textbooks in mathematics

New and Essential

MATHEMATICSTEXTBOOKS IN

http://www.crcpress.com/product/isbn/9781466504998



Contents

Combinatorics and Discrete Math ....................................3

General and Introductory Math ........................................7

Differential Equations and Nonlinearity ..........................10

Math for Finance ............................................................11

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

Math for Engineering and Computer Science ................14

Math for Biology and Medicine ......................................15

Algebra ............................................................................17

Mathematical Computation ............................................18

Probability and Statistics ..................................................18

Set Theory and Logic ......................................................19

Applied Math ..................................................................20

Mathematical Modeling ..................................................21

Operations Research ........................................................22

AZM01_BZM01_5.5x8.5 TMC_12.28.12_HF/gtr

Page 9

Page 9 2

Page 12 Page 7

Page 6

For more information and complete tables of contents or to

*request your complimentary eBookor print exam copy

visit

www.crctextbooks.com1-800-634-7064 • [email protected]

Give Your Students Access to Cutting-Edge

Research Tools.

CRCnetBASE is an award-winning eBook platform that provides easily accessible and searchable information across all disciplines.Ask your librarian to sign up for a free trial at CRCnetBASE.com

http://issuu.com/action/page?page=6


















3

Combinatorics and Discrete Math

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

Discrete Mathematicswith Duckssarah-marie belcastroResearch Associate, Smith College, Northampton, Massachusetts, USA

• Balances mathematics and computer science

• Follows the basic curriculum outlined bySIGCSE guidelines

• Includes classroom activities and notes forinstructors

Solutions manual available upon qualifying course adoption

Selected Contents:

The BasicsCounting and ProofsSets and LogicGraphs and FunctionsInductionAlgorithms with CiphersCombinatoricsBinomial Coefficients and Pascal’s TriangleBalls and Boxes and PIE—Counting TechniquesRecurrencesCutting Up Food (Counting and Geometry)Graph TheoryTreesEuler’s Formula and ApplicationsGraph TraversalsGraph ColoringOther MaterialProbability and ExpectationFun with CardinalityAdditional ProblemsSolutions to Check Yourself Problems The Greek Alphabet and Some Uses for Some Letters

List of Symbols Glossary Bibliography

Catalog no. K14547, June 2012, 580 pp.ISBN: 978-1-4665-0499-8, $59.95 / £39.95Also available as an eBook

“This book can certainly be used to teach the stan-dard course in discrete mathematics designed forcomputer science majors. The lighter touch of duckreferences does amuse you and does not ever over-shadow or disguise the mathematical concepts.”

—MAA Reviews, August 2012

“When I used Discrete Mathematics with Ducks inclass, I assigned readings, and my students came toclass full of questions and ideas. Every day we had agood time in one way or another; these classes werea highlight of my teaching career. I give a lot of cred-it to this book, thanks to the author’s skill at blend-ing rigor, great examples, casual humor, and precisewriting.”

—David Perkins, author of Calculus and Its Origins

“I had a lot of fun teaching from Discrete Mathematicswith Ducks … I think the discovery/exploratory/prob-lem-solving approach is ABSOLUTELY the way thiscourse should be taught, and of all the discrete books Ihave looked at, this text does the best job of supportingthat kind of approach to the subject while still givingenough of the material in writing to fill in the gaps. … Ifound that the material provided and the instructornotes cut down on my prep time, and I definitely referredto them. Having the in-class activities included is a hugebenefit to this book.”

—Dana Rowland, Merrimack College

“… an incredible book … readable by students, use-ful for instructors, and constructed with style andflair. This book will make it much easier to teach anexciting, student-centered discrete mathematicscourse that will also serve as an excellent introduc-tion to advanced critical thinking, problem solving,and proofs.”

—Douglas Shaw, University of Northern Iowa

Suitable for an introductory discrete mathematicscourse, this text covers the subfields of mathematicsand computer science that fall under the generalumbrella term. It fits the ideas of the basic curriculumas outlined in the SIGCSE guidelines into a frameworkthat focuses on content rather than technique. Thebook covers standard and practical topics required indiscrete math classes. The author also incorporatesclassroom activities as well as instructor’s notes at theend of every chapter.


4 Request Your Complimentary eBook or Print Exam Copy at www.crctextbooks.com


BijectiveCombinatoricsNicholas LoehrVirginia Polytechnic Institute andState University, Blacksburg, USA

“This textbook, aimed at beginning graduate stu-dents, is the first to survey the subject emphasizingthe role of bijections. … The exposition is careful anddeliberate, and leaves no stone unturned … a wel-come addition to the literature and a very nicebook.”

—Mathematical Reviews, 2012d

“A rule I have found to be true is that any bookclaiming to be suitable for beginners and yet leadingto the frontiers of unsolved research problems doesneither well. This book is the exception to that rule.… I found this book engaging. The proofs are veryclear, and in many cases several proofs are offered.… an excellent choice for a first course in combina-torics for senior undergraduates. … This is a verynice book that deserves serious consideration.”

—MAA Reviews, September 2011

“The book is clearly written and packed with exam-ples and problems (it provides answers and hints toselected problems at the end). The organization issuperior, with helpful tables of notation and defini-tions at the end of each chapter, along with a point-by-point summary of the chief topics. … the book isan excellent one, and is a comprehensive and wel-come addition to the area.”

—Computing Reviews, August 2011

Selected Contents:

Introduction. Basic Counting. CombinatorialIdentities and Recursions. Counting Problems inGraph Theory. Inclusion-Exclusion and RelatedTechniques. Ranking and Unranking. CountingWeighted Objects. Formal Power Series. TheCombinatorics of Formal Power Series. Permutationsand Group Actions. Tableaux and SymmetricPolynomials. Abaci and Antisymmetric Polynomials.Additional Topics. Answers and Hints to SelectedExercises. Bibliography. Index.

Catalog no. K12206, February 2011, 612 pp.ISBN: 978-1-4398-4884-5, $104.95 / £66.99

DiscreteStructures withContemporaryApplicationsAlexander StanoyevitchCalifornia State University-Dominguez Hills, Carson, USA

“… this is the most physically readable textbookthat I have seen in a long time. … there are manyexamples and in many cases proofs of the theoremsare included. A large number of exercises are provid-ed and split into two categories, the traditionalmath problem and exercises to be performed on acomputer. … The two most important courses in thecomputer science major are the first programmingand discrete math classes. … this book is an excel-lent text for the development of the needed skills inmath.”

—MAA Reviews, March 2011

Reflecting many of the recent advances and trends inthis area, this classroom-tested text covers the coretopics in discrete structures as outlined by the ACMand explores an assortment of novel applications,including simulations, genetic algorithms, networkflows, probabilistic primality tests, public key cryptog-raphy, and coding theory. It presents algorithms inpseudo code and offers sample programs via theauthor’s website. The text also includes a wide varietyof examples and exercises, with solutions in theappendices. In addition, computer exercises teachstudents how to write their own programs. A solutionsmanual is available upon qualifying course adoption.

Selected Contents:

Logic and Sets. Relations and Functions, BooleanAlgebra, and Circuit Design. The Integers, Induction,and Recursion. Number Systems. CountingTechniques, Combinatorics, and GeneratingFunctions. Discrete Probability and Simulation.Complexity of Algorithms. Graphs, Trees, andAssociated Algorithms. Graph Traversal andOptimization Problems. Randomized Search andOptimization Algorithms. Appendices. References.Index.

Catalog no. K10918, January 2011, 1002 pp.ISBN: 978-1-4398-1768-1, $99.95 / £44.99Also available as an eBook



5



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

Barry TesmanDickinson College, Carlisle,Pennsylvania, USA

“The book has been substantially rewritten withmore than 200 pages of new materials and manychanges in the exercises. There are also many newexamples … I strongly endorse this book. It is suit-able for motivated math, computer science, or engi-neering sophomores and even beginning graduatestudents. In fact bright high school students wouldlove this book … I really love this book. It is a gem.”

—IACR Book Reviews, 2011

“… complete introductory textbook in combina-torics. It not only covers nearly every topic in thesubject, but gives several realistic applications foreach topic. … much more breadth than its competi-tors. … valuable as a source of applications and forenrichment reading.”

—MAA Reviews, December 2009

“This book is a required textbook for my graduatecourse in discrete mathematics. Both my studentsand I have found it to be an excellent resource withinteresting application examples from a variety offields interspersed throughout the text. … an appro-priate text for junior, senior, and graduate studentsalike. …”

—Dawit Haile, Virginia State University

Selected Contents:

What Is Combinatorics? THE BASIC TOOLS OFCOMBINATORICS: Basic Counting Rules.Introduction to Graph Theory. Relations. THECOUNTING PROBLEM: Generating Functions andTheir Applications. Recurrence Relations. ThePrinciple of Inclusion and Exclusion. The PólyaTheory of Counting. THE EXISTENCE PROBLEM:Combinatorial Designs. Coding Theory. ExistenceProblems in Graph Theory. COMBINATORIAL OPTIMIZATION: Matching and Covering.Optimization Problems for Graphs and Networks.Appendix. Indices.


Graphs &DigraphsFifth EditionGary Chartrand,Linda Lesniak, andPing Zhang

“… an ideal textbook for the advanced undergradu-ate or beginning graduate course. The authors haveupdated their notation to reflect the current practicein this still-growing area of study. … the legendaryFrank Harary, author of the second graph theorytext ever produced, is one of the figures profiled. Hisbook was the standard in the discipline for severaldecades. Chartrand, Lesniak, and Zhang have pro-duced a worthy successor.”

—MAA Reviews, June 2012(This book is in the MAA’s basic library list.)

“As with the earlier editions, the current text empha-sizes clear exposition, well-written proofs, and manyoriginal and innovative exercises of varying difficul-ty and challenge. … The fifth edition continues andextends these fine traditions.”

—Zentralblatt MATH 1211

“Now in its fifth edition, its success as a textbook isindicative of its quality and its clarity of presentation… It provides all you might need to know aboutgraph embeddings and graph colorings. Moreover,it analyzes many other topics that more general dis-crete mathematics monographs do not always cover… this thorough textbook includes hundreds of exer-cises at the end of each section. Hints and solutionsfor odd-numbered exercises are included in theappendix, making it especially suitable for self-learn-ing.”

—Computing Reviews, September 2011


Selected Contents:

Introduction to Graphs. Trees and Connectivity.Eulerian and Hamiltonian Graphs. Digraphs. Graphs:History and Symmetry. Planar Graphs. GraphEmbeddings. Vertex Colorings. Map Colorings.Matchings, Factorization, and Domination. EdgeColorings. Extremal Graph Theory. Hints andSolutions to Odd-Numbered Exercises. Bibliography.Indices. List of Symbols.

Catalog no. K11263, October 2010, 598 pp.ISBN: 978-1-4398-2627-0, $89.95 / £49.99Also available as an eBook





Combinatoricsof PermutationsSecond EditionMiklós BónaUniversity of Florida, Gainesville, USA

“… a comprehensive, engaging, and eminentlyreadable introduction to all aspects of the combina-torics of permutations. … This book can be utilizedat a variety of levels, from random samplings of thetreasures therein to a comprehensive attempt tomaster all the material and solve all the exercises. Inwhatever direction the reader’s tastes lead, thoroughenjoyment and appreciation of a beautiful area ofcombinatorics are certain to ensue.”

—Richard Stanley, MIT

A 2006 CHOICE Outstanding Academic Title, the firstedition of this bestseller was lauded for its detailed yetengaging treatment of permutations. With much ofthe book significantly revised and expanded, this sec-ond edition continues to clearly show the usefulnessof the subject. Along with more exercises and prob-lems, this edition includes new material on alternatingpermutations, multivariate applications, patternavoidance, and asymptotically normal distributions. Anew chapter focuses on three sorting algorithms frommolecular biology. A solutions manual is availableupon qualifying course adoption.

Selected Contents:

In One Line and Close. Permutations as LinearOrders. In One Line and Anywhere. Permutations asLinear Orders. Inversions. In Many Circles.Permutations as Products of Cycles. In Any Way butThis. Pattern Avoidance. The Basics. In This Way butNicely. Pattern Avoidance. Follow-Up. Mean andInsensitive. Random Permutations. Permutations ver-sus Everything Else. Algebraic Combinatorics ofPermutations. Get Them All. Algorithms andPermutations. How Did We Get Here? Permutationsas Genome Rearrangements. Solutions to Odd-Numbered Exercises. References. List of FrequentlyUsed Notation. Index.


Coming soon!

ComputationalNumber TheoryAbhijit DasIndian Institute of Technology,Kharagpur

This text introduces the vast and fascinating area ofcomputational number theory. It treats algorithms forcommon number-theoretic problems in an elemen-tary fashion, eliminating the need for an extensiveprerequisite of algebra and analysis.

The book contains detailed examples illustratingalmost every algorithmic concept discussed. It alsoincludes practical applications of arithmetic algo-rithms in public-key cryptography. The GP/PARI calcu-lator is used throughout to demonstrate the arith-metic algorithms. Every chapter ends with many exer-cises and partial solutions are given in the appendix.

• Covers many important computational issuesand recent developments in number theory

• Uses GP/PARI as a calculator to illustrate thealgorithms

• Describes the use of public-key cryptography asan application

• Presents an elementary treatment of the topic,eliminating the need for an extensivebackground in mathematics

• Contains numerous examples as well as exercisesat the end of every chapter, with partial solutions in an appendix

Selected Contents:

Arithmetic of Integers. Arithmetic of Finite Fields.Arithmetic of Polynomials. Arithmetic of EllipticCurves. Primality Testing. Integer Factorization.Discrete Logarithms. Large Sparse Linear Systems.Cryptography.

Catalog no. K12950, March 2013, c. 611 pp.ISBN: 978-1-4398-6615-3, $89.95 / £57.99Also available as an eBook



7

General and Introductory Math


New!

Number, Shape,& SymmetryAn Introduction toNumber Theory,Geometry, andGroup TheoryDiane L. Herrmann and Paul J. Sally, Jr.University of Chicago, Illinois, USA

“All budding mathematicians should have theopportunity to savour this marvelously engagingbook. The authors bring to the text an extensivebackground working with students and have mas-tered the fine art of both motivating and delightingthem with mathematics. Their experience is evidenton every page: creative practice problems draw thereader into the discussion, while frequent examplesand detailed diagrams keep each section lively andappealing. Herrmann and Sally have carefully chart-ed a course that takes the reader through numbertheory, introductory group theory, and geometry,with an emphasis on symmetries in the latter twosubjects. The result is a labour of love that shouldinspire young minds for years to come.”

—Sam Vandervelde, author of Bridge to HigherMathematics and coordinator of the

Mandelbrot Competition

“Number, Shape, & Symmetry accomplishes therare feat of presenting real and deep mathematics ina clear and accessible manner. This book distills thebeauty of some of the most fundamental ideas ofmathematics and is a terrific resource for anyoneinterested in exploring these subjects.”

—Bridget Tenner, DePaul University


Selected Contents:

The Triangle Game. The Beginnings of NumberTheory. Axioms in Number Theory. Divisibility andPrimes. The Division and Euclidean Algorithms.Variations on a Theme. Congruences and Groups.Applications of Congruences. Rational Numbers andReal Numbers. Introduction to Geometry andSymmetry. Polygons and Their Construction.Symmetry Groups. Permutations. Polyhedra. GraphTheory. Tessellations. Connections. Appendix.Glossary. Bibliography. Index.

Catalog no. K15328, October 2012, 444 pp.ISBN: 978-1-4665-5464-1, $69.95 / £44.99Also available as an eBook

CryptologyClassical and Modernwith MapletsRichard E. KlimaAppalachian State University,Boone, North Carolina, USA

Neil P. SigmonRadford University, Virginia, USA

“All told, the authors have done an admirable job ofbalancing the competing goals of producing a textthat can be read by people with limited mathemat-ics background, but at the same time is maintainedat a college level. This is not ‘cryptology for dum-mies,’ watered down to the point of uselessness …This is a book that not only meets but exceeds itsgoal of being a suitable text for a course in cryptol-ogy for non-majors. It is highly recommended foranybody teaching such a course, and it certainlybelongs in any good university library.”

—MAA Reviews, September 2012

In a clear, nontechnical manner, this text explains howfundamental mathematical concepts are the bases ofcryptographic algorithms. It covers the Enigmamachine and Navajo code used during World War II,describes the implementation and cryptanalysis ofclassical ciphers, and gives straightforward explana-tions of the AES, public-key ciphers, and messageauthentication. The book assumes minimal mathe-matical prerequisites and incorporates easy-to-useMaplets throughout that provide practical examplesof the techniques. The Maplets are available for down-load online. A solutions manual is available upon qual-ifying course adoption.

Selected Contents:

Introduction to Cryptology. Substitution Ciphers.Transposition Ciphers. The Enigma Machine andNavajo Code. Shift and Affine Ciphers. Alberti andVigenère Ciphers. Hill Ciphers. RSA Ciphers. ElGamalCiphers. The Advanced Encryption Standard.Message Authentication. Bibliography. Hints orAnswers to Selected Exercises. Index.






A MathematicalLook at PoliticsE. Arthur Robinson, Jr.and Daniel H. UllmanGeorge Washington University,Washington, D.C., USA

“The book finds a nice compromise between formal-ity and accessibility. The authors take care to buildfrom examples, isolate what is important, and gen-eralize into theorems. It is expected that the readerhas only limited mathematical experience, so mucheffort is put toward making very clear what is and isnot being said. … The exercises that close eachchapter are interesting and often quite challenging… Topics are introduced and motivated thoughtful-ly. Definitions are clear, and the authors take thetime to explain why they need to be with well-cho-sen examples. When the proofs come (and they docome), they are set up properly. … This is a verythoughtfully written text that should be made avail-able to anyone with an interest in learning or teach-ing this topic.”

—MAA Reviews, July 2011

• Explains how to read and write proofs

• Includes real-world scenarios as well as theory

• Details various types of decision problems andhow to solve them

• Presents a large number of exercises and problems at the end of each chapter

Selected Contents:

Voting: Two Candidates. Social Choice Functions.Criteria for Social Choice. Which Methods Are Good?Arrow’s Theorem. Variations on the Theme.Apportionment: Hamilton’s Method. DivisorMethods. Criteria and Impossibility. The Method ofBalinski and Young. Deciding among DivisorMethods. History of Apportionment in the UnitedStates. Conflict: Strategies and Outcomes. Chanceand Expectation. Solving Zero-Sum Games. Conflictand Cooperation. Nash Equilibria. The Prisoner’sDilemma. The Electoral College: Weighted Voting.Whose Advantage? Solutions to Odd-NumberedExercises and Problems. Bibliography. Index.

Catalog no. K11044, December 2010, 477 pp.ISBN: 978-1-4398-1983-8, $54.95 / £34.99Also available as an eBook

Agents, Games,and EvolutionStrategies at Workand PlaySteven Orla KimbroughUniversity of Pennsylvania,Philadelphia, USA

Based on the author’s course at the University ofPennsylvania, this book explores a number of basicgames using agent-based models where agents havefixed strategies. The author uses agent-based modelsto present a wide range of applications in whichstrategic interaction is present and for which designissues have genuine practical significance. The textcovers the Prisoner’s Dilemma, Stag Hunt, Battle ofthe Sexes, and many other games of interest in thesocial sciences. All computational methods are imple-mented in NetLogo and the required mathematicalbackground is included in an appendix.

• Presents sample models that may be used toexplore strategic decision making in a widevariety of contexts

• Provides examples of interest in many differentfields, including business and economics, politics, philosophy, engineerin -g, biology, and policy analysis

• Requires minimal mathematical requirements,offering the necessary mathematical backgroundin an appendix

• Includes 12 easily used, documented NetLogomodels to illustrate findings and support furtherexploration

• Links to “games in the wild,” not merely to stylized models of games

• Details useful methods for dealing with strategicsituations

• Contains extensive study questions at the end ofeach chapter

Selected Contents:

Starters. Mixed Motives. Markets and Applications.Topics in Strategic Analysis. Appendices.Bibliography. Index.




9



New!

Project OrigamiActivities forExploringMathematics,Second EditionThomas HullThis widely praised, classroom-tested text presents aflexible, discovery-based approach to learning origa-mi-math topics. It helps students see how origamiintersects a variety of mathematical topics, from themore obvious realm of geometry to the fields of alge-bra, number theory, and combinatorics. With over100 new pages, this edition now includes 30 activitiesand offers better solutions and teaching tips for allactivities.

• Presents 30 origami activities, complete withhandouts, solutions, and instructor’s guides

• Covers many mathematical areas, includinggeometry, multivariable calculus, and graph theory

• Offers a flexible approach to using the materialin a variety of math courses

• Improves the solutions and teaching tips for allactivities

• Provides PDFs of the handouts on the book’sCRC Press web page

Selected Contents:

Folding Equilateral Triangles in a Square. OrigamiTrigonometry. Dividing a Length into Equal Nths:Fujimoto Approximation. Dividing a Length intoEqual Nths Exactly. Origami Helix. Folding aParabola. Can Origami Trisect an Angle? SolvingCubic Equations. Lill’s Method. Folding Strips intoKnots. Haga’s “Origamics.” Modular Star Ring.Folding a Butterfly Bomb. Molly’s Hexahedron.Business Card Modulars. Five Intersecting Tetrahedra.Making Origami Buckyballs. Making Origami Tori.Modular Menger Sponge. Folding and Coloring aCrane. Exploring Flat Vertex Folds.Impossible CreasePatterns. Folding a Square Twist. Counting Flat Folds.Self-Similar Wave. Matrix Model of Flat Vertex Folds.Matrix Model of 3D Vertex Folds. Origami andHomomorphisms. Rigid Folds 1: Gaussian Curvature.Rigid Folds 2: Spherical Trigonometry. Appendix.Bibliography. Index.

Catalog no. K16368, January 2013, 364 pp.Soft Cover ISBN: 978-1-4665-6791-7$49.95 / £31.99Also available as an eBook

Coming soon!

Mathematicsand MusicComposition,Perception, and PerformanceJames S. Walker and Gary DonUniversity of Wisconsin,Eau Claire, USA

This text emphasizes the connection between mathe-matics and many different music genres. It assists stu-dents in understanding basic musical scores by pro-viding numerous examples of music notation. Thebook also describes the powerful time-frequencymethod of spectrograms, which helps in analyzingmusic as it is heard rather than analyzing notes on ascore. The book’s website offers video demos, links toarticles, software, musical scores, and course materi-als. A solutions manual is available upon qualifyingcourse adoption.

Catalog no. K13012, April 2013, c. 328 pp.Soft Cover ISBN: 978-1-4398-6709-9$59.95 / £38.99Also available as an eBook

Coming soon! Gauss’ JerseyDean HathoutThis text focuses on “Gauss problems”: problems thatif tackled in the traditional way, can be very tediousand time consuming, but if approached in a moreinsightful fashion, can yield the solution much moreeasily and elegantly. It presents an insightful combina-tion of acquired techniques as opposed to the usualroutine plodding through mathematical techniques.The book discusses the famous example of Gauss’summation of the first 100 natural numbers by group-ing them rather than summing them one by one.

Catalog no. K14699, April 2013, c. 211 pp.ISBN: 978-1-4665-0864-4, $24.95 / £18.95Also available as an eBook





Differential Equations and Nonlinearity

Encounters with Chaos and FractalsSecond EditionDenny GulickUniversity of Maryland, College Park, USA

Revised and updated, this second edition provides anaccessible introduction to both chaotic dynamics andfractal geometry for students with a calculus back-ground. With more than enough material for a one-semester course, it incorporates important mathemat-ical concepts associated with these areas and backs upthe definitions and results with motivation, examples,and applications.

Laying the groundwork for later chapters, the textbegins with examples of mathematical behaviorexhibited by chaotic systems, first in one dimensionand then in two and three dimensions. Focusing onfractal geometry, the author goes on to introduce infi-nitely complicated fractals. He analyzes them andexplains how to obtain computer renditions of them.The book concludes with the famous Julia sets and theMandelbrot set.

• Provides an updated presentation of chaoticdynamics

• Contains new and expanded material on fractalsthat illustrates how to obtain computer renderings of them

• Covers Julia and Mandelbrot sets

• Includes a substantial number of new exercisesat the end of each section and MATLAB®

programs in the appendix, with selected solutions at the back of the book

Selected Contents:

Periodic Points. One-Dimensional Chaos. Two-Dimensional Chaos. Systems of DifferentialEquations. Introduction to Fractals. Creating FractalsSets. Complex Fractals: Julia Sets and the MandelbrotSet. Computer Programs. Answers to SelectedExercises. References. Index.

Catalog no. C5173, April 2012, 387 pp.ISBN: 978-1-58488-517-7, $79.95 / £49.99Also available as an eBook

New!

Ordinary and PartialDifferentialEquationsVictor Henner, Tatyana Belozerova,and Mikhail KhennerThis text provides a complete and accessible courseon ODEs and PDEs using many examples and exercis-es as well as intuitive, easy-to-use software. The bookincludes all the topics that form the core of a modernundergraduate or beginning graduate course in dif-ferential equations. It also discusses other optional butimportant topics such as integral equations, Fourierseries, and special functions. Requiring no user pro-gramming, the accompanying computer softwareallows students to fully investigate problems.

• Provides full coverage of ODEs and PDEs forstudents in the physical, engineering, biological,and mathematical sciences

• Uses a teaching-by-examples philosophy—including extensive examples and exercises

• Offers user-friendly software (with tutorials, GUI,and solution visualization capability) for the analytical solution and investigation of PDEs and ODEs

• Presents advanced topics on ODEs and PDEs


Selected Contents:

First-Order Differential Equations. Second-OrderDifferential Equations. Systems of DifferentialEquations. Boundary Value Problems for Second-Order ODE and Sturm-Liouville Theory. QualitativeMethods and Stability of ODE Solutions. Method ofLaplace Transforms for ODE. Integral Equations.Series Solutions of ODEs and Bessel and LegendreEquations. Fourier Series. Introduction to PDE. One-Dimensional Hyperbolic Equations. Two-DimensionalHyperbolic Equations. One-Dimensional ParabolicEquations. Two-Dimensional Parabolic Equations.Elliptic Equations. Appendices. Bibliography.




11

Math for Finance


Monte CarloSimulation withApplications toFinanceHui WangBrown University, Providence,Rhode Island, USA

Developed from the author’s course on Monte Carlosimulation at Brown University, this text provides aself-contained introduction to Monte Carlo methodsin financial engineering. It covers common variancereduction techniques, the cross-entropy method, andthe simulation of diffusion process models. Requiringminimal background in mathematics and finance, thebook includes numerous examples of option pricing,risk analysis, and sensitivity analysis as well as manyhand-and-paper and MATLAB® coding exercises at theend of every chapter.

• Presents common variance reduction techniquesas well as the cross-entropy method

• Covers the simulation of diffusion process models

• Requires minimal background in mathematicsand finance

• Contains numerous examples of option pricing,risk analysis, and sensitivity analysis

• Includes many hand-and-paper and MATLABcoding exercises at the end of every chapter

Selected Contents:

Review of Probability. Brownian Motion. ArbitrageFree Pricing. Monte Carlo Simulation. GeneratingRandom Variables. Variance Reduction Techniques.Importance Sampling. Stochastic Calculus.Simulation of Diffusions. Sensitivity Analysis.Appendices. Bibliography. Index.

Catalog no. K12713, May 2012, 292 pp.ISBN: 978-1-4398-5824-0, $79.95 / £49.99Also available as an eBook

An Introductionto ExoticOption PricingPeter BuchenUniversity of Sydney, Australia

In an easy-to-understand, nontechnical yet mathe-matically elegant manner, this book shows how toprice exotic options, including complex ones, withoutperforming complicated integrations or formally solv-ing PDEs. It develops special pricing techniques basedon the no-arbitrage principle and fully derives everyprice formula for the exotic options. The author incor-porates a significant amount of original, previouslyunpublished material, such as the use of log-volutionsand Mellin transforms to solve the Black–Scholes PDE.He also demystifies many esoteric issues underpinningthe mathematical treatment of the subject.

• Fully derives every price formula for the exoticoptions

• Develops special pricing techniques based onthe no-arbitrage principle

• Contains a significant amount of original,previously unpublished material

• Demystifies many esoteric issues underpinningthe mathematical treatment of the subject

• Includes challenging problems at the end ofeach chapter to illustrate the special pricingtechniques


Selected Contents:

Technical Background: Financial Preliminaries.Mathematical Preliminaries. Gaussian RandomVariables. Applications to Exotic Option Pricing:Simple Exotic Options. Dual Expiry Options. Two-Asset Rainbow Options. Barrier Options. LookbackOptions. Asian Options. Exotic Multi-Options.References. Index.

Catalog no. C9100, February 2012, 296 pp.ISBN: 978-1-4200-9100-7, $79.95 / £49.99Also available as an eBook




Math for Finance

New!

ComputationalMethods inFinanceAli HirsaCaspian Capital Management,LLC, New York, USA

“A natural polymath, the author is at once ateacher, a trader, a quant, and now an author of abook for the ages. The content reflects the author’svast experience teaching master’s level courses atColumbia and NYU, while simultaneously research-ing and trading on quantitative finance in leadingbanks and hedge funds.”

—Peter Carr, Morgan Stanley and NYU CourantInstitute of Mathematical Sciences

“A long-time expert in computational finance, AliHirsa brings his excellent expository skills to bear onnot just one technique but the whole panoply, fromfinite difference solutions to PDEs/PIDEs throughsimulation to calibration and parameter estima-tion.”

—Emanuel Derman, Columbia University and authorof Models Behaving Badly

• Addresses key computational methods infinance, including transform techniques,the finite difference method, and Monte Carlosimulation

• Covers model calibration and optimization

• Describes techniques, such as Kalman and particle filters, for parameter estimation

• Provides algorithms that can be easily coded

• Includes case studies and exercises

Selected Contents:

I Pricing and Valuation: Stochastic Processes andRisk-Neutral Pricing. Derivatives Pricing via TransformTechniques. Introduction to Finite Differences.Derivative Pricing via Numerical Solutions of PDEs.Derivative Pricing via Numerical Solutions of PIDEs.Simulation Methods for Derivatives Pricing. II Calibration and Estimation: Model Calibration.Filtering and Parameter Estimation. References.Index.

Catalog no. K11454, September 2012, 444 pp.ISBN: 978-1-4398-2957-8, $89.95 / £59.99Also available as an eBook

OptionValuationA First Course in FinancialMathematicsHugo D. JunghennThe George WashingtonUniversity, Washington, D.C., USA

Largely self-contained, this classroom-tested text pro-vides a straightforward introduction to the mathe-matics and models used in the valuation of financialderivatives. It examines the principles of option pric-ing in detail via standard binomial and stochastic cal-culus models and develops the requisite mathematicalbackground as needed. Numerous examples andexercises help students gain expertise with financialcalculus methods and increase their general mathe-matical sophistication.

• Offers a straightforward account of theprinciples and models of option pricing

• Focuses on the (discrete time) binomial modeland the (continuous time) Black-Scholes-Mertonmodel

• Develops probability theory and finance theoryfrom first principles

• Covers various types of financial derivatives,including currency forwards, put and calloptions, and path-dependent options

• Uses the notion of variation of a function toillustrate the similarities and differences betweenclassical calculus and stochastic calculus

• Presents a martingale approach to optionpricing

• Contains many examples and end-of-chapterexercises


Selected Contents:

Interest and Present Value. Probability Spaces.Random Variables. Options and Arbitrage. Discrete-Time Portfolio Processes. Expectation of a RandomVariable. The Binomial Model. ConditionalExpectation and Discrete-Time Martingales. TheBinomial Model Revisited. Stochastic Calculus. TheBlack-Scholes-Merton Model. Continuous-TimeMartingales. The BSM Model Revisited. OtherOptions. Appendices. Bibliography. Index.

Catalog no. K14090, November 2011, 266 pp.ISBN: 978-1-4398-8911-4, $59.95 / £38.99Also available as an eBook



13

Math for Finance


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

“… a nice book for researchers and practitioners. …this book can be regarded as a wonderful applica-tion of stochastic analysis, as it includes not onlydetailed theoretical proofs but also practical illustra-tive examples. With the systematic and feasiblenumeraire techniques, the book can serve as aneveryday reference book for practitioners, but also asa powerful tool to deal with pricing and hedging forcomplicated financial assets. Most importantly, therepresentation of prices as a pairwise relationship oftwo assets is the most novel characteristic of thisbook, which could lead to deeper understanding ofderivative contracts.”

—Mathematical Reviews, 2012f

“Jan Vecer has taken years of teaching experienceand practitioners’ feedback to unify a previouslycomplicated topic into the most elegant and easilyaccessible numeraire textbook to come down thepike. … There should be more such books.”

—Uwe Wystup, MathFinance AG

This classroom-tested text provides a deep under-standing of derivative contracts. It treats price as anumber of units of one asset needed for an acquisitionof a unit of another asset instead of expressing pricesin dollar terms exclusively. This numeraire approachleads to simpler pricing options for complex products,such as barrier, lookback, quanto, and Asian options.

Selected Contents:

Introduction. Elements of Finance. Binomial Model.Diffusion Models. Interest Rate Contracts. BarrierOptions. Lookback Options. American Options.Contracts on Three or More Assets: Quantos,Rainbows and “Friends.” Asian Options. JumpModels. Appendix. Solutions to Selected Exercises.References. Index.


Coming soon!

RiskManagementand SimulationAparna GuptaRensselaer Polytechnic University,Troy, New York, USA

This book presents the modeling techniques andmethodologies used to solve problems of risk man-agement that are relevant to market, credit, opera-tional, and business risk. The author connects riskmanagement with simulation to show how the toolcan be used to minimize risk in an organization andthen arrive at a solution. Topics covered includeframeworks for risk management, regulations, build-ing models of risk, credit risk management, asset-lia-bility management, and strategic risk management.MATLAB® is used in examples and exercises, with codeavailable on the author’s website.

• Focuses on simulation modeling and analysis

• Connects risk management and simulation

• Discusses the range of tools used in riskmanagement

• Includes many applied examples, problems, and exercises

• Provides support for students taking the CFA,GARP, and actuarial exams

• Offers MATLAB code on the author’s website

Selected Contents:

Defining Risk. Frameworks for Risk Management.Regulations and Risk Management. Principles ofSimulation and Generating. Random Variates.Modeling Risk Evolving over Time. Building andSolving Models of Risk. Managing Equity MarketRisk. Managing Interest Rates and Other MarketRisks. Asset-Liability Management. Credit RiskManagement. Risk Management using Insurance.Operational, Business and Strategic RiskManagement. Advanced Simulation Topics.

Catalog no. K11622, August 2013, c. 416 pp.ISBN: 978-1-4398-3594-4, $99.95 / £63.99Also available as an eBook




Geometry and Topology Math for Engineering and Computer Science

CollegeGeometryA UnifiedDevelopmentDavid C. KayUniversity of North Carolina,Ashville, USA (retired)

This text unifies Euclidean, elliptic, and hyperbolicgeometry within an axiomatic framework. It coverstopological shapes of geometric objects and includesmore than 700 carefully crafted problems. Numerousexamples show how geometry has real and far-reach-ing implications. The author approaches every topicas a fresh, new concept and carefully defines andexplains geometric principles.

• Covers topological shapes of geometric objects

• Includes “Moments for Reflection” sections thatchallenge students to think for themselves andencourage self-discovery

• Offers instructions on specific experiments usingthe Geometer’s Sketchpad software

• Contains more than 500 drawings and 80 examples to illustrate concepts and problemsolving

• Presents historical notes that point out thehuman aspects of geometric discovery

• Incorporates research projects for undergraduatestudents

• Provides more than 700 carefully crafted problems, with selected solutions at the back of the book


Selected Contents:

Lines, Distance, Segments, and Rays. Angles, AngleMeasure, and Plane Separation. Unified Geometry:Triangles and Congruence. Quadrilaterals, Polygons,and Circles. Three Geometries. Inequalities forQuadrilaterals: Unified Trigonometry. Beyond Euclid:Modern Geometry. Transformations in ModernGeometry. Non-Euclidean Geometry: AnalyticalApproach. Appendices. Solutions to SelectedProblems. Bibliography. Index.


Linear Algebraand Probabilityfor ComputerScienceApplicationsErnest DavisNew York University, New York, USA

Based on the author’s course at NYU, this classroom-tested book gives an introduction to two mathemati-cal fields that are fundamental in many areas of com-puter science. After an introductory chapter on MAT-LAB®, the text is divided into two sections, with thefirst focusing on linear algebra and the second dis-cussing probability. The book covers applications froma range of computer science areas, including com-puter vision, robotics, natural language processing,statistical analysis, game playing, graph theory, scien-tific computing, decision theory, coding, networkanalysis, data compression, and signal processing.Each chapter includes MATLAB functions, MATLABprogramming assignments, and problems.

• Focuses on mathematical techniques that aremost relevant to computer scientists

• Assumes as little mathematical background aspossible

• Covers applications from computer graphics,web search, machine learning, cryptography,and a host of other computer science areas

• Includes MATLAB functions, MATLAB programming assignments, and problems ineach chapter, with code on the author’s website

Selected Contents:

MATLAB. LINEAR ALGEBRA: Vectors. Matrices. VectorSpaces. Algorithms. Geometry. Change of Basis, DFT,and SVD. PROBABILITY: Probability. NumericalRandom Variables. Markov Models. ConfidenceIntervals. Monte Carlo Methods. Information andEntropy. Maximum Likelihood Estimation.References. Notation. Index.

Catalog no. K14397, May 2012, 431 pp.ISBN: 978-1-4665-0155-3, $59.95 / £39.95Also available as an eBook



15

Math for Biology and Medicine


Coming soon!

Radar SystemsAnalysis andDesign UsingMATLAB®

Third EditionBassem R. MahafzadeciBel Research Inc.,Huntsville, Alabama, USA

Using the most recent version of MATLAB®, the thirdedition of this popular text incorporates recentadvances along with many new problems and exam-ples. It adds coverage of radar cross-section and polar-ization, matched filter and radar ambiguity function,radar wave propagation, adaptive array processing,multiple input-output radars, space-time adaptiveprocessing, phase noise, and Doppler processing.MATLAB codes are available for download on thebook’s CRC Press web page.

• Includes new information on radar cross-sectionand polarization, matched filter and radarambiguity function, and radar wave propagation

• Provides all the necessary mathematical background

• Presents MATLAB programs for each chapter toenhance understanding and supply a source ofradar systems design requirements


Selected Contents:

Radar Principles. Radar Signals and Signal Processing.Radar Special Considerations. Radar Detection. RadarSpecial Topics. Bibliography. Index.

Catalog no. K13984, June 2013, c. 768 pp.ISBN: 978-1-4398-8495-9, $129.95 / £82.00Also available as an eBook

Dynamics ofBiologicalSystemsMichael SmallHong Kong PolytechnicUniversity

With exercises and projects in each chapter, this class-room-tested text shows how to apply a variety ofmathematical and computational techniques tomodel and analyze the temporal and spatial phenom-ena of biological systems. The mathematical modelsand computer simulations offer insight into cardiacpacemakers, artificial electrical defibrillation, pan-demics, pattern formation, flocking behavior, theinteraction of autonomous agents, and hierarchicaland structured network topologies. MATLAB® imple-mentations of algorithms and case studies are avail-able on the author’s website.

• Uses complex systems, complex networks, anddynamics to derive models and computersimulations of various biological systems

• Presents a wide range of models, from ECG signal processing to pandemic modeling to population dynamics

• Requires no advanced knowledge ofmathematics

• Includes exercises as well as computational andresearch projects at the end of each chapter

• Offers MATLAB implementations of many keyalgorithms and various case studies on theauthor’s website


Selected Contents:

Biological Systems and Dynamics. PopulationDynamics of a Single Species. Observability ofDynamic Variables. Biomedical Signal Processing.Computational Neurophysiology. MathematicalNeurodynamics. Population Dynamics. Action,Reaction and Diffusion. Autonomous Agents.Complex Networks. Conclusion. References. Index.

Catalog no. K12463, August 2011, 284 pp.ISBN: 978-1-4398-5336-8, $79.95 / £49.99Also available as an eBook

Math for Engineering and Computer Science




Math for Biology and Medicine

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

“Instructors who are already teaching a stochasticprocesses course and want to introduce biologicalexamples will find this book to be a gold mine of use-ful material. … the book will be a useful addition tothe library of anyone interested in stochasticprocesses who wants to learn more about their bio-logical applications. I certainly learned a great dealfrom it!”

—MAA Reviews, January 2012

“… a good introductory textbook for junior gradu-ate students who are interested in mathematicalbiology. … this book is written in plain language sostudents with a basic probability background caneasily grasp the material. … this book covers a richset of selected topics with a clear focus on Markov-type processes. … the author has made a greateffort to encourage the use of stochastic models inpractice by providing many pieces of MATLAB codes,which are usually unavailable in other books on sto-chastic processes. Finally, compared with the previ-ous edition, this newly released version particularlyextends the stochastic differential equation part byincluding the multivariate Kolmogorov equationsand the Itô formula.”

—Mathematical Reviews, Issue 2011m

Selected Contents:

Review of Probability Theory and an Introduction toStochastic Processes. Discrete-Time Markov Chains.Biological Applications of Discrete-Time MarkovChains. Discrete-Time Branching Processes.Continuous-Time Markov Chains. Continuous-TimeBirth and Death Chains. Biological Applications ofContinuous-Time Markov Chains. Diffusion Processesand Stochastic Differential Equations. BiologicalApplications of Stochastic Differential Equations.Appendix. Index.


BiologicalComputationEhud LammTel-Aviv University, Israel

Ron UngerBar-Ilan University, Ramat-Gan, Israel

“Biological computing … is ready for our education-al mainstream. This beautiful undergraduate text byLamm and Unger may be the first step. This bookexpertly presents fundamental concepts of molecularbiology in its first chapter, and then goes on todevelop many computing classics from biology. … Ienjoyed reading this text. The exercises flex theimagination, the definitions are clear and precise,and the explanations are unusually powerful. I havebeen searching for a text like this for years, and nowI look forward to using it.”

—Computing Reviews, August 2011

“I read this book in one breath—it opens vistas onhow the fields of computation and biology caninspire each other. I particularly enjoyed the analo-gies between immune systems and software thatfights computer viruses.”

—Uri Alon, Weizmann Institute of Science and authorof An Introduction to Systems Biology: Design Principles of Biological Circuits

A unified overview of computer science ideas inspiredby biology, Biological Computation presents themost fundamental and significant concepts in thisarea. In the book, students discover profound ideasabout computer science through biological examples,such as the use of DNA for performing computationsand how evolution solves optimization problems.PowerPoint slides for instructors are available online.

Selected Contents:

Introduction and Biological Background. CellularAutomata. Evolutionary Computation. ArtificialNeural Networks. Molecular Computation. TheNever-Ending Story: Additional Topics at theInterface between Biology and Computation.

Catalog no. C7959, May 2011, 343 pp.ISBN: 978-1-4200-8795-6, $79.95 / £49.99



17

Math for Biology and Medicine Algebra


Coming soon!

DynamicalModels inMedicineYang KuangArizona State University, Tempe, USA

John NagyScottsdale Community College,Arizona, USA

This self-contained book focuses on three categoriesof disease: cancer, viral diseases, and dynamical dis-eases. It presents the medical and biological back-ground of these diseases, specific issues for modeling,and existing methods and their limitations. It intro-duces mathematical and programming tools, alongwith analytical and numerical studies of models.

The authors provide end-of-chapter exercises andprojects, with hints and answers to selected problemsat the back of the book. A supplementary websiteoffers lecture notes, homework problems, useful com-puter programs, and other reference material.

• Presents models that are well motivated andwell rooted in both biology and themathematical ecology framework

• Derives, analyzes, and tests many models

• Contains interesting and up-to-date biologicalbackground on the diseases being modeled

Selected Contents:

MATHEMATICAL ONCOLOGY: Etiology.Pathogenesis. Treatment. MATHEMATICALIMMUNOLOGY AND VIROLOGY: A Primer of Virusesand Immunity. Influenza Models. HIV Models.DYNAMIC DISEASES: Dynamical Diseases,Oscillations, and Chaos. Biological Oscillators.Models of Dynamical Diseases. APPENDICES. REFERENCES.

Catalog no. C990X, July 2013, c. 500 pp.ISBN: 978-1-58488-990-8, $79.95 / £49.99Also available as an eBook

UniversalAlgebraFundamentals andSelected TopicsClifford BergmanIowa State University, Ames, USA

“… the book under review, by Clifford Bergman, ismost welcome: we need more of this sort of thing …it is clearly written and pleasant to read … theauthor provides motivation as well as examples andexercises galore. At first glance it looks to me like theexercises are well-structured and should do the jobof bringing the student or reader along at a decentpace from ignorance to both an appreciation for thesubject and some facility with it. It’s definitely anarea worth pursuing for a graduate student with theright disposition.”

—MAA Reviews, December 2011

Starting with the most basic notions, this text intro-duces all the key elements needed to read and under-stand current research in the field. The first part of thebook focuses on core components and the secondpart covers topics that demonstrate the power andbreadth of the subject, such as directly representablevarieties. Examples and exercises are includedthroughout the text.

• Emphasizes clones and varieties of algebras

• Offers an extensive presentation of tame congruence theory

• Uses a set of examples throughout the text toillustrate key concepts

• Introduces tools and techniques as needed andlinks them to applications

• Includes carefully chosen exercises that help students develop proficiency in each topic

Selected Contents:

FUNDAMENTALS OF UNIVERSAL ALGEBRA: Algebras.Lattices. The Nuts and Bolts of Universal Algebra.Clones, Terms, and Equational Classes. SELECTEDTOPICS: Congruence Distributive Varieties.Arithmetical Varieties. Maltsev Varieties. FiniteAlgebras and Locally Finite Varieties. Bibliography.Index.

Catalog no. K12346, September 2011, 320 pp.ISBN: 978-1-4398-5129-6, $99.95 / £63.99Also available as an eBook




Mathematical Computation

New!

Probability and StochasticModelingVladimir I. RotarSan Diego State University,California, USA

“This is a superbly written text on probability andstochastic processes for students who have had twosemesters of calculus and an introductory course inlinear algebra. … Important and well-chosen exam-ples illustrate the theory throughout, and a largebody of exercises supplements the text. It gives alucid presentation of basic probability theory … . Aspecial feature of this book is a marvelous expositionof many interesting aspects of financial mathemat-ics that are generally considered rather intricate andinaccessible at this level. … an outstanding additionto the field requiring only a modest background inmathematics.”

—Rabi Bhattacharya, University of Arizona

“The successful combination of a variety of exam-ples, exercises, and applications with deep and non-trivial ideas makes the book interesting not only forbeginning students, but also for professionals work-ing with probabilistic problems. … an ideal textbookfor anyone interested in probability theory and itsapplications.”

—Youri Davydov, Université des Sciences etTechnologies de Lille

Solutions manual and figure slides available upon qualifying course adoption

Selected Contents:

Independence and Conditional Probability. DiscreteRandom Variables. Generating Functions. BranchingProcesses. Random Walk Revisited. Markov Chains.Continuous Random Variables. Distributions in theGeneral Case. Simulation. Moment GeneratingFunctions. The Central Limit Theorem forIndependent Random Variables. Covariance Analysis.The Multivariate Normal Distribution. TheMultivariate Central Limit Theorem. Maxima andMinima of Random Variables. Elements of ReliabilityTheory. Hazard Rate and Survival Probabilities.Stochastic Processes: Preliminaries. Counting andQueuing Processes. Birth and Death Processes: A General Scheme. Elements of Renewal Theory.Martingales in Discrete Time. …

Catalog no. K13311, August 2012, 508 pp.ISBN: 978-1-4398-7206-2, $79.95 / £49.99Also available as an eBook

Probability and Statistics

An Introductionto NumericalMethodsA MATLAB®

Approach,Third EditionAbdelwahab KharabAbu Dhabi University,United Arab Emirates

Ronald B. GuentherOregon State University, Corvallis, USA

Highly recommended by CHOICE, this popular textcontinues to present a wide range of useful andimportant algorithms for scientific and engineeringapplications. Along with MATLAB® GUIs throughout,this third edition incorporates a new chapter on thenumerical solution of integral equations and a newsection on nonlinear PDEs. The authors use MATLABto illustrate each numerical method, providing fulldetails of the computer results and supplying theMATLAB functions on a CD-ROM.

• Covers the most common numerical methodsencountered in science and engineering

• Illustrates the methods using MATLAB

• Presents numerous examples and exercises, withselected answers at the back of the book

• Supplies MATLAB functions on an accompanyingCD-ROM


Selected Contents:

Introduction. Number System and Errors. Roots ofEquations. System of Linear Equations. Interpolation.Interpolation with Spline Functions. The Method ofLeast Squares. Numerical Optimization. NumericalDifferentiation. Numerical Integration. NumericalMethods for Linear Integral Equations. NumericalMethods for Differential Equations. Boundary-ValueProblems. Eigenvalues and Eigenvectors. PartialDifferential Equations. Bibliography and References.Appendices. Answers to Selected Exercises. Index.

Catalog no. K13161, November 2011, 576 pp.ISBN: 978-1-4398-6899-7, $89.95 / £44.99Also available as an eBook



19For more information and complete contents, visit www.crctextbooks.com

Probability,Statistics, andReliability forEngineers andScientistsThird EditionBilal M. Ayyub andRichard H. McCuenUniversity of Maryland, College Park, USA

The third edition of this bestselling text presents prob-ability, statistics, reliability, and risk methods with anideal balance of theory and applications. It placesincreased emphasis on simulation, particularly as amodeling tool, applying it progressively with projectsthat continue in each chapter. This edition also fea-tures expanded discussions of ANOVA and a thoroughtreatment of Monte Carlo simulation.

• Emphasizes risk and reliability for theengineering statistics market from a practicalpoint of view

• Includes various applications in engineering

• Provides additional material on simulation, themathematics related to uncertainty, the randfunction, sample variability, dependence, thePoisson process, and more

• Contains additional illustrations on histogramsamples and hypothesis testing along with Venn diagrams for conditional probabilities

Solutions manual and PowerPoint slides availableupon qualifying course adoption

Selected Contents:

Introduction. Data Description and Treatment.Fundamentals of Probability. Probability Distributionsfor Discrete Random Variables. ProbabilityDistributions for Continuous Random Variables.Multiple Random Variables. Simulation.Fundamentals of Statistical Analysis. HypothesisTesting. Analysis of Variance. Confidence Intervalsand Sample Size Determination. Regression Analysis.Multiple and Nonlinear Regression Analysis.Reliability Analysis of Components. Reliability andRisk Analysis of Systems. Bayesian Methods.Appendices. Index.

Catalog no. K10476, April 2011, 663 pp.ISBN: 978-1-4398-0951-8, $119.95 / £76.99Also available as an eBook

Elements ofAdvancedMathematicsThird EditionSteven G. KrantzWashington University, St. Louis, Missouri, USA

“… one of the difficulties that students have withuniversity mathematics is being able to relate it towhat they’ve done at school. … But another prob-lem to be addressed is to re-present mathematics asa way of knowing—rather than a static body of for-malised knowledge. In this book, Steven Krantz tack-les this anomaly by including many open-endedproblems in the rich collections of exercises. … Thenew chapters on theoretical computer science areconcisely lucid, and I learned much by reading them.… this book engages the reader in really meaningfulaspects of mathematics: it is well organized and iswritten with accuracy. … it is recommended as apossible course text for those who are planning toteach a foundation course.”


This bestselling text provides a path for students tounderstand the rigor, axiomatics, set theory, andproofs of mathematics. This third edition adds fournew chapters on point-set topology, theoretical com-puter science, the P/NP problem, and zero-knowl-edge proofs and RSA encryption. It also includes moreexercises sets in each chapter, expanded treatment ofproofs, and new proof techniques. A solutions manu-al is available upon qualifying course adoption.

Selected Contents:

Basic Logic. Methods of Proof. Set Theory. Relationsand Functions. Axioms of Set Theory, Paradoxes, andRigor. Number Systems. More on the Real NumberSystem. A Glimpse of Topology. TheoreticalComputer Science. The P/NP Problem. Examples ofAxiomatic Theories. Zero-Knowledge Proofs.Solutions to Selected Exercises. Bibliography. Index.

Catalog no. K14300, March 2012, 367 pp.ISBN: 978-1-4398-9834-5, $89.95 / £44.99Also available as an eBook

Probability and Statistics Set Theory and Logic




Applied Math

PhysicalOceanographyA MathematicalIntroduction withMATLAB®

Reza Malek-MadaniU.S. Naval Academy, Annapolis, Maryland, USA

Accessible to advanced undergraduate students, thistext demonstrates how to use the basic tenets of mul-tivariate calculus to derive the governing equations offluid dynamics in a rotating frame. It also explainshow to use linear algebra and PDEs to solve basic ini-tial-boundary value problems that have become thehallmark of physical oceanography. The book makesthe most of MATLAB®’s matrix algebraic functions, dif-ferential equation solvers, and visualization capabilitiesand includes chapter projects that incorporate MAT-LAB programming.

• Explores how mathematics plays a critical role inthe investigation of geophysical fluid dynamics,wind-driven ocean circulation, shallow water,and other applications in physical oceanography

• Reviews calculus, differential equations, linearalgebra, and the basic use of MATLAB

• Includes simple examples that introduce featuresof fluid flows

• Presents research from pioneers in the mathematical modeling of physical oceanography, including Stommel, Munk,Veronis, and Lorenz

• Covers the work of applied mathematicians whoare making significant impacts on developingtools for modern physical oceanography

• Contains end-of-chapter projects thatincorporate MATLAB programming

Selected Contents:

An Introduction to MATLAB. Matrix Algebra.Differential and Integral Calculus. OrdinaryDifferential Equations. Numerical Methods for ODEs.Equations of Fluid Dynamics. Equations ofGeophysical Fluid Dynamics. Shallow WaterEquations. Wind-Driven Ocean Circulation: TheStommel and Munk Models. Some Special Topics.Appendix.

Catalog no. C830X, April 2012, 456 pp.ISBN: 978-1-58488-830-7, $79.95 / £49.99Also available as an eBook

Mathematicsfor theEnvironmentMartin WalterUniversity of Colorado, Boulder, USA

“The book is heavily referenced … there are manydetailed exercises designed to highlight how mathe-matics can be used to explain natural phenomenaand human behavior and its consequences. … thisbook could serve as a text for courses in appliedmathematics and a resource for study material inmany other subject areas …”


A truly interdisciplinary, concrete study of mathemat-ics, this classroom-tested text shows students how toemploy simple mathematical tools, such as arithmetic,to uncover fundamental conflicts between the logic ofhuman civilization and the logic of nature. These toolscan then be used to understand and effectively dealwith economic, environmental, and social issues,including climate change, media literacy, and muchmore.

• Explains how mathematics can be used tounderstand and hopefully solve some of theworld’s most pressing problems, including therecent financial meltdown and interrelatedenergy and climate crises

• Includes numerous applications, from populationand economic models, epidemics, financialmathematics, and DNA computing to climatechange, pollution, solar energy, and medialiteracy

• Requires good comprehension of high school-level mathematics

• Offers many problem sets within each section

• Encourages the use of spreadsheets to help withproblem solving

Figure slides available upon qualifying course adoption

Selected Contents:

Mathematics Is Connected to Everything Else. Mathand Nature: The Nature of Math. One of the OldestMathematical Patterns. Counting. Box Models:Population, Money, Recycling. Chance: Health,Surveillance, Spies, and Voting. Economics. MediaLiteracy. References. Index.




21

Applied Math Mathematical Modeling


OptimalEstimation ofDynamicSystemsSecond EditionJohn L. CrassidisState University of New York-Buffalo, USA

John L. JunkinsTexas A&M University, College Station, USA

An ideal self-study guide for senior undergraduate andbeginning graduate students, this book highlights theimportance of both physical and numerical modelingin solving dynamics-based estimation problems foundin engineering systems, such as spacecraft attitudedetermination, GPS navigation, orbit determination,and aircraft tracking. With more than 100 pages ofnew material, this reorganized and expanded editionincorporates new theoretical results, a new chapter onadvanced sequential state estimation, and additionalexamples and exercises.

• Presents rigorous, detailed treatments of leastsquares and Kalman filtering

• Discusses several advanced estimation concepts,such as multiple-model adaptive estimation andunscented, particle, Gaussian sum, and ensemble filtering

• Applies estimation theory to actual dynamicsystems, including flight paths, space orbits,and machine control

• Includes tables for all algorithms to enable quickaccess for programming purposes

• Integrates the required prerequisites (matrixproperties, probability, statistics, and optimization methods) in the appendices

• Contains 350 analytical and computer-basedproblems

• Provides the MATLAB® codes for all examples onthe book’s website

Selected Contents:

Least Squares Approximation. Probability Conceptsin Least Squares. Sequential State Estimation.Advanced Topics in Sequential State Estimation.Batch State Estimation. Parameter Estimation:Applications. Estimation of Dynamic Systems:Applications. Optimal Control and EstimationTheory. Appendices. Index.

Catalog no. K11836, October 2011, c. 749 pp.ISBN: 978-1-4398-3985-0, $139.95 / £89.00Also available as an eBook

MathematicalModelling withCase StudiesA DifferentialEquations ApproachUsing Maple™ and MATLAB®,Second EditionBelinda BarnesAustralian National University, Canberra

Glenn Robert FulfordUniversity of Technology, Brisbane, Australia

“The book is written in a very lucid manner, withnumerous case studies and examples thoroughly dis-cussed. The material is very well organized, gener-ously illustrated, and delightfully presented. …scores of nicely designed exercises can be used forindependent study. …”

—Zentralblatt MATH, 1168

“The book can be useful for students of mathemati-cal modeling. They will find many skills for modelingand solving real problems. Useful sheets for Mapleand MATLAB are included for numerical solution.The most important feature of the book is that itcontains many real-life examples. … the best treas-ury of real case problems seen in a single book.”

—EMS Newsletter, September 2009

This textbook carefully details the process of con-structing a model. It includes many case studies toprovide a practical understanding of how the modelsare used in current research. Maple™ and MATLAB®

codes are supplied in the text and online so results canbe reproduced exactly. A solutions manual is availableupon qualifying course adoption.

Selected Contents:

Compartmental Models. Models of SinglePopulations. Numerical Solution of DifferentialEquations. Interacting Population Models. Phase-Plane Analysis. Linearization Analysis. Some ExtendedPopulation Models. Formulating Basic Heat Models.Solving Time-Dependent Heat Problems. SolvingHeat Conduction Problems. Introduction to PartialDifferential Equations. Appendices. References.Index.

Catalog no. C8348, December 2008, 368 pp.ISBN: 978-1-4200-8348-4, $87.95 / £33.99Also available as an eBook




Operations Research

Value-AddedDecisionMaking forManagersKenneth ChelstWayne State University, Detroit,Michigan, USA

Yavuz Burak CanbolatAbbott Laboratories, AbbottPark, Illinois, USA

Developed from the authors’ longstanding course ondecision and risk analysis, this text explores the impor-tant interaction between decisions and managementaction and clarifies the barriers to rational decisionmaking. The authors analyze strengths and weakness-es of the best alternatives, enabling decision makers toimprove on these alternatives by adding value andreducing risk. Numerous examples highlight real-world situations from everyday life, public policy, andindustry. Software tutorials, PowerPoint presentations,and solutions to numeric examples are available onthe book’s website.

Selected Contents:

STRUCTURING HARD DECISIONS: The Case for aStructured Analytic Decision Process. FramingDecisions with Influence Diagrams. CommonDecision Templates. DECISIONS WITH MULTIPLEOBJECTIVES: Structure Decisions with MultipleObjectives. Structured Trade-Offs for MultipleObjective Decisions: Multi-Attribute Utility Theory.Value and Risk Management for Multi-ObjectiveDecisions. Multiple Objective Decisions with LimitedData: Analytical Hierarchy Process. DECISIONS ANDMANAGEMENT UNDER UNCERTAINTY: Value-AddedRisk-Management Framework and Strategies.Spreadsheet Simulation for Decisions withUncertainty. Decisions with Uncertainty: DecisionTrees. Structured Risk Management and the Value ofInformation and Delay. Risk Attitude and UtilityTheory. CHALLENGES TO “RATIONAL” DECISIONS:Forecast Bias and Expert Interviews. Decision Bias.DECISIONS WITH MULTIPLE PERSPECTIVES: Value-Added Negotiations. Ethical Decisions. StrategicDirection, Planning, and Decision Making.Appendices. Index.

Catalog no. C7572, October 2011, 578 pp.ISBN: 978-1-4200-7572-4, $139.95 / £89.00Also available as an eBook

Coming soon!

BusinessProcessModeling,Simulation andDesignSecond EditionManuel LagunaUniversity of Colorado, Boulder, USA

Johan MarklundLund University, Sweden

The second edition of this popular text looks at busi-ness process design from a broad quantitative model-ing perspective and addresses various managerialissues. It gives students a thorough understanding ofthe wide range of tools available for modeling, ana-lyzing, and designing business processes. This editionincludes new material on change management, proj-ect management, task analysis, and performanceoptimization. It also adds details on the theory of con-straints and completely revises coverage of businessprocess modeling and simulation as well as using thesoftware tool ExtendSim LT, which is available fordownload.

• Integrates discrete event simulation as a tool forimproving and designing business processes

• Includes many case studies that offer a practicalview of the issues related to process design

• Presents deterministic models and basic queuingsystems as alternative methods for processanalysis and design

• Discusses the use of data envelopment forbenchmarking processes

• Uses the notion of simulation-optimizationthroughout


Selected Contents:

Introduction to Business Process Design. ProcessManagement and Process-Oriented ImprovementProcesses. A Simulation-Based Framework forBusiness Processes Design Projects. Basic Tools forProcess Design. Managing Process Flows.Introduction to Queuing and Simulation.Introduction to Extend. Modeling and SimulatingBusiness Processes. Input and Output Data Analysis.Optimizing Business Process Performance. ProcessBenchmarking with Data Envelopment Analysis.

Catalog no. K13989, May 2013, c. 520 pp.ISBN: 978-1-4398-8525-3, $99.95 / £63.99Also available as an ebook



Over the past fifteen years, CRC Press has developed an out-standing collection of textbooks to serve the mathematical

community. Our range is broad, from introductory textbookson mathematics for liberal arts to graduate level textbooks in

financial mathematics and cryptography.

We aim to publish the highest quality texts at prices studentscan afford. If you have a manuscript in progress or an idea

you want to explore, we would like to hear from you.

Proposals may be submitted directly to:

CRC Press/Taylor & Francis6000 Broken Sound Parkway NW, Suite 300

Boca Raton, FL 33487, USA

Sunil NairPublisher

[email protected]

Want to Publish With Us?CRC Press/Taylor & Francis Seeks Authors




6000

Bro

ken

Soun

d Pa

rkw

ay, N

W, S

uite

300

Boca

Rat

on, F

L 33

487,

USA

ww

w.c

rcte

xtbo

oks.

com

PR

ES

OR

TE

D

STA

ND

AR

D

US

PO

STA

GE

PA

ID

CR

C P

RE

SS

JOIN THE

•E-

exam

cop

ies

are

deliv

ered

qui

cker

and

eas

ier

atwww.crctextboo

ks.com

•C

usto

m P

ublis

hing

now

ava

ilabl

e in

e-fo

rmat

at

www.crctextboo

ks.com

/custompub

textbooks in mathematics

Documents