Australia

Written in an accessiblemanner, this book offers an overview of theexpanding field of mathematical inequalitiesand their applications. Instead of focusing onnarrow treatments of various mathematicalinequalities, the authors present a number ofclassical and recent results across the field, cov-ering integral inequalities, discrete inequalities,and inequalities in abstract spaces. They alsomake new connections and investigate intimaterelationships between inequalities.


Textbook

AppliedFunctionalAnalysisSecond EditionJ. Tinsley Oden andLeszek F. DemkowiczThe University of Texas at Austin,USA

The second edition of this bestselling textincludes revisions of many original examples,along with new examples that often reflect theauthors’ own vast research experiences and per-spectives. It also provides many more exercises.New discussions cover Bayesian statistical infer-ence, multilinear algebra and determinants, thesingular value decomposition theorem,Hadamard finite part integrals, and more.Solutions manual available for qualifying instructors

Catalog no. C1956, March 2010, 596 pp.ISBN: 978-1-4200-9195-3, $119.95 / £76.99






Number Theory

Coming soon!

AlgebraicNumber TheorySecond EditionRichard A. MollinUniversity of Calgary, Alberta, Canada

Praise for the First Edition

“This is a remarkable book that will be a valu-able reference for many people, including me.The book shows great care in preparation, andthe ample details and motivation will beappreciated by lots of students. The solidpunches at the end of each chapter will beappreciated by everybody. It deserves successwith many adoptions as a text.”—Irving Kaplansky, Mathematical Sciences Research

Institute, Berkeley, California, USA

“An extremely well-written and clear presenta-tion of algebraic number theory suitable forbeginning graduate students. The many exer-cises, applications, and references are a veryvaluable feature of the book.”

—Kenneth Williams, Carleton University, Ottawa, Ontario, Canada

The second edition of this popular book featurescoverage of L-functions and function fields toprovide a more modern view of the field. Thisedition also introduces class groups for bothbinary and quadratic forms, making it much easier to prove the finiteness of the class numberof both groups via an isomorphism. Along withupdated problem sets and additional examples,the text provides new results on the relationshipbetween quadratic residue symbols and funda-mental units of real quadratic fields in conjunc-tion with prime representation. Solutions manual available for qualifying instructors


Textbook

AdvancedNumber Theorywith ApplicationsRichard A. MollinUniversity of Calgary, Alberta, Canada

“When I was looking overbooks for my course, I wasvery pleased by yours, and look forward toteaching from it. …”

—David Barth-Hart, Associate Head, School ofMathematical Sciences, Rochester Institute of

Technology, New York, USA

“This terrific book is testimony to RichardMollin’s mathematical erudition, wonderfultaste, and also his breadth of culture. … awondrous book, successfully fulfilling theauthor’s purpose of effecting a bridge to mod-ern number theory for the somewhat initiated.… it’s very nice to find in Mollin’s book a highquality and coherent treatment of this beauti-ful material and pointers in abundance towhere to go next.”

—Michael Berg, Loyola Marymount University, MAA Review, 2009

By covering a wide range of algebraic, analytic,combinatorial, cryptographic, and geometricaspects of number theory, this text provides themost up-to-date and comprehensive materialfor a second course in this field. With numerousexamples and exercises, it begins with coverageof algebraic number theory, binary quadraticforms, Diophantine approximation, arithmeticfunctions, p-adic analysis, Dirichlet characters,density, and primes. The author then appliesthese tools to Diophantine equations, beforedeveloping elliptic curves and modular forms.He also presents Fermat’s Last Theorem, the ABCconjecture, and sieve methods.Solutions manual available for qualifying instructors




25

Mathematics for Engineering


A Shock-FittingPrimerManuel D. SalasNASA Langley Research Center,Hampton, Virginia, USA

This text presents the prop-er numerical treatment ofshock waves and other dis-continuities. It introduceskey techniques using a sim-ple scalar equation and then extends to a morecomplex system of equations. The author alsopresents a new, simplified shock-fitting methodand compares it to the standard technique.Along with many end-of-chapter problems andexamples, the book includes a CD-ROM of MATLAB® codes that illustrate the shock-fittingtechniques discussed in the text.


AdvancedDifferentialQuadratureMethodsZhi ZongDalian University of Technology,People’s Republic of China

Yingyan ZhangNational University of Singapore

This work discusses the limitations of direct DQmethods and common strategies to removethese limitations. It presents the formulations ofseveral new DQ methods and applies thesenovel DQ methods to solve problems that arebeyond the capabilities of the direct DQmethod. The authors also provide FORTRANcode for readers to quickly acquire hands-onexperience with DQ methods.


Optimal ReferenceShaping forDynamicalSystemsTheory andApplicationsTarunraj SinghUniversity at Buffalo, New York, USA

Supplying MATLAB® code and a suite of real-world problems, this book provides a rigorousyet accessible presentation of the theory andnumerical techniques used to shape control sys-tem inputs for achieving precise control whenmodeling uncertainties exist. It includes up-to-date techniques for the design of command-shaped profiles for precise, robust, and rapidpoint-to-point control of underdamped systems.


QuasilinearHyperbolicSystems,CompressibleFlows, and WavesVishnu D. SharmaIndian Institute of Technology,Bombay, India

Filled with practical exam-ples, this book presents a self-contained discus-sion of quasilinear hyperbolic equations and sys-tems with applications. It emphasizes nonlineartheory and introduces some of the most activeresearch in the field. The author elucidates allnecessary mathematical concepts in the firstthree chapters and then highlights the applica-tion of various approaches to solve practicalphysical problems from areas, including gasdy-namics, radiation gasdynamics, magnetogasdy-namics, nonequilibrium flows, and shallowwater theory.

Catalog no. K11669, April 2010, 282 pp.ISBN: 978-1-4398-3690-3, $99.95 / £63.99






Mathematics for Engineering

New!

MATLAB® PrimerEighth EditionTimothy A. DavisUniversity of Florida, Gainesville, USA

Highlighting the newaspects of MATLAB® 7.10and expanding on manyexisting features, this eighth edition continues tooffer a hands-on, step-by-step introduction tousing the powerful tools of MATLAB. It includesa new chapter on object-oriented programmingas well as a synopsis of the most frequently usedfunctions, operators, and special characters. M-files and MEX-files for large examples areavailable at www.crcpress.com

Catalog no. K11404, August 2010, 248 pp.Soft CoverISBN: 978-1-4398-2862-5, $21.99 / £13.99

Textbook

MATLAB® withApplications toEngineering,Physics andFinanceDavid Baez-LopezUniversidad de las Américas,Puebla, Mexico

This text explains how to perform complexmathematical tasks with MATLAB® programs.The author first describes simple functions andthen addresses more advanced topics. He alsopresents examples of Simulink® for system mod-eling and simulation. The text explores the useof MATLAB in digital signal processing, chemicaland food engineering, astronomy, optics, andfinancial derivatives. MATLAB examples and programs can be downloaded from the book’swebsite.Solutions manual available for qualifying instructors


New!

InteractiveDynamic-SystemSimulationSecond EditionGranino A. KornChelan, Washington, USA

Showing you how to usepersonal computers for modeling and simula-tion, this practical tutorial discusses how toeffectively simulate dynamical systems, such asaerospace vehicles, power plants, chemicalprocesses, control systems, and physiologicalsystems. This edition introduces a new vectoriz-ing compiler, incorporates a new treatment ofthe difference equation programs, and presentsimproved versions of several classical simulationprograms. An accompanying CD-ROM includesa complete, industrial-strength simulation pro-gram package.


New!Textbook

AdvancedMathematicalMethods inScience andEngineeringSecond EditionS.I. HayekPennsylvania State University, University Park, USA

This update of a bestselling text presents meth-ods of applied mathematics that are particularlysuited to address physical problems in scienceand engineering. This edition incorporates anew chapter on numerical methods as well asnew appendices on vector algebra, calculus, andmatrix algebra. The author provides a completetreatment of ODEs and PDEs and includes manysolved examples and problems with answers.

Catalog no. C1977, June 2010, 866 pp.ISBN: 978-1-4200-8197-8, $129.95 / £82.00





27

Mathematics for Engineering / Mathematics for Biology and Medicine


New!Textbook

AdvancedEngineeringMathematicswith MATLAB®Third EditionDean G. DuffyFormer Instructor, US Naval Academy, Annapolis, Maryland, USA

Along with new examples, problems, and projects, this updated and expanded editionincorporates new chapters on Green’s functions,probability, and random processes. It alsoincludes a new section that uses the matrixexponential to solve systems of differential equa-tions as well as more numerical methods forsolving differential equations, includingAdams–Bashforth and finite element methods.Download MATLAB® scripts at www.crcpress.comSolutions manual available for qualifying instructors


Cell MechanicsFrom Single Scale-Based Models toMultiscale ModelingEdited by

Arnaud ChauvièreThe University of Texas, Houston, USA

Luigi PreziosiPolitecnico di Torino, Italy

Claude VerdierUniversité Joseph Fourier and CNRS, Grenoble, France

This book brings together new insight andresearch on mechanical, mathematical, physical,and biological approaches for simulating thebehavior of cells, specifically tumor cells. It illus-trates how phenomena occurring at variousscales can be modeled and coupled to accountfor multiscale aspects. The text discusses experi-mental and theoretical topics, including biologi-cal and complex modeling issues.


Spatial EcologyEdited by

Stephen Cantrell, Chris Cosner, and Shigui RuanUniversity of Miami, Coral Gables, Florida, USA

Exploring the relationshipbetween mathematics andecology, Spatial Ecologyfocuses on emerging challenges in the field.These challenges consist of understanding theimpact of space on community structure, incor-porating the scale and structure of landscapesinto mathematical models, and developing connections between spatial ecology and evolu-tionary theory, epidemiology, and economics.The book shows how various models, such asreaction- diffusion, multivariate state-space, andmetapopulation models, are used in ecologicalapplications.


New!

ComputationalHydrodynamicsof Capsules andBiological CellsEdited byC. PozrikidisUniversity of Massachusetts,Amherst, USA

A roadmap to the current state of the art in com-putational cellular mechanics and biofluiddy-namics, this volume provides a comprehensiveand rigorous introduction to the fundamentalconcepts, mathematical formulation, alternativeapproaches, and predictions of this evolvingfield. It covers advanced numerical methods forsimulating the motion of rigid particles(platelets) and the flow-induced deformation ofliquid capsules and cells enclosed by viscoelasticmembranes. MATLAB® code and other data areavailable on the book’s website.







Mathematics for Biology and Medicine

New!

MultiscaleCancer ModelingEdited by

Thomas S. DeisboeckMassachusetts General Hospitaland Harvard Medical School,Boston, USA

Georgios S. StamatakosInstitute of Communication and Computer Systems,National Technical University of Athens, Greece

With contributions from some of the top in silicomodeling groups in the United States andEurope, Multiscale Cancer Modeling discussesthe scientific and technical expertise necessaryto conduct innovative cancer modeling researchacross scales. It presents modeling methods and results at the forefront of cancer simulationat all levels of biocomplexity and explains howcombinations of multilevel cancer models canenhance our understanding of cancer and canhelp optimize its treatment.


Textbook

DifferentialEquations andMathematicalBiologySecond EditionD.S. JonesUniversity of Dundee, ScotlandM.J. PlankUniversity of Canterbury, Christchurch, New ZealandB.D. SleemanUniversity of Leeds, UK

“… more valuable and better motivated thanever …The writing is clear, though the model-ing is not oversimplified. … The authors deservecongratulations as well as course adoptions.”

—SIAM Review, Sept. 2010, Vol. 52, No. 3

“…a very solid book … The authors succeedbecause they do a splendid job of integratingtheir treatment of differential equations withthe applications …”

—MAA Reviews, April 2010Download MATLAB® files at www.crcpress.com


New!

Introduction toComputationalProteomicsGolan YonaStanford University, California, USA

A thorough introduction toproteome analysis, thisbook tackles the different steps and problemsinvolved with protein analysis, classification, andmeta-organization. It starts with the analysis ofindividual entities and works its way through theanalysis of more complex entities, from proteinfamilies to interactions, cellular pathways, andgene networks. Software downloads, data sets,and other material are available at biozon.org

Catalog no. C5556, November 2010, c. 688 pp.ISBN: 978-1-58488-555-9, $89.95 / £57.99

Textbook

Algorithms inBioinformaticsA PracticalIntroductionWing-Kin SungNational University of Singapore

“…a timely publicationthat details several algorithms widely used inbioinformatics. … This work can serve as a ref-erence guide for students and researchersattempting to implement or learn algorithmsrelevant to bioinformatics. … Summing Up:Recommended.”

—CHOICE, June 2010Access supplementary material on the author’s website Solutions manual available for qualifying instructors






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Mathematics for Biology and Medicine / Operations Research


New!Textbook

BiologicalComputationEhud LammTel-Aviv University, Israel

Ron UngerBar-Ilan University, Ramat-Gan, Israel

“This is a wonderful treatise on bio-inspiredcomputation, written from a computer scienceperspective. The authors are extremely knowl-edgeable about their subject, and the materialthey cover is both broad and deep. The bookshould benefit anyone interested in the connec-tion between computer science and biology … .”

—David Harel, The William Sussman ProfessorialChair, Department of Computer Science andApplied Mathematics, Weizmann Institute of

Science, Rehovot, Israel

Catalog no. C7959, November 2010, c. 344 pp.ISBN: 978-1-4200-8795-6, $79.95 / £49.99

New!

ConceptualModeling forDiscrete-EventSimulationEdited by

Stewart Robinson, Roger Brooks, Kathy Kotiadis, and Durk-Jouke Van Der Zee

Bringing together an international group ofleading researchers from computer science,operational research, engineering, and other disciplines, this volume provides comprehensivecoverage of the state of the art in simulationconceptual modeling. It guides readers throughthe conceptual modeling process and presentsapplications in the military, business, and healthsectors. Each of the book’s six parts focuses on a different aspect of conceptual modeling forsimulation.


New!Textbook

An Introductionto StochasticProcesses withApplications toBiologySecond EditionLinda J.S. AllenTexas Tech University, Lubbock, USA

With MATLAB® throughout, this book is organ-ized according to the three types of stochasticprocesses: discrete time Markov chains, continu-ous time Markov chains, and continuous timeand state Markov processes. This edition containsa new chapter on the biological applications ofstochastic differential equations and new sectionson alternative methods for derivation of a sto-chastic differential equation, data and parameterestimation, Monte Carlo simulation, and more.


Optimal Designof QueueingSystemsShaler Stidham, Jr.University of North Carolina,Chapel Hill, USA

Written by a long-time, recognized researcher onmodels for the optimaldesign and control of queues and networks ofqueues, this book explores how to set theparameters of a queueing system, before put-ting it into operation. It considers various optimality criteria, including individual, social,class, and facility optimal solutions. The bookshows how design models can control flow toachieve a variety of objectives.







Operations Research

Textbook

Linear andNonlinearProgrammingwith Maple™An Interactive,Applications-BasedApproachPaul E. FishbackGrand Valley State University, Allendale, Michigan, USA

Integrating a hands-on learning approach, astrong linear algebra focus, Maple™ software,and real-world applications, this text introducesthe mathematical concepts and principlesunderlying linear and nonlinear programming. Itdraws on the simplex method to develop themajor ideas of duality and sensitivity analysis andprovides applications and exercises from variousdisciplines. Maple worksheets and code areavailable on the book’s website.

Catalog no. C064X, January 2010, 413 pp.ISBN: 978-1-4200-9064-2, $89.95 / £57.99

Textbook

Introduction toProbability withMathematica®Second EditionKevin J. HastingsKnox College, Galesburg, Illinois, USA

This second edition showshow to easily create simulations from templatesand solve problems using Mathematica® 7.0.Along with new sections on order statistics,transformations of multivariate normal randomvariables, and Brownian motion, this editionoffers an expanded section on Markov chains,more example data of the normal distribution,and more attention on conditional expectation.It also includes problems from Actuarial Exam P.The accompanying CD-ROM contains updatedMathematica notebooks.Solutions manual available for qualifying instructors


Textbook

Modeling andAnalysis ofStochasticSystemsSecond EditionVidyadhar G. KulkarniUniversity of North Carolina,Chapel Hill, USA

This text covers the most important classes ofstochastic processes used in the modeling ofdiverse systems. Along with new appendicesthat collect results from analysis and differentialand difference equations, this edition contains anew chapter on diffusion processes with appli-cations to finance. It also offers a more stream-lined, application-oriented approach to renewal,regenerative, and Markov regenerative process-es. Download MATLAB®-based programs fromthe author’s website. Solutions manual available for qualifying instructors


Textbook

StochasticProcessesAn Introduction,Second EditionPeter W. Jones and Peter SmithKeele University, Staffordshire, UK

Using Mathematica® and R,this updated text discusses the modeling andanalysis of random experiments using the theo-ry of probability. It illustrates discrete randomprocesses through the classical gambler’s ruinproblem and its variants, covers continuous random processes, and provides many workedexamples and problems. The book’s websiteincludes the Mathematica and R programs.Solutions manual available for qualifying instructors viapassword on the book’s website

Catalog no. K10004, January 2010, 232 pp.Soft CoverISBN: 978-1-4200-9960-7, $79.95 / £34.99





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mathematics - october 2010

Documents

orthogonal spaces

introducesvector spaces

introductory mathematics

inner product spaces

treatmentof symplectic

simple results

tensor products

vector spacesand