Mathematics Textbooks - August 2010

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Contents

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

Discrete Mathematics/Combinatorics....................7

Differential Equations ..........................................12

Introductory Mathematics ..................................13

Mathematical Modeling ......................................16

Mathematics for Finance......................................17

Algebraic Geometry and Number Theory ..........20

Real, Complex, and Functional Analysis ..............20

Mathematics for Engineering ..............................23

Mathematics for Biology/

Computational Biology ........................................28

Probability Theory and Applications ....................29

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Algebra

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New!

Finite-Dimensional Linear AlgebraMark S. GockenbachMichigan Technological University, Houghton, USA

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

Drawing on material from the author’s owncourse, this textbook gives students a strong the-oretical understanding of linear algebra. It offersmany illustrations of how linear algebra is usedthroughout mathematics in such diverse areas ascombinatorics, differential equations, optimiza-tion, and approximation. The author takes stu-dents through an axiomatic development of vec-tor spaces, linear operators, eigenvalues, norms,and inner products. In addition to discussing thespecial properties of symmetric matrices, he cov-ers the Jordan canonical form, an important the-oretical tool, and the singular value decomposi-tion, a powerful tool for computation. The finalchapters present introductions to numerical linearalgebra and analysis in vector spaces.

Features

• Provides a thorough foundation for the studyof advanced mathematics

• Contains a range of exercises in each section,including some that can be solved using acomputer package such as MATLAB®

• Incorporates mini-projects that encouragestudents to develop topics not covered in thetext

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

• Presents important concepts and methodsfrom numerical linear algebra

Solutions manual available for qualifying instructors

Contents

Some Problems Posed on Vector SpacesFields and Vector SpacesLinear OperatorsDeterminants and EigenvaluesThe Jordan Canonical FormThe Spectral Theory of Symmetric MatricesThe spectral theorem for symmetric matrices The spectral theorem for normal matricesOptimization and the Hessian matrixLagrange multipliers Spectral methods for differential equationsThe Singular Value DecompositionThe SVD for general matrices Solving least-squares problems using the SVD The SVD and linear inverse problems The Smith normal form of a matrixMatrix Factorizations and Numerical LinearAlgebra

The LU factorization Partial pivoting The Cholesky factorization Matrix norms The sensitivity of linear systems to errors Numerical stability The sensitivity of the least-squares problem The QR factorization Eigenvalues and simultaneous iteration The QR algorithmAnalysis in Vector SpacesAnalysis in Rn

Infinite-dimensional vector spaces Functional analysisWeak convergence

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Algebra

Applied AlgebraCodes, Ciphers and Discrete 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

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

Designed for an applied algebra course for stu-dents who have had prior classes in abstract orlinear algebra, this text presents practical meth-ods for solving problems in data security and dataintegrity. While the content has been reworkedand improved, this edition continues to covermany algorithms that arise in cryptography anderror-control codes.

New to the Second Edition

• Double the number of exercises

• New appendix that reviews prerequisite top-ics in algebra and number theory

• A CD-ROM containing an interactive versionof the book that is powered by ScientificNotebook®

• Interactive examples

• Computing hints

• Self-tests

• Some details of problem solutions beyondthose in the printed text

Explaining the mathematics as needed, this textthoroughly explores how mathematical tech-niques can be used to solve practical problems. Itincludes algorithms that offer common-senseapproaches to problems, such as computinglarge powers, and explains the Rijndael algorithmto help students understand the data encryptionstandard.


Contents

Integers and Computer Algebra

Codes

Euclidean Algorithm

Ciphers

Error-Control Codes

Chinese Remainder Theorem

Theorems of Fermat and Euler

Public Key Ciphers

The Rivest–Shamir–Adleman Cipher System

Electronic Signatures

A System for Exchanging Messages

Knapsack Ciphers

Digital Signature Standard

Finite Fields

Error-Correcting Codes

BCH Codes

A BCH Decoder

Reed–Solomon Codes

Advanced Encryption Standard

Polynomial Algorithms and Fast FourierTransforms

Lagrange Interpolation Formula

Kronecker’s Algorithm

Neville’s Iterated Interpolation Algorithm

Secure Multiparty Protocols

Discrete Fourier Transforms

Fast Fourier Interpolation

Solutions to Odd Problems



5

Algebra


A Modern Introduction to Linear AlgebraHenry RicardoMedgar Evers College, Brooklyn, New York, USA

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

“This work is a sound presentation of linear alge-bra. … Each topic is carefully and thoroughlycovered via the pedagogy … The volume includesmore than 1,200 exercises, some to be complet-ed manually and others intended to be solvedusing a computer algebra system. … The gener-ality of approach makes this work appropriatefor students in virtually any discipline. SummingUp: Recommended.”

—CHOICE, June 2010

“The author of this text, Henry Ricardo, has iden-tified several shortcomings of typical courses onlinear algebra and provides an exciting offering,how to overcome them …”

—Matthias Gobbert, University of Maryland, Baltimore, USA

Features

• Provides a rigorous yet accessible matrix-oriented introduction to the essential concepts of linear algebra

• Follows the recommendations for a firstcourse in linear algebra provided by theLinear Algebra Curriculum Study Group,Augmenting the Teaching of Linear Algebrathrough the use of Software Tools project,and the Linear Algebra Modules Project

• Contains numerous exercises of varying levelsof difficulty

• Reviews basic mathematical tools in theappendices

• Presents proofs for nearly all results

• Includes a host of examples and variousapplications reflecting some of the many disciplines that use linear algebra


Contents

VectorsSystems of EquationsMatrix AlgebraEigenvalues, Eigenvectors, and DiagonalizationVector SpacesLinear TransformationsLinear Transformations The Range and Null Space of a LinearTransformation

The Algebra of Linear Transformations Matrix Representation of a Linear Transformation Invertible Linear Transformations Isomorphisms Similarity Similarity Invariants of OperatorsInner Product SpacesComplex Vector Spaces Inner Products Orthogonality and Orthonormal BasesThe Gram–Schmidt Process Unitary Matrices and Orthogonal Matrices Schur Factorization and the Cayley–HamiltonTheorem

The QR Factorization and Applications Orthogonal Complements ProjectionsHermitian Matrices and Quadratic FormsLinear Functionals and the Adjoint of anOperator

Hermitian Matrices Normal MatricesQuadratic Forms Singular Value DecompositionThe Polar DecompositionAnswers/Hints to Odd-Numbered Problems




Algebra

AbstractAlgebraAn InteractiveApproachWilliam PaulsenArkansas State University,Jonesboro, USA

“The textbook gives an introduction to algebra.… The book can be used for an undergraduate-level course or a second semester graduate-levelcourse.”

—Gerhard Pfister, Zentralblatt MATH 1173

Features

• Offers the option of using technology in theclassroom by incorporating GAP andMathematica® commands

• Discusses topics not covered in similar texts,such as semi-direct products and skew fields

• Includes many diagrams produced byMathematica to help students visualize diffi-cult concepts, such as homomorphisms andpermutations

• Contains numerous homework problems ofboth the interactive and standard types

• Provides a CD-ROM with GAP packages andMathematica notebooks


Contents

Understanding the Group Concept. TheStructure within a Group. Patterns within theCosets of Groups. Mappings between Groups.Permutation Groups. Building Larger Groupsfrom Smaller Groups. The Search for NormalSubgroups. Solvable and Insoluble Groups.Introduction to Rings. The Structure withinRings. Integral Domains and Fields. UniqueFactorization. Finite Division Rings. The Theoryof Fields. Galois Theory. Bibliography. Answers toOdd Problems. Index.

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

New!

AdvancedLinear AlgebraBruce CoopersteinUniversity of California, SantaCruz, USA

Designed for advanced undergraduate andbeginning graduate students, this textbook focus-es on vector spaces and the maps between themthat preserve their structure (linear transforma-tions). Starting with familiar concepts and slowlybuilding to deeper results, it shows students thebeauty of linear algebra and prepares them forfurther study in mathematics. The author discuss-es the structure theory of an operator, varioustopics on inner product spaces, and the trace anddeterminant functions of a linear operator. Healso covers bilinear forms with a full treatment ofsymplectic spaces and orthogonal spaces andexplains the construction of tensor, symmetric,and exterior algebras.

Features

• Takes a gentle approach that gradually buildsfrom simple concepts to complex ideas andresults

• Begins each section with an outline of previ-ously introduced concepts and results neces-sary for mastering the new material

• Includes a wide variety of exercises and prob-lems, with selected solutions in the appen-dices


Contents

Vector Spaces. Linear Transformations.Polynomials. Theory of a Single Linear Operator.Inner Product Spaces. Linear Operators on InnerProduct Spaces. Trace and Determinant of aLinear Operator. Bilinear Maps and Forms.Tensor Products. Appendices. Index.

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



7

Discrete Mathematics/Combinatorics


New!

How to CountAn Introduction to Combinatorics, Second EditionR.B.J.T. Allenby and Alan SlomsonUniversity of Leeds, UK

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

Completely revised, this textbook shows how tosolve numerous classic and other interesting com-binatorial problems. The authors take an easilyaccessible approach that introduces problemsbefore leading into the theory involved.

This second edition incorporates 50 percent morematerial. It includes seven new chapters thatcover occupancy problems, Stirling and Catalannumbers, graph theory, trees, Dirichlet’s pigeon-hole principle, Ramsey theory, and rook polyno-mials. This edition also contains more than 450exercises.

Ideal for a first course in combinatorics, this textrequires only a modest amount of mathematicalbackground. In an engaging way, it covers manycombinatorial tools, such as the inclusion-exclu-sion principle, generating functions, recurrencerelations, and Pólya’s counting theorem.

Features

• Explains how to solve various combinatorialproblems

• Uses problems to introduce the theory

• Contains enough material for a short courseon graph theory

• Presents proofs of key results as well asnumerous worked examples

• Includes paired exercises, along with a fullsolution to one of the exercises in each pair

• Lists suggestions for further reading


Contents

Permutations and Combinations

Occupancy Problems

The Inclusion-Exclusion Principle

Stirling and Catalan Numbers

Partitions and Dot Diagrams

Generating Functions and Recurrence Relations

Partitions and Generating Functions

Introduction to Graphs

Trees

Groups of Permutations

Group Actions

Counting Patterns

Pólya Counting

Dirichlet’s Pigeonhole Principle

Ramsey Theory

Rook Polynomials and Matchings

Solutions to the A Exercises





New!

Introduction to Cryptography withMathematical Foundations and ComputerImplementationsAlexander StanoyevitchCalifornia State University–Dominguez Hills, Carson, USA

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

From the exciting history of its development inancient times to the present day, this self-con-tained introduction provides a focused tour of thecentral concepts of cryptography, suitable for awide variety of mathematics and computer sci-ence courses. Rather than present an encyclope-dic treatment of topics in cryptography, the textdelineates cryptographic concepts in chronologi-cal order, developing the mathematics as needed.

Written in an engaging yet rigorous style, eachchapter introduces important concepts with cleardefinitions and theorems. Numerous examplesexplain key points while figures and tables helpillustrate more difficult or subtle concepts. Eachchapter is punctuated with “Exercises for theReader;” complete solutions for these are includ-ed in an appendix. Carefully crafted exercise setsare also provided at the end of each chapter, anddetailed solutions to most odd-numbered exercis-es can be found in a designated appendix.

The computer implementation section at the endof every chapter guides students through theprocess of writing their own programs. A sup-porting website provides an extensive set of sam-ple programs as well as downloadable platform-independent applet pages for some core pro-grams and algorithms.


Contents

Divisibility and Modular Arithmetic The Evolution of Codemaking until theComputer EraMatrices and the Hill CryptosystemThe Evolution of Codebreaking until theComputer EraRepresentation and Arithmetic of Integers inDifferent BasesBlock Cryptosystems and the DataEncryption Standard (DES) Some Number Theory and AlgorithmsPublic Key Cryptography Finite Fields in General and GF(28) inParticularThe Advanced Encryption Standard (AES)ProtocolElliptic Curve CryptographyElliptic Curves over the Real Numbers The Addition Operation for Elliptic Curves GroupsElliptic Curves over ZpThe Variety of Sizes of Modular Elliptic Curves The Addition Operation for Elliptic Curves overZp

The Discrete Logarithm Problem on ModularElliptic Curves

An Elliptic Curve Version of the Diffie–HellmanKey Exchange

Fast Integer Multiplication of Points on ModularElliptic Curves

Representing Plaintexts on Modular Elliptic Curves An Elliptic Curve Version of the El GamalCryptosystem

A Factoring Algorithm Based on Elliptic CurvesExercises and Computer Implementations appearat the end of each chapter. Solutions and othermaterial are available in the appendices.



9



New!

Access Control, Security, and TrustA Logical ApproachShiu-Kai Chin and Susan OlderSyracuse University, New York, USA

Catalog no. C8628, July 2010, 351 pp.ISBN: 978-1-58488-862-8, $89.95

Developed from the authors’ courses at SyracuseUniversity and the U.S. Air Force ResearchLaboratory, this book equips students with anaccess control logic they can use to specify andverify their security designs. Throughout the text,the authors use a single access control logic basedon a simple propositional modal logic. Taking alogical, rigorous approach to access control, theyshow students how logic is a useful tool for ana-lyzing security designs and spelling out the condi-tions upon which access control decisions depend.

The first part of the book presents the syntax andsemantics of access control logic, basic access con-trol concepts, and an introduction to confidential-ity and integrity policies. The second section cov-ers access control in networks, delegation, proto-cols, and the use of cryptography. In the third sec-tion, the authors focus on hardware and virtualmachines. The final part discusses confidentiality,integrity, and role-based access control.

Features

• Employs propositional modal logic to explainaccess control principles

• Shows how to perform derivations and calcu-lations with mathematical precision andaccuracy

• Presents numerous examples ranging fromthe control of physical memory in hardwareto multilevel security policies

• Includes exercises that deal with application,analysis, synthesis, and evaluation

• Offers HOL-4 implementation and slides foreach chapter available for download onwww.crctextbooks.com


Contents

Access Control, Security, Trust, and Logic

PRELIMINARIES

A Language for Access Control

Reasoning about Access Control

Basic Concepts

Security Policies

DISTRIBUTED ACCESS CONTROL

Digital Authentication

Delegation

Networks: Case Studies

ISOLATION AND SHARING

A Primer on Computer Hardware

Virtual Machines and Memory Protection

Access Control Using Descriptors andCapabilities

Access Control Using Lists and Rings

ACCESS POLICIES

Confidentiality and Integrity Policies

Role-Based Access Control

A Summary and list of Further Reading appear atthe end of each chapter.





Discrete MathematicsProofs, Structures, and Applications, Third EditionRowan GarnierSurrey, UK

John TaylorUniversity of Brighton, UK


“This is a textbook on discrete mathematics forundergraduate students in computer science andmathematics. … The style of exposition is veryclear, step by step and the level is well adaptedto undergraduates in computer science. Thetreatment is mathematically rigorous; thereforeit is also suitable for mathematics students.Besides the theory, there are many concreteexamples and exercises (with solutions!) to devel-op the routine of the student. So I can recom-mend warmly this book as a textbook for acourse. It looks very attractive and has a nicetypography. …”

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

This third edition continues to provide a rigorousyet accessible exposition of discrete mathematics,including the core mathematical foundation ofcomputer science. In the expanded first chapter,the text includes a new section on the formalproof of the validity of arguments in proposition-al logic before moving on to predicate logic. Thisedition also contains a new chapter on elemen-tary number theory and congruences. This chap-ter explores groups that arise in modular arith-metic and RSA encryption, a widely used publickey encryption scheme that enables practical andsecure means of encrypting data.


Contents

Logic

Mathematical Proof

Sets

Relations

Functions

Matrix Algebra

Systems of Linear Equations

Algebraic Structures

Introduction to Number Theory

Boolean Algebra

Introduction

Properties of Boolean Algebras

Boolean Functions

Switching Circuits

Logic Networks

Minimization of Boolean Expressions

Graph Theory

Applications of Graph Theory

Introduction

Rooted Trees

Sorting

Searching Strategies

Weighted Graphs

The Shortest Path and Traveling SalesmanProblems

Networks and Flows

Hints and Solutions to Selected Exercises



11



AppliedCombinatoricsSecond EditionFred S. RobertsRutgers University, Piscataway,New Jersey, USA

Barry TesmanDickinson College, Carlisle,Pennsylvania, USA

“This is an overwhelmingly complete introducto-ry textbook in combinatorics. It not only coversnearly every topic in the subject, but gives sever-al realistic applications for each topic. … muchmore breadth than its competitors. …”

—MAA Reviews, Dec. 2009

“The writing style is excellent. … The explana-tions are detailed enough that the students canfollow the arguments readily. The motivatingexamples are a truly strong point for the text. Noother text with which I am familiar comes evenclose to the number of applications presentedhere.”

—John Elwin, San Diego State University, California,USA

“This book is a required textbook for my gradu-ate course in discrete mathematics. … an excel-lent resource … clearly reinforces both the prac-tical and theoretical understanding in a way stu-dents are able to correlate. …”

—Dawit Haile, Virginia State University, Petersburg,USA

Now with solutions to selected problems

Contents

What Is Combinatorics? THE BASIC TOOLS OFCOMBINATORICS: Basic Counting Rules.Introduction to Graph Theory. Relations. THECOUNTING PROBLEM: Generating Functionsand Their Applications. Recurrence Relations.The Principle of Inclusion and Exclusion. ThePólya Theory of Counting. THE EXISTENCEPROBLEM: Combinatorial Designs. CodingTheory. Existence Problems in Graph Theory.COMBINATORIAL OPTIMIZATION: Matchingand Covering. Optimization Problems for Graphsand Networks. Appendix. Indices.

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

Coming soon!

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

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

This textbook is primarily for undergraduate stu-dents in mathematics taking an introductorycourse in combinatorics. It briefly discusses sever-al examples of typical combinatorial problemsand provides basic information on sets, prooftechniques, enumeration, and graph theory. Thenext few chapters explore the pigeonhole princi-ple, inclusion/exclusion, and enumerative func-tions and the relations between them. Theauthors describe generating functions and recur-rences, important families of functions, and thetheorems of Pólya and Redfield. They also presentintroductions to computer algebra and grouptheory, before considering graphs, codes, Latinsquares, and experimental designs. The last chap-ter further illustrates the interaction between lin-ear algebra and combinatorics.

Features

• Provides background material in the appen-dices on sets, induction, proof techniques,vectors, and matrices

• Includes exercises and problems in eachchapter, with some solutions at the back ofthe book

• Discusses Maple™, Mathematica®, and othertechnological tools where appropriate

Contents

Introduction. Fundamentals of Enumeration. ThePigeonhole Principle and Ramsey’s Theorem. ThePrinciple of Inclusion and Exclusion. GeneratingFunctions and Recurrence Relations. Catalan, Belland Stirling Numbers. Symmetries and thePólya–Redfield Method. Introduction to GraphTheory. Further Graph Theory. Coding Theory.Latin Squares. Balanced Incomplete BlockDesigns. Linear Algebra Methods inCombinatorics. Appendices. Solutions to Set AExercises. Hints for Problems. Solutions toProblems. References. Index.

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




Differential Equations

New!

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

Bringing the computer into the classroom, thistext emphasizes the use of computer software inteaching linear and nonlinear differential equa-tions and systems. Designed to be independentof any particular software package, the bookincludes a CD-ROM with the software used togenerate the solutions and graphs for the exam-ples. The appendices contain complete instruc-tions for running the software.

Features

• Provides an even balance between theory,computer solution, and application

• Includes numerical case studies that highlightpossible pitfalls when computing a numericalsolution without first considering the appro-priate theory

• Shows how to solve population growth, epi-demic, and predator-prey models

• Requires no prior knowledge of program-ming languages


Contents

Introduction. The Initial Value Problem y′ = f(x, y); y(c) =d. Applications of the Initial ValueProblem y′ = f (x, y); y(c) =d. N-th OrderLinear Differential Equations. The LaplaceTransform Method. Applications of LinearDifferential Equations with Constant Coefficients.Systems of First-Order Differential Equations.Linear Systems of First-Order DifferentialEquations. Applications of Linear Systems withConstant Coefficients. Applications of Systems ofEquations. Appendices. Answers to SelectedExercises. References. Index.

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

New!

SolutionTechniques forElementaryPartialDifferentialEquationsSecond EditionChristian ConstandaUniversity of Tulsa, Oklahoma, USA

“This concise, well-written book, which includesa profusion of worked examples and exercises,serves as an excellent text in undergraduate andgraduate learning … .”

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

“… In my opinion, this is quite simply the bestbook of its kind that I have seen thus far. Thebook not only contains solution methods forsome very important classes of PDEs, in an easy-to-read format, but is also student-friendly andteacher-friendly at the same time. It is definitelya textbook that should be adopted.”—From the Foreword by Peter Schiavone, University of

Alberta, Edmonton, Canada

Winner of the 2002 CHOICE OutstandingAcademic Title Award!


Contents

Ordinary Differential Equations: Brief Revision.Fourier Series. Sturm–Liouville Problems. SomeFundamental Equations of Mathematical Physics.The Method of Separation of Variables. LinearNonhomogeneous Problems. The Method ofEigenfunction Expansion. The FourierTransformations. The Laplace Transformation.The Method of Green’s Functions. GeneralSecond-Order Linear Partial DifferentialEquations with Two Independent Variables. TheMethod of Characteristics. Perturbation andAsymptotic Methods. Complex VariableMethods. Answers to Odd-Numbered Exercises.Appendix. Bibliography. Index.

Catalog no. K10569, June 2010, 343 pp.Soft Cover, ISBN: 978-1-4398-1139-9, $69.95



13

Introductory Mathematics


New!

A Concise Introduction to Pure MathematicsThird EditionMartin LiebeckImperial College, London, UK

Catalog no. K11624, August 2010, 268 pp.Soft Cover, ISBN: 978-1-4398-3598-2, $59.95

“… When I used it for a course, students couldnot get enough … . The material is very well cho-sen and arranged, and teaching from Liebeck’sbook has in many different ways been among mymost rewarding teaching experiences during thelast 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 proof willno longer be foreign, but also mathematics willnot be viewed as some abstract black box. …”

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

A robust bridge between high school and higherlevel mathematics, this text presents some of themost fundamental and beautiful ideas in puremathematics. It covers not only standard materialbut also many interesting topics not usuallyencountered at this level. This third edition con-tains three new chapters that provide an intro-duction to mathematical analysis. It also includessolutions to the odd-numbered exercises.

Features

• Describes methods for writing proofs

• Develops the theory of basic number sys-tems, including integers, real numbers, andcomplex numbers, from first principles

• Covers important topics, such as solvingcubic equations, studying the five Platonicsolids, coding secret information, and com-paring the sizes of two infinite sets

• Contains new chapters on mathematicalanalysis that offer an introduction to the the-ory of limits and continuous functions

• Includes a range of exercises, with solutionsto odd-numbered problems at the back ofthe book

• Requires only a solid foundation in highschool mathematics


Contents

Sets and Proofs

Number Systems

Decimals

Inequalities

nth Roots and Rational Powers

Complex Numbers

Polynomial Equations

Induction

Euler’s Formula and Platonic Solids

The Integers

Prime Factorization

More on Prime Numbers

Congruence of Integers

More on Congruence

Secret Codes

Counting and Choosing

More on Sets

Equivalence Relations

Functions

Permutations

Infinity

Introduction to Analysis: Bounds

More Analysis: Limits

Yet More Analysis: Continuity

Solutions to Odd-Numbered Exercises

Further Reading

Index of Symbols

Index




Introduction to Mathematical LogicFifth EditionElliott MendelsonQueens College, Flushing, New York, USA


“Since its first edition, this fine book has been atext of choice for a beginner’s course on mathe-matical logic. … There are many fine books onmathematical logic, but Mendelson’s textbookremains a sure choice for a first course for itsclear explanations and organization: definitions,examples and results fit together in a harmonicway, making the book a pleasure to read. …”

—MAA Reviews, Dec. 2009

Retaining all the key features of its predecessors,this fifth edition of a long-established, bestsellingtext covers the basic topics of a solid first coursein mathematical logic. This edition includes a newsection covering basic ideas and results aboutnonstandard models of number theory, a secondappendix that introduces modal propositionallogic, an expanded bibliography, and additionalexercises and selected answers.

Continuing to expose students to natural proofsand set-theoretic methods, the author explorespropositional logic, first-order logic, first-ordernumber theory, axiomatic set theory, and the the-ory of computability. He also discusses the majorresults of Gödel, Church, Kleene, Rosser, andTuring.

Features

• Provides a compact introduction to the prin-cipal topics of mathematical logic

• Presents the fundamental assumptions andproof techniques that form the basis of math-ematical logic

• Includes many examples and exercises

ContentsThe Propositional CalculusFirst-Order Logic and Model TheoryQuantifiersFirst-Order Languages and Their Interpretations.Satisfiability and Truth. Models

First-Order TheoriesProperties of First-Order Theories Additional Metatheorems and Derived Rules Rule C Completeness Theorems First-Order Theories with EqualityDefinitions of New Function Letters andIndividual Constants

Prenex Normal Forms Isomorphism of Interpretations. Categoricity ofTheories

Generalized First-Order Theories. Completenessand Decidability

Elementary Equivalence. Elementary ExtensionsUltrapowers: Nonstandard AnalysisSemantic Trees Quantification Theory Allowing Empty DomainsFormal Number Theory Axiomatic Set TheoryAn Axiom System Ordinal Numbers Equinumerosity. Finite and Denumerable Sets Hartogs’ Theorem. Initial Ordinals. OrdinalArithmetic

The Axiom of Choice. The Axiom of RegularityOther Axiomatizations of Set TheoryComputability Algorithms. Turing Machines Diagrams Partial Recursive Functions. Unsolvable ProblemsThe Kleene–Mostowski Hierarchy. RecursivelyEnumerable Sets

Other Notions of ComputabilityDecision ProblemsAnswers to Selected Exercises



15



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

Presenting a fun and interesting way to teach anintroductory mathematics course, this bookshows students how discrete probability, statis-tics, and elementary discrete mathematics areused in games, sports, and gambling situations. Itdraws on numerous examples, questions, andproblems to explain the application of mathe-matical theory to various real-life games. Onlyrequiring high school algebra, the text offers flex-ibility in choosing what material to cover in abasic mathematics course. For each topic, theauthor includes exercises based on real gamesand sports data.

Features

• Encourages students to think mathematicallyand apply the fundamentals to real gamingsituations

• Explores concepts, such as binomial distribu-tions and combinatorics, through commongames and sports, including backgammon,poker, roulette, baseball, football, and hockey

• Discusses more unusual topics, such as math-ematical card tricks and old TV shows

• Contains many in-class group problems andhomework exercises

Contents

Basic Probability. The Game’s Afoot. RepeatedPlay. Card Tricks and More. Dealing with Data.Testing and Relationships. Games and Puzzles.Combinatorial Games. Appendix. References.Index.


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

Written in a conversational style, yet maintainingthe proper level of mathematical rigor, this acces-sible textbook teaches students how to reasonlogically, read proofs critically, and write validmathematical proofs. It facilitates a smooth tran-sition from courses designed to develop compu-tational skills and problem solving abilities tocourses that emphasize theorem proving. In theappendix, the author includes some basic guide-lines to follow when writing proofs.

Features

• Provides a thorough presentation of logic byincluding both formal and informal proofs

• Explains how to develop integers from natu-ral numbers, rational numbers from integers,and real numbers from rational numbers

• Proves many theorems from different areas inmathematics

• Illustrates how to write proofs and solveproblems through numerous examples

• Presents several biographical sketches andhistorical comments

• Defines numerous technical terms

• Includes many exercises of varying difficultyat the end of each section


Contents

Logic. Deductive Mathematical Systems andProofs. Set Theory. Relations. Functions.Mathematical Induction. Cardinalities of Sets.Proofs from Group Theory. Appendix. Answersto Selected Exercises. References. Index.





Mathematical Modeling

An IntegratedIntroduction toComputerGraphics andGeometricModelingRonald GoldmanRice University, Houston, Texas,USA

“… this book may be the first book on geometricmodeling that also covers computer graphics. Inaddition, it may be the first book on computergraphics that integrates a thorough introductionto ‘freedom’ curves and surfaces and to themathematical foundations for computer graph-ics. … the book is well suited for an undergradu-ate course. … The entire book is very well pre-sented and obviously written by a distinguishedand creative researcher and educator. It certain-ly is a textbook I would recommend. …”

—Computer-Aided Design, 42, 2010

“… The author has used his experiences of teach-ing and research to write a book that will, I amsure, become a valuable reference source foryears to come. …”

—International Statistical Review, 2010

Taking a novel, more appealing approach thancurrent texts, this book focuses on graphics, mod-eling, and mathematical methods. The authoralso brings back the turtle from obscurity to intro-duce several major concepts in computer graph-ics. The text includes many exercises and pro-gramming projects as well as PowerPoint slideson a website.

Contents

Two-Dimensional Computer Graphics: FromCommon Curves to Intricate Fractals.Mathematical Methods for Three-DimensionalComputer Graphics. Three-DimensionalComputer Graphics: Realistic Rendering.Geometric Modeling: Freedom Curves andSurfaces. Further Readings. Index.


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

“ … The book can be recommended to advancedundergraduate students for whom mathematicsis a bit more than just proving theorems.Teachers can find suggestions for motivations forintroductory parts of lectures on ordinary differ-ential equations and partial differential equa-tions.”

—EMS Newsletter, Sept. 2009

Integrating real-world applications into the tradi-tional mathematics curriculum, this text providesstudents with a fundamental understanding ofhow mathematics is applied to problems in sci-ence and engineering. For each case study prob-lem, the authors discuss why a model is neededand what goals can be achieved with the model.

Exploring what mathematics can reveal aboutapplications, the book focuses on the design ofappropriate experiments to validate the develop-ment of mathematical models. It guides studentsthrough the modeling process, from empiricalobservations and formalization of properties tomodel analysis and interpretation of results. Onthe included CD-ROM, students can downloadreal experimental data for projects presented asexercises in the book.

Contents

Introduction: The Iterative Modeling Process.Modeling and Inverse Problems. Mathematicaland Statistical Aspects of Inverse Problems. MassBalance and Mass Transport. Heat Conduction.Structural Modeling: Force/Moments Balance.Beam Vibrational Control and Real-TimeImplementation. Wave Propagation. Size-Structured Population Models. Appendices.




17

Mathematics for Finance


New!

Portfolio OptimizationMichael J. BestUniversity of Waterloo, Ontario, Canada

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

Eschewing a more theoretical approach,Portfolio Optimization shows students how themathematical tools of linear algebra and opti-mization can quickly and clearly formulate impor-tant ideas on the subject. This practical bookextends the concepts of the Markowitz “budgetconstraint only” model to a linearly constrainedmodel. Through reading the book, students seehow the basic portfolio optimization problemhelps in choosing profitable investments.

The text includes MATLAB® to help with problemsolving. Although the author clearly describeshow to implement each technique by hand, heincludes several MATLAB programs designed toimplement the methods and offers these pro-grams on the accompanying CD-ROM.

Features

• Requires only elementary linear algebra

• Uses MATLAB to help with problem solving

• Includes exercises at the end of each chapter

• Provides a CD-ROM with MATLAB programs

• Explains how the basic portfolio optimizationproblem can help determine the optimalinvestment of an investor’s wealth in eachasset owned

• Develops the key ideas of portfolio optimiza-tion from the topics of optimization and lin-ear algebra

• Explores how quadratic programming isessential to solving practical portfolio opti-mization problems


ContentsOptimizationQuadratic MinimizationNonlinear OptimizationExtreme PointsComputer ResultsThe Efficient FrontierThe Efficient FrontierComputer ResultsThe Capital Asset Pricing ModelThe Capital Market LineThe Security Market LineComputer ResultsSharpe Ratios and Implied Risk-Free ReturnsDirect DerivationOptimization DerivationFree Solutions to ProblemsComputer ResultsQuadratic Programming GeometryGeometry of Quadratic Programs (QPs)The Geometry of QP Optimality ConditionsThe Geometry of Quadratic FunctionsOptimality Conditions for QPsA QP Solution AlgorithmQPSolver: A QP Solution AlgorithmComputer ResultsPortfolio Optimization with Linear InequalityConstraints

An ExampleThe General CaseComputer ResultsDetermination of the Entire Efficient FrontierPQPSolver: Generates the Entire Efficient FrontierComputer ResultsSharpe Ratios under Constraints and KinksSharpe Ratios under ConstraintsKinks and Sharpe RatiosComputer ResultsAppendixReferencesExercises appear at the end of each chapter.




Stochastic Financial ModelsDouglas KennedyTrinity College, Cambridge, UK


“This book is a superb beginning-level text forsenior undergraduate/graduate mathemati-cians, which is based on lectures delivered by itsauthor to many generations of appreciativeCambridge mathematicians. Many of my ownPh.D. and masters students have taken Dr.Kennedy’s course to uniformly good reviews; thisreadable book will make its material available toa worldwide 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’s advancedundergraduate and graduate courses at theUniversity of Cambridge, this text provides ahands-on, sound introduction to mathematicalfinance. The author first presents the classical top-ics of utility and the mean-variance approach toportfolio choice. Focusing on derivative pricing,the text then covers the binomial model, the gen-eral discrete-time model, Brownian motion, theBlack–Scholes model and various interest-ratemodels.

Features

• Presents a self-contained treatment of mathe-matical models in finance by including therelevant mathematical background

• Takes a hands-on approach to calculations,enabling students to derive the prices ofmany common financial products

• Assumes no prior knowledge of stochasticcalculus or measure-theoretic probability

• Includes exercises in each chapter and solu-tions in an appendix

Contents

Portfolio Choice

Introduction

Utility

Mean-variance analysis

The Binomial Model

One-period model

Multi-period model

A General Discrete-Time Model

One-period model

Multi-period model

Brownian Motion

Introduction

Hitting-time distributions

Girsanov’s theorem

Brownian motion as a limit

Stochastic calculus

The Black–Scholes Model

Introduction

The Black–Scholes formula

Hedging and the Black–Scholes equation

Path-dependent claims

Dividend-paying assets

Interest-Rate Models

Introduction

Survey of interest-rate models

Gaussian random-field model

Appendix A: Mathematical Preliminaries

Appendix B: Solutions to the Exercises

Further Reading

References

Index

Exercises appear at the end of each chapter.


19



Introduction toFinancialModels forManagementand PlanningJames R. Morris andJohn P. DaleyUniversity of Colorado, Denver,USA

This authoritative text provides graduate-levelinstruction on the development of models forfinancial management and planning. By workingthrough the problems and models in the text,students learn how computer-based modelsshould be structured to analyze a firm’s invest-ment and financing. Emphasizing Monte Carlosimulation, the authors cover modeling problemsrelated to financial management, firm valuation,forecasting, and security pricing. While the pri-mary focus is on models related to corporatefinancial management, the book also introducesstudents to a variety of models related to securitymarkets, stock and bond investments, portfoliomanagement, and options.

Features

• Covers all key aspects of financial modeling

• Introduces powerful tools for the financialtoolbox and shows how to use them to buildsuccessful models

• Contains extensive exercises throughout thetext

• Provides complementary access to the MonteCarlo simulation software @Risk

Solutions manual and PowerPoint slides availablefor qualifying instructors

Contents

Tools for Financial Planning and Modeling:Financial Analysis. Tools for Financial Planningand Modeling: Simulation. Introduction toForecasting Methods. A Closer Look at theDetails of a Financial Model. Modeling SecurityPrices and Investment Portfolios. OptimizationModels. References. Index.


Interest RateModelingTheory and PracticeLixin WuUniversity of Science &Technology, Kowloon, HongKong

“The book presents in a balanced way both the-ory and applications of interest rate modeling.… The book can serve as a textbook. It is self-contained in mathematics and presents rigorousjustifications for almost all results. Many exercis-es are provided which often require computerimplementation. …”

—Pavel Stoynov, Zentralblatt MATH 1173

Containing many results that are new or existonly in recent research articles, this text portraysthe theory of interest rate modeling as a three-dimensional object of finance, mathematics, andcomputation. It introduces all models with finan-cial-economical justifications, develops optionsalong the martingale approach, and handlesoption evaluations with precise numerical meth-ods. Taking a top-down approach, the authorshows students how to build and use models. Thetext includes exercises and real-world examples,along with code, tables, and figures accessible onthe author’s website.


Contents

The Basics of Stochastic Calculus. The MartingaleRepresentation Theorem. Interest Rates andBonds. The Heath–Jarrow–Morton Model. Short-Rate Models and Lattice Implementation. TheLIBOR Market Model. Calibration of LIBORMarket Model. Volatility and CorrelationAdjustments. Affine Term Structure Models.References. Index.





Algebraic Geometry and Number Theory

AdvancedNumber TheorywithApplicationsRichard A. MollinUniversity of Calgary, Alberta,Canada

“When I was looking over books for my course, Iwas very pleased by yours, and look forward toteaching from it.”

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

Technology, New York, USA

“… a wondrous book, successfully fulfilling theauthor’s purpose of effecting a bridge to modernnumber theory for the somewhat initiated. … it’svery nice to find in Mollin’s book a high qualityand coherent treatment of this beautiful materi-al and pointers in abundance to where to gonext.”

—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 material fora second course in this field. It includes numerousexamples and exercises and enables students toeasily cross-reference and find the appropriatedata.


Contents

Algebraic Number Theory and Quadratic Fields.Ideals. Binary Quadratic Forms. DiophantineApproximation. Arithmetic Functions.Introduction to p-Adic Analysis. Dirichlet:Characters, Density, and Primes in Progression.Applications to Diophantine Equations. EllipticCurves. Modular Forms. Appendix. Bibliography.Solutions to Odd-Numbered Exercises. Indices.


Limits ofGraphs inGroup Theoryand ComputerScienceEdited by

Goulnara ArzhantsevaUniversity of Geneva,Switzerland

Alain ValetteUniversity of Neuchatel, Switzerland

Covering the geometric, combinatorial, and com-putational aspects of group theory, this bookfocuses on the study of large families of finitegraphs with certain expanding properties andtheir embeddings into Hilbert and Banach spaces.It investigates the structure of finitely generatedgroups giving rise to such graphs and exploresnew interactions with broad areas of theoreticalcomputer science.

Catalog no. N10060, 2009, 280 pp.ISBN: 978-1-4398-0400-1, $94.50

Measure &ProbabilityS.R. AthreyaIndian Academy of Sciences,Bangalore, India

V.S. SunderInstitute of MathematicalSciences, Chennai, India

“… The book is neatly written and can be rec-ommended as an introduction to all studentswho intend to start courses on advanced modernprobability.”

—EMS Newsletter, Sept. 2009

This book begins with the construction ofLebesgue measure via Caratheodory’s outermeasure approach and goes on to discuss inte-gration and standard convergence theorems. Italso presents the elements of probability theory,the law of large numbers, central limit theorem,discrete time Markov chains, stationary distribu-tions, and limit theorems.

Catalog no. N10021, 2009, 232 pp.ISBN: 978-1-4398-0126-0, $69.95

Real, Complex, and Functional Analysis




21



New!

Applied Functional AnalysisSecond EditionJ. Tinsley Oden and Leszek F. DemkowiczUniversity of Texas at Austin, USA

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

Ideal for a two-semester course, this proven text-book teaches students how to prove theoremsand prepares them for further study of moreadvanced mathematical topics. It helps them suc-ceed in formulating research questions in a math-ematically rigorous way.

While retaining the structure of its bestsellingpredecessor, this second edition includes revisionsof many original examples, along with new exam-ples that often reflect the authors’ own vastresearch experiences and perspectives. The exam-ples in the text motivate students to appreciatethe value of mathematical rigor.


• Completely revised section on lim sup andlim inf

• New discussions of connected sets, probabili-ty, Bayesian statistical inference, and the gen-eralized (integral) Minkowski inequality

• New sections on elements of multilinear alge-bra and determinants, the singular valuedecomposition theorem, the Cauchy princi-pal value, and Hadamard finite part integrals

• New example of a Lebesgue non-measurableset

• Many more exercises

This text presents the mathematical foundationsthat lead to classical results in functional analysis.It prepares students to learn the variational theo-ry of partial differential equations, distributionsand Sobolev spaces, and numerical analysis withan emphasis on finite element methods.


Contents

PreliminariesElementary Logic and Set TheoryRelationsFunctionsCardinality of SetsFoundations of Abstract AlgebraElementary Topology in RnElements of Differential and Integral CalculusLinear AlgebraVector Spaces—The Basic ConceptsLinear TransformationsAlgebraic DualsEuclidean SpacesLebesgue Measure and IntegrationLebesgue MeasureLebesgue Integration TheoryTopological and Metric SpacesElementary TopologyTheory of Metric SpacesBanach SpacesTopological Vector SpacesHahn–Banach Extension TheoremBounded (Continuous) Linear Operators onNormed Spaces

Closed OperatorsTopological Duals. Weak CompactnessClosed Range Theorem. Solvability of LinearEquationsHilbert SpacesBasic TheoryDuality in Hilbert SpacesElements of Spectral TheoryReferences




Real andComplexAnalysisChristopher Apelianand Steve SuraceDrew University, Madison, New Jersey, USA

with Akhil Mathew

Unlike other undergraduate-level texts, Real andComplex Analysis develops both the real andcomplex theory together. It takes a unified, ele-gant approach to the theory that is consistentwith the recommendations of the MAA’s 2004Curriculum Guide.

By presenting real and complex analysis together,the authors illustrate the connections and differ-ences between these two branches of analysisright from the beginning. This combined devel-opment also allows for a more streamlinedapproach to real and complex function theory.

Enhanced by more than 1,000 exercises, the textcovers all the essential topics usually found in sep-arate treatments of real analysis and complexanalysis. Consequently, students will no longerhave to use two separate textbooks—one for realfunction theory and one for complex functiontheory. The book’s website offers hints and solu-tions to selected exercises as well as further read-ing suggestions.

Contents

The Spaces R, Rk, and C. Point-Set Topology.Limits and Convergence. Functions: Definitionsand Limits. Functions: Continuity andConvergence. The Derivative. Real Integration.Complex Integration. Taylor Series, LaurentSeries, and the Residue Calculus. ComplexFunctions as Mappings. Bibliography. Index.


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

With examples, exercises, and illustrations to aug-ment the teaching process, this text provides aclear, insightful, and thorough introduction to thebasics of modern topology. It presents the tradi-tional concepts of topological space, open andclosed sets, separation axioms, and more, alongwith applications of the ideas in Morse, manifold,homotopy, and homology theories. The text con-tains material on graph theory and dynamical sys-tems, both of which are insightful applications oftopological ideas. Taking a fresh and accessibleapproach to a venerable subject, it gives studentsthe foundation for further mathematical study inreal analysis, abstract algebra, and beyond.

Features

• Presents a thorough treatment of algebraictopology

• Offers numerous examples, illustrations, andexercises to make learning the topic easier

• Draws on examples in mathematics, physics,economics, engineering, and other disci-plines

• Includes several appendices that supply back-ground information on logic, real variabletheory, set theory, and algebraic structures

Contents

Fundamentals. Advanced Properties ofTopological Spaces. Basic Algebraic Topology.Manifold Theory. Moore–Smith Convergenceand Nets. Function Spaces. Knot Theory. GraphTheory. Dynamical Systems. Appendices.Solutions of Selected Exercises. Bibliography.Index.




23

Mathematics for Engineering


Coming soon!

Advanced Engineering Mathematics with MATLAB®

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

Catalog no. K10835, October 2010, 1144 pp.ISBN: 978-1-4398-1624-0, $109.95

Retaining the format and writing style that madeprevious editions so popular, this text builds asolid background in the mathematics requiredthroughout the engineering disciplines. It coverscomplex variables, ordinary and partial differen-tial equations, transform methods, vector algebra,and linear algebra.

The third edition includes two new chapters: oneon probability to introduce the topic along withMarkov chains and a second on stochasticprocesses that introduces a stochastic modelingapproach. This edition also places an increasedemphasis on MATLAB® through additional exam-ples, problems, and projects.

Features

• Incorporates the use of MATLAB to help stu-dents visualize and understand the mathe-matics and solve problems requiring heavycomputation

• Brings relevance to the material throughmany examples, most drawn from the engi-neering and scientific literature

• Introduces the z transform, which is of greatimportance in digital technologies

• Includes a chapter on the Hilbert transform,crucial to work in communications

• Contains an abundance of exercises that helpbuild problem-solving skills


Contents

Complex Variables

First-Order Ordinary Differential Equations

Higher-Order Ordinary Differential Equations

Fourier Series

The Fourier Transform

The Laplace Transform

The Z-Transform

The Hilbert Transform

The Sturm-Liouville Problem

The Wave Equation

The Heat Equation

Laplace’s Equation

Vector Calculus

Linear Algebra

Answers to the Odd-Numbered Problems





New!

Advanced Mathematical Methods in Scienceand EngineeringSecond EditionS.I. HayekPennsylvania State University, University Park, USA

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

An update of a classroom-tested bestseller, this secondedition continues to give students the strong founda-tion needed to apply mathematical techniques to thephysical phenomena encountered in scientific andengineering applications. Numerous examples illustratethe various methods of solution and answers to theend-of-chapter problems are included at the back ofthe book.

After introducing integration and solution methods ofODEs, the book presents Bessel and Legendre functionsas well as the derivation and methods of solution of lin-ear boundary value problems for physical systems inone spatial dimension governed by ODEs. It also coverscomplex variables, calculus, and integrals; linear PDEsin classical physics and engineering; the derivation ofintegral transforms; Green’s functions for ODEs andPDEs; asymptotic methods for evaluating integrals; andthe asymptotic solution of ODEs.

New to this edition, the final chapter offers an extensivetreatment of numerical methods for solving non-linearequations, finite difference differentiation and integra-tion, initial value and boundary value ODEs, and PDEsin mathematical physics. Chapters that cover boundaryvalue problems and PDEs contain derivations of thegoverning differential equations in many fields ofapplied physics and engineering, such as wavemechanics, acoustics, heat flow in solids, diffusion ofliquids and gases, and fluid flow.

Features

• Incorporates a new chapter on numerical methods

• Contains new appendices on vector algebra, calculus, and matrix algebra

• Provides a complete treatment of ODEs and PDEs

• Covers Green’s functions for unbounded andbounded media

• Explores self-adjoint systems and orthogonal series

• Includes many solved examples and problems withanswers

Contents

Ordinary Differential Equations

Series Solutions of Ordinary DifferentialEquations

Special Functions

Boundary Value Problems and EigenvalueProblems

Functions of a Complex Variable

Partial Differential Equations ofMathematical Physics

Integral Transforms

Green’s Functions

Asymptotic Methods

Numerical Methods

Appendix A: Infinite Series

Appendix B: Special Functions

Appendix C: Orthogonal CoordinateSystems

Appendix D: Dirac Delta Functions

Appendix E: Plots of Special Functions

Appendix F: Vector Analysis

Appendix G: Matrix Algebra

References

Answers

Index



25



Classical and Modern Numerical AnalysisTheory, Methods, and PracticeAzmy S. Ackleh, Edward James Allen, Ralph Baker Kearfott, and Padmanabhan Seshaiyer


This advanced, graduate-level introduction tothe theory and methods of numerical analysisprovides a sound foundation in numericalanalysis for more specialized topics, such asfinite element theory, advanced numerical lin-ear algebra, and optimization. It supplies thenecessary background in numerical methodsso that students can apply the techniques andunderstand the mathematical literature in thisarea.

The authors illustrate the concepts with manyexamples as well as analytical and computa-tional exercises at the end of each chapter.Although the book is independent of a specif-ic computer program, MATLAB® code is usedto illustrate various concepts.

Features

• Provides a clear and solid introduction tothe theory and application of computa-tional methods for applied mathematicsproblems

• Helps prepare students for doctoralexaminations in numerical analysis

• Presents the most important advancedaspects of numerical linear algebra, finiteelement theory, approximation theory,optimization, and integral equations

• Covers interval computation methods innumerical analysis

• Includes fully worked out solutions forselected problems

• Offers the MATLAB files on the authors’website

Solutions manual available for qualifyinginstructors

ContentsMathematical Review and Computer Arithmetic Numerical Solution of Nonlinear Equations ofOne Variable Numerical Linear Algebra Approximation TheoryEigenvalue-Eigenvector Computation Numerical Differentiation and Integration Initial Value Problems for Ordinary DifferentialEquations

Introduction Euler’s Method Single-Step Methods: Taylor Series andRunge–Kutta

Error Control and the Runge–Kutta–FehlbergMethod

Multistep Methods Predictor-Corrector Methods Stiff Systems Extrapolation Methods Application to Parameter Estimation in DifferentialEquationsNumerical Solution of Systems of NonlinearEquations

Introduction and Fréchet Derivatives Successive Approximation (Fixed Point Iteration)and the Contraction Mapping Theorem

Newton’s Method and VariationsMultivariate Interval Newton MethodsQuasi-Newton Methods (Broyden’s Method)Methods for Finding All SolutionsOptimization Local OptimizationConstrained Local Optimization Constrained Optimization and Nonlinear Systems Linear ProgrammingDynamic Programming Global (Non-Convex) OptimizationBoundary Value Problems and IntegralEquations Solutions to Selected ExercisesExercises appear at the end of each chapter.

For more complete contents, visitwww.crctextbooks.com




Essentials ofControlTechniques andTheoryJohn BillingsleyUniversity of SouthernQueensland, Toowoomba,Australia

Carefully separating the essential from the orna-mental, this book presents the nuts and bolts fordesigning a successful controller. It shows stu-dents how mathematics can help us understandthe concepts that underpin the controller’seffects. It also provides software simulation exam-ples and other material at www.esscont.com


Catalog no. 91239, January 2010, 339 pp.ISBN: 978-1-4200-9123-6, $89.95

New!

Introduction tothe Simulationof DynamicsUsing Simulink®Michael A. GrayAmerican University,Washington, D.C., USA

Designed for undergraduate students in the gen-eral science, engineering, and mathematics com-munity, this text shows how to use the powerfultool of Simulink to investigate and form intuitionsabout the behavior of dynamical systems. It clear-ly explains how to transition from physical mod-els described by mathematical equations directlyto executable Simulink simulations. PowerPointslides and solutions to exercises are offered athttp://nw08.american.edu/~gray/index.htm

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

AdvancedLinear Algebrafor Engineerswith MATLAB®

Sohail A. Dianat and Eli S. SaberRochester Institute ofTechnology, New York, USA

Designed to elevate the analytical and problem-solving skills of engineering students, this textprovides systematic instruction that enables thosestudents to make full use of the advanced capa-bilities that MATLAB® provides. Offering a broadselection of progressive exercises and MATLABproblems, each chapter features carefully chosenexamples that demonstrate underlying ideas atwork in practical scenarios.


Catalog no. 95234, 2009, 346 pp.ISBN: 978-1-4200-9523-4, $99.95

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 book introducesundergraduate students to the mathematicalconcepts and principles underlying linear andnonlinear programming. It fills the gap betweenmanagement science books lacking mathematicaldetail and rigor and graduate-level books onmathematical programming. Maple worksheetsand code can be found on the book’s website.


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





27



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

This book explains how to perform complexmathematical tasks with MATLAB® programs. Theauthor first describes simple functions such as dif-ferentiation, integration, and plotting. He thenaddresses advanced topics, including program-ming, producing executables, publishing resultsdirectly from MATLAB programs, and creatinggraphical user interfaces. The text also presentsexamples of Simulink for system modeling andsimulation. It explores the use of MATLAB in digi-tal signal processing, chemical and food engi-neering, astronomy, optics, financial derivatives,and much more.

Features

• Brings together diverse applications of MATLAB in many areas

• Provides a gradual introduction to MATLABfunctions and programming

• Covers the graphical user interfaces in MATLAB and Simulink

• Presents Simulink for scientific and engineering system simulation

• Contains more than 160 practical workedexamples and numerous end-of-chapter exercises

• Offers downloadable MATLAB examples andprograms on the book’s website


Contents

Introduction to MATLAB. Variables andFunctions. Matrices and Linear Algebra. Calculus.Plotting with MATLAB. Programming in MAT-LAB. Graphical User Interfaces. Simulink. MAT-LAB Applications to Engineering. MATLABApplications to Physics. MATLAB Applications toFinance. Index.


AdvancedEngineeringMathematicswith ModelingApplicationsS. Graham KellyUniversity of Akron, Ohio, USA

Presenting mathematical theory at an under-standable level, this graduate-level text explorestopics from real and functional analysis, such asvector spaces, inner products, norms, and linearoperators, to formulate mathematical models ofengineering problems for both discrete and con-tinuous systems. The author presents theoremsand proofs, but without the full detail found inmathematical books, so that development of thetheory does not obscure its application to engi-neering problems. He applies principles and the-orems of linear algebra to derive solutions, includ-ing proofs of theorems when they are instructive.Tying mathematical theory to applications, thisbook provides engineering students with a strongfoundation in mathematical terminology andmethods.

Features

• Emphasizes mathematical modeling, dimen-sional analysis, scaling, and their applicationto macroscale and nanoscale problems

• Explores eigenvalue problems for discreteand continuous systems and many applica-tions

• Develops and applies approximate methods,such as Rayleigh–Ritz and finite elementmethods

• Presents applications that use contemporaryresearch in areas such as nanotechnology


Contents

Foundations of Mathematical Modeling. LinearAlgebra. Ordinary Differential Equations.Variational Methods. Eigenvalue Problems. PartialDifferential Equations. Index.

Catalog no. 9533, 2009, 522 pp.ISBN: 978-0-8493-9533-8, $111.95




Mathematics for Biology/Computational Biology

Differential Equations and MathematicalBiologySecond EditionD.S. JonesUniversity of Dundee, Scotland

M.J. PlankUniversity of Canterbury, Christchurch, New Zealand

B.D. SleemanUniversity of Leeds, UK


“… Where this text stands out is in its thoughtfulorganization and the clarity of its writing. This isa very solid book … The authors succeed becausethey do a splendid job of integrating their treat-ment of differential equations with the applica-tions, and they don’t try to do too much. … Eachchapter comes with a collection of well-selectedexercises, and plenty of references for furtherreading.”

—MAA Reviews, April 2010

Ideal for courses on differential equations withapplications to mathematical biology or as anintroduction to mathematical biology, this best-selling text introduces the fundamental modelingand analytical techniques used to understand bio-logical phenomena. It discusses the modeling ofbiological behavior, including the heartbeat cycle,chemical reactions, nerve pulses, predator–preymodels, and epidemics.


• A section on spiral waves

• Recent developments in tumor biology

• More on the numerical solution of differentialequations and numerical bifurcation analysis

• MATLAB® files available for download onlineat www.crctextbooks.com

• Many additional examples and exercises

The book uses various differential equations tomodel biological behavior. It explains how bifur-cation and chaotic behavior play key roles in fun-damental problems of biological modeling. Theauthors also present a unique treatment of pat-tern formation in developmental biology basedon Turing’s famous idea of diffusion-driven insta-bilities.

Contents

Linear Ordinary Differential Equations withConstant Coefficients

Systems of Linear Ordinary DifferentialEquations

Modelling Biological Phenomena

First-Order Systems of Ordinary DifferentialEquations

Mathematics of Heart Physiology

Mathematics of Nerve Impulse Transmission

Chemical Reactions

Predator and Prey

Partial Differential Equations

Evolutionary Equations

Problems of Diffusion

Bifurcation and Chaos

Numerical Bifurcation Analysis

Growth of Tumors

Introduction

Mathematical model I of tumor growth

Spherical tumor growth based on model I

Stability of tumor growth based on model I

Mathematical model II of tumor growth

Spherical tumor growth based on model II

Stability of tumor growth based on model II

Epidemics

The Kermack–McKendrick model

Vaccination

An incubation model

Spreading in space

Answers to Selected Exercises



29

Mathematics for Biology/Computational Biology

Probability Theory and Applications


Algorithms inBioinformaticsA PracticalIntroductionWing-Kin SungNational University of Singapore

“… an excellent guide. The book is appropriatefor advanced undergraduates and graduates inmathematics or CS. … The 27-page introductionis the most efficient concept-building summaryand explication of molecular biology that I haveencountered. … This self-contained, well-designed, and well-written book, with its manygood exercises, bibliographic references, andphoto-quality figures, is an ideal introduction tobioinformatics.”

—George Hacken, Computing Reviews, March 2010



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

Updated to conform to Mathematica® 7.0, thissecond edition continues to show students howto easily create simulations from templates andsolve problems using Mathematica. It alsoincludes additional problems from ActuarialExam P as well as new examples, exercises, anddata sets. The accompanying CD-ROM containsupdated Mathematica notebooks.



Coming soon!

BiologicalComputationEhud LammTel-Aviv University, Israel

Ron UngerBar-Ilan University, Ramat-Gan,Israel

Created for advanced undergraduate students,Biological Computation covers major themes ofbio-inspired computing, including cellularautomata, molecular computation, genetic algo-rithms, and neural networks. Providing theoreticaland coding exercises, this self-contained textrequires no previous knowledge of biology. It pro-vides valuable insight to students from biomed-ical backgrounds looking to gain the computa-tional skills needed to make entry into the fields ofsystems biology, biological modeling, and simula-tions.

Catalog no. C7959, October 2010, c. 344 pp.ISBN: 978-1-4200-8795-6, $79.95

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

Based on a highly popular, well-establishedcourse taught by the authors, this updated text-book makes the material accessible to students byavoiding specialized applications and insteadhighlighting simple applications and examples. Itincludes over 50 worked examples and more than200 end-of-chapter problems with selectedanswers in the back of the book. The authors pro-vide Mathematica® and R programs on the book’swebsite.

Solutions manual available for qualifying instructorsvia password on the book’s website

Catalog no. K10004, January 2010, 232 pp.Soft Cover, ISBN: 978-1-4200-9960-7, $79.95





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Mathematics Textbooks - August 2010

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