Contents Combinatorics and Discrete Mathematics ................3 General and Introductory Mathematics ....................8 Differential Equations and Nonlinearity ..................10 Mathematics for Finance..........................................11 Geometry and Topology..........................................15 Page 20
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Mathematics for Engineering ..................................16 Mathematics for Biology and Medicine ..................17 Algebra......................................................................18 Mathematical Computation ....................................19 Probability and Statistics with Applications..............20 Set Theory and Logic................................................20 Applied Mathematics................................................21 Mathematical Modeling ..........................................22
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Operations Research ................................................22
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Combinatorics and Discrete Mathematics
New!
Discrete Mathematics with Ducks sarah-marie belcastro Research Associate, Smith College, Northampton, Massachusetts, USA
“When I used Discrete Mathematics with Ducks in class, I assigned readings, and my students came to class full of questions and ideas. Every day we had a good time in one way or another; these classes were a highlight of my teaching career. I give a lot of credit to this book, thanks to the author’s skill at blending rigor, great examples, casual humor, and precise writing.” —David Perkins, author of Calculus and Its Origins
“I had a lot of fun teaching from Discrete Mathematics with Ducks! … I think the discovery/exploratory/ problem solving approach is ABSOLUTELY the way this course should be taught, and of all the discrete books I have looked at, this text does the best job of supporting that kind of approach to the subject while still giving enough of the material in writing to fill in the gaps. … I found that the material provided and the instructor notes cut down on my prep time, and I definitely referred to them. Having the in-class activities included is a huge benefit to this book.” —Dana Rowland, Merrimack College
“… an incredible book … readable by students, useful for instructors, and constructed with style and flair. This book will make it much easier to teach an exciting, student-centered discrete mathematics course that will also serve as an excellent introduction to advanced critical thinking, problem-solving, and proofs. And there are ducks!” —Douglas Shaw, University of Northern Iowa
Containing exercises and materials that engage students at all levels, Discrete Mathematics with Ducks presents a gentle introduction for students who find the proofs and abstractions of mathematics challenging. This classroom-tested text uses discrete mathematics as the context for introducing proof writing. Facilitating effective and active learning, each chapter contains a mixture of discovery activities, expository text, in-class exercises, and homework problems. • Elementary exercises at the end of each expository section prompt students to review the material. • Try This! sections encourage students to construct fundamental components of the concepts, theorems, and proofs discussed. • Sets of discovery problems and illustrative examples reinforce learning. • Bonus sections can be used for take-home exams, projects, or further study. • Instructor Notes sections offer suggestions on how to use the material in each chapter. Solutions manual available with qualifying course adoption
Discrete Mathematics with Ducks offers students a diverse introduction to the field and a solid foundation for further study in discrete mathematics and complies with SIGCSE guidelines. The book shows how combinatorics and graph theory are used in both computer science and mathematics
Selected Contents: BASICS: Basic Counting. Set Theory and Logic. Graphs. Induction. Algorithms and Ciphers. COMBINATORICS: Binomial Coefficients and Permutations. Balls and Boxes and PIE. Recurrence. Counting and Geometry. GRAPH THEORY: Trees. Euler’s Formula. Traversals. Coloring. SUPPLEMENTAL/OPTIONAL MATERIAL: Probability. Cardinality.
Catalog no. K14547, June 2012, 580 pp., ISBN: 978-1-4665-0499-8, $59.95 Also available as an eBook
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Combinatorics and Discrete Mathematics
How to Count An Introduction to Combinatorics, Second Edition R.B.J.T. Allenby and Alan Slomson University of Leeds, UK
“The reasons I adopted this book are simple: it’s the best one-volume book on combinatorics for undergraduates. It begins slowly and gently, but does not avoid subtleties or difficulties. It includes the right mixture of topics without bloat, and always with an eye to good mathematical taste and coherence. … I was very much impressed with the first edition when I encountered it in 1994. I like the second edition even more. …” —Paul Zeitz, University of San Francisco
• Explains how to solve various combinatorial problems, from Euler’s problem of polygon division, Fibonacci numbers, and the Königsberg bridges problem to the four-color problem, labeled trees, and card shuffling • Contains enough material for a short course on graph theory • Presents proofs of key results as well as numerous worked examples • Includes paired exercises, along with a full solution to one of the exercises in each pair • Lists suggestions for further reading Solutions manual available with qualifying course adoption
Selected Contents: What’s It All About? 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. Books for Further Reading. Index.
Catalog no. C8260, August 2010, 444 pp. ISBN: 978-1-4200-8260-9, $79.95 Also available as an eBook
Bijective Combinatorics Nicholas Loehr Virginia Polytechnic Institute and State University, Blacksburg, USA
“This textbook, aimed at beginning graduate students, is the first to survey the subject emphasizing the role of bijections. … The exposition is careful and deliberate, and leaves no stone unturned … a welcome addition to the literature and a very nice book.” —David Callan, Mathematical Reviews, 2012d
“I found this book engaging. The proofs are very clear, and in many cases several proofs are offered. … an excellent choice for a first course in combinatorics for senior undergraduates. … This is a very nice book that deserves serious consideration.” —Peter Rabinovitch, MAA Reviews, September 2011
“The book is clearly written and packed with examples and problems. The organization is superior, with helpful tables of notation and definitions at the end of each chapter, along with a point-bypoint summary of the chief topics. … the book is an excellent one, and is a comprehensive and welcome addition to the area.” —Angele M. Hamel, Computing Reviews, August 2011
• Presents a readable yet rigorous exposition of enumerative combinatorics • Contains numerous worked examples and applications as well as nearly 1,000 exercises • Offers solutions, hints, or partial answers to many of the exercises at the end of the book • Includes errata and other pertinent information on the author’s website
Selected Contents: Basic Counting. Combinatorial Identities and Recursions. Counting Problems in Graph Theory. Inclusion-Exclusion and Related Techniques. Ranking and Unranking. Counting Weighted Objects. Formal Power Series. The Combinatorics of Formal Power Series. Permutations and Group Actions. Tableaux and Symmetric Polynomials. Abaci and Antisymmetric Polynomials. Additional Topics. Answers and Hints to Selected Exercises. Bibliography. Index.
Catalog no. K12206, February 2011, 612 pp. ISBN: 978-1-4398-4884-5, $99.95
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Combinatorics and Discrete Mathematics
Discrete Structures with Contemporary Applications Alexander Stanoyevitch
Introduction to Combinatorics W.D. Wallis Southern Illinois University, Carbondale, USA
California State University–Dominguez Hills, Carson, USA
J.C. George
“…this is the most physically readable textbook that I have seen in a long time. … there are many examples and in many cases proofs of the theorems are included. A large number of exercises are provided and split into two categories, the traditional math problem and exercises to be performed on a computer. … The two most important courses in the computer science major are the first programming and discrete math classes. … this book is an excellent text for the development of the needed skills in math.”
“… thoughtfully written, contain[s] plenty of material and exercises … provides numerous fragments of Mathematica code and this is a nice touch. …”
—Charles Ashbacher, MAA Reviews, March 2011
• Follows the recommendations of the ACM • Introduces several supplementary topics that can form an excellent basis for student projects • Includes a wide variety of examples and exercises, with solutions in the appendices • Incorporates computer exercises that teach students how to write their own programs • Covers many recent applications of discrete mathematics, including simulations and genetic algorithms • Presents algorithms in pseudo code • Offers sample programs via the author’s website • Illustrates difficult concepts with over 300 figures Solutions manual available with qualifying course adoption
Selected Contents: Logic and Sets. Relations and Functions, Boolean Algebra, and Circuit Design. The Integers, Induction, and Recursion. Number Systems. Counting Techniques, Combinatorics, and Generating Functions. Discrete Probability and Simulation. Complexity of Algorithms. Graphs, Trees, and Associated Algorithms. Graph Traversal and Optimization Problems. Randomized Search and Optimization Algorithms. Appendices. References. Index.
Catalog no. K10918, January 2011, 1002 pp. ISBN: 978-1-4398-1768-1, $99.95
Gordon College, Barnesville, Georgia, USA
—MAA Reviews, February 2011
With many modern examples, this undergraduatelevel introduction to combinatorics presents approaches for solving counting and structural questions. It provides basic information on sets, proof techniques, enumeration, and graph theory. The authors also explore the interaction between linear algebra and combinatorics. • Covers key families of functions, including Catalan, Bell, and Stirling numbers • Explains graph theory, coding theory, and design theory • Illustrates traditional problems with modern examples, such as digital music tracks • Discusses Maple™, Mathematica®, and other technological tools where appropriate • Provides several appendices that offer background material as well as brief biographies of mathematicians relevant to the topics • Includes exercises and problems in each chapter, with some solutions at the back of the book
Selected Contents: Fundamentals of Enumeration. The Pigeonhole Principle and Ramsey’s Theorem. The Principle of Inclusion and Exclusion. Generating Functions and Recurrence Relations. Catalan, Bell and Stirling Numbers. Symmetries and the Pólya–Redfield Method. Introduction to Graph Theory. Further Graph Theory. Coding Theory. Latin Squares. Balanced Incomplete Block Designs. Linear Algebra Methods in Combinatorics. Appendices. Solutions to Set A Exercises. Hints for Problems. Solutions to Problems. References. Index.
Catalog no. K10310, September 2010, 397 pp. ISBN: 978-1-4398-0622-7, $83.95 Also available as an eBook
Also available as an eBook
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Combinatorics and Discrete Mathematics Applied Combinatorics Second Edition Fred Roberts Rutgers University, Piscataway, New Jersey, USA
Barry Tesman Dickinson College, Carlisle, Pennsylvania, USA
Introduction to Cryptography with Mathematical Foundations and Computer Implementations Alexander Stanoyevitch
“The book has been substantially rewritten with more than 200 pages of new materials and many changes in the exercises. There are also many new examples … I strongly endorse this book. … It is a gem.” —IACR Book Reviews, 2011
“This is an overwhelmingly complete introductory textbook in combinatorics. It not only covers nearly every topic in the subject, but gives several realistic applications for each topic. … much more breadth than its competitors. …” —MAA Reviews, December 2009
“The writing style is excellent. … No other text with which I am familiar comes even close to the number of applications presented here.”
California State University–Dominguez Hills, Carson, USA
“I strongly recommend this book as an introductory book on cryptography for undergraduates.” —IACR Book Reviews, April 2011
“… a particularly good entry in a crowded field. … Stanoyevitch’s writing style is clear and engaging, and the book has many examples illustrating the mathematical concepts throughout. … It is clear that Stanoyevitch designed this book to be used by students and that he has taught this type of student many times before. The book feels carefully structured in a way that builds nicely … it is definitely a solid choice and will be on the short list of books that I would recommend to a student wanting to learn about the field.”
—John Elwin, San Diego State University
—MAA Reviews, May 2011
“This book is a required textbook for my graduate course in discrete mathematics. Both my students and I have found it to be an excellent resource with interesting application examples from a variety of fields interspersed throughout the text.”
“It is apparent that Prof. Stanoyevitch put a lot of pedagogical and intellectual effort into making a textbook — a book aimed at students that makes life easier for the instructor. In addition, the book’s companion site features short MATLAB m-files and applets for quick demos. … a very well done, thoughtful introduction to cryptography.”
—Dawit Haile, Virginia State University
“Roberts and Tesman’s book covers all the major areas of combinatorics in a clear, insightful fashion. But what really sets it apart is its impressive use of applications. I know of no other text which comes close.” —Thomas Quint, University of Nevada
Selected Contents: What Is Combinatorics? THE BASIC TOOLS OF COMBINATORICS: Basic Counting Rules. Introduction to Graph Theory. Relations. THE COUNTING PROBLEM: Generating Functions and Their Applications. Recurrence Relations. The Principle of Inclusion and Exclusion. The Pólya Theory of Counting. THE EXISTENCE PROBLEM: Combinatorial Designs. Coding Theory. Existence Problems in Graph Theory. COMBINATORIAL OPTIMIZATION: Matching and Covering. Optimization Problems for Graphs and Networks. Appendix. Indices.
—Daniel Bilar, University of New Orleans Solutions manual available with qualifying course adoption
Selected Contents: Divisibility and Modular Arithmetic. The Evolution of Codemaking until the Computer Era. Matrices and the Hill Cryptosystem. The Evolution of Codebreaking until the Computer Era. Representation and Arithmetic of Integers in Different Bases. Block Cryptosystems and the Data Encryption Standard (DES). Some Number Theory and Algorithms. Public Key Cryptography. Finite Fields in General and GF(28) in Particular. The Advanced Encryption Standard (AES) Protocol. Elliptic Curve Cryptography. Appendices. References.
Catalog no. K10916, August 2010, 669 pp. ISBN: 978-1-4398-1763-6, $89.95 Also available as an eBook
Catalog no. K10016, June 2009, 848 pp. ISBN: 978-1-4200-9982-9, $104.95 Also available as an eBook
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Combinatorics and Discrete Mathematics Graphs & Digraphs Fifth Edition
New!
Gary Chartrand Western Michigan University, Kalamazoo, USA
Combinatorics of Permutations
Linda Lesniak
Second Edition
Drew University, Madison, New Jersey, USA
Ping Zhang Western Michigan University, Kalamazoo, USA
“… an ideal textbook for the advanced undergraduate or beginning graduate course. … [Frank Harary’s] book was the standard in the discipline for several decades. Chartrand, Lesniak and Zhang have produced a worthy successor.” —John T. Saccoman, MAA Reviews, June 2012 (This book is in the MAA’s basic library list.)
“As with the earlier editions, the current text emphasizes clear exposition, well-written proofs, and many original and innovative exercises of varying difficulty and challenge. … The fifth edition continues and extends these fine traditions.” —Arthur T. White, Zentralblatt MATH 1211
“Now in its fifth edition, its success as a textbook is indicative of its quality and its clarity of presentation … It provides all you might need to know about graph embeddings and graph colorings. Moreover, it analyzes many other topics that more general discrete mathematics monographs do not always cover … this thorough textbook includes hundreds of exercises at the end of each section. Hints and solutions for odd-numbered exercises are included in the appendix, making it especially suitable for self-learning.” —Fernando Berzal, Computing Reviews, September 2011 Solutions manual available with qualifying course adoption
Selected Contents: Introduction to Graphs. Trees and Connectivity. Eulerian and Hamiltonian Graphs. Digraphs. Graphs: History and Symmetry. Planar Graphs. Graph Embeddings. Vertex Colorings. Map Colorings. Matchings, Factorization, and Domination. Edge Colorings. Extremal Graph Theory. Hints and Solutions to Odd-Numbered Exercises. Bibliography. Indices. List of Symbols.
Catalog no. K11263, October 2010, 598 pp. ISBN: 978-1-4398-2627-0, $89.95 Also available as an eBook
Miklós Bóna University of Florida, Gainesville, USA
“… a comprehensive, engaging, and eminently readable introduction to all aspects of the combinatorics of permutations. … This book can be utilized at a variety of levels, from random samplings of the treasures therein to a comprehensive attempt to master all the material and solve all the exercises. …” —From the Foreword by Richard Stanley, MIT
A 2006 CHOICE Outstanding Academic Title, the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. With much of the book significantly revised and expanded, this second edition continues to clearly show the usefulness of the subject. Along with more exercises and problems, this edition includes new material on sorting algorithms from molecular biology, alternating permutations, multivariate applications, pattern avoidance, and asymptotically normal distributions. • Requires only an introductory-level background in combinatorics • Contains more exercises and problems in each chapter • Presents numerous up-to-date references at the back of the book Solutions manual available with qualifying course adoption
Selected Contents: In One Line and Close. Permutations as Linear Orders. In One Line and Anywhere. Permutations as Linear Orders. Inversions. In Many Circles. Permutations as Products of Cycles. In Any Way but This. Pattern Avoidance. The Basics. In This Way but Nicely. Pattern Avoidance. Follow-Up. Mean and Insensitive. Random Permutations. Permutations versus Everything Else. Algebraic Combinatorics of Permutations. Get Them All. Algorithms and Permutations. How Did We Get Here? Permutations as Genome Rearrangements. Solutions to OddNumbered Exercises. References. List of Frequently Used Notation. Index.
Catalog no. K12299, June 2012, 478 pp. ISBN: 978-1-4398-5051-0, $89.95 Also available as an eBook
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General and Introductory Mathematics New!
Number, Shape, and Symmetry An Introduction to Number Theory, Geometry, and Group Theory
New!
Cryptology Classical and Modern with Maplets Richard E. Klima Appalachian State University, Boone, North Carolina, USA
Diane L. Herrmann and Paul J. Sally, Jr.
Neil P. Sigmon
University of Chicago, Illinois, USA
Requiring minimal mathematical prerequisites, this text explains in a clear, nontechnical manner how fundamental mathematical concepts are the bases of cryptographic algorithms. Easy-to-use Maplets provide practical examples of the techniques and are available for download online. • Illustrates the importance of cryptology in cultural and historical contexts, including the Enigma machine and Navajo code used during World War II • Describes the implementation and cryptanalysis of classical ciphers, such as substitution, transposition, shift, affine, Vigenère, and Hill • Gives straightforward explanations of the AES, public-key ciphers, and message authentication • Requires no prior programming knowledge or background in college-level mathematics • Integrates the easy-to-use technology of Maplets throughout • Offers material for teaching nonmathematical courses • Provides exercises in each chapter section, including some that can be used as projects • Presents all Maplet-based examples and exercises in separate sections • Supplies Maplet exercises and all of the Maplets used in the text online
This textbook shows how number theory and geometry are the essential components in the teaching and learning of mathematics for students in primary grades. The book synthesizes basic ideas that lead to an appreciation of the deeper mathematical ideas that grow from these foundations. The authors draw on their extensive experience teaching undergraduate nonscience majors, students in the Young Scholars Program, and public school K-8 teachers in the Seminars for Endorsement of Science and Mathematics Educators (SESAME). • Provides the foundation for teaching and learning mathematics • Draws on the authors’ extensive teaching experience • Covers divisibility and primes, congruences, rational numbers and real numbers, Euclidean algorithms, and more Solutions manual available with qualifying course adoption
Selected Contents: The Triangle Game. The Beginnings of Number Theory. Axioms in Number Theory. Divisibility and Primes. The Division and Euclidean Algorithms. Variations on a Theme. Congruences and Groups. Applications of Congruences. Rational Numbers and Real Numbers. Introduction to Geometry. Polygons and Their Construction. Symmetry Groups. Permutations. Polyhedra. Graph Theory. Tessellations. Connections.
Catalog no. K15328, October 2012, c. 528 pp. ISBN: 978-1-4665-5464-1, $69.95 Also available as an eBook
Radford University, Virginia, USA
Solutions manual available with qualifying course adoption
Selected Contents: Introduction to Cryptology. Substitution Ciphers. Transposition Ciphers. The Enigma Machine and Navajo Code. Shift and Affine Ciphers. Alberti and Vigenère Ciphers. Hill Ciphers. RSA Ciphers. ElGamal Ciphers. The Advanced Encryption Standard. Message Authentication. Bibliography. Hints or Answers to Selected Exercises. Index.
Catalog no. K13332, June 2012, 548 pp. ISBN: 978-1-4398-7241-3, $79.95 Also available as an eBook
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General and Introductory Mathematics
A Mathematical Look at Politics E. Arthur Robinson, Jr. and Daniel H. Ullman
Agents, Games, and Evolution Strategies at Work and Play Steven Orla Kimbrough The Wharton School, University of Pennsylvania, Philadelphia, USA
George Washington University, Washington, D.C., USA
“The book finds a nice compromise between formality and accessibility. The authors take care to build from examples, isolate what is important, and generalize into theorems. … The exercises that close each chapter are interesting and often quite challenging … Topics are introduced and motivated thoughtfully. … This is a very thoughtfully written text that should be made available to anyone with an interest in learning or teaching this topic.” —MAA Reviews, July 2011
Catalog no. K11044, December 2010, 477 pp. ISBN: 978-1-4398-1983-8, $51.95 Also available as an eBook
A Concise Introduction to Pure Mathematics Third Edition Martin Liebeck Imperial College, London, UK
“A diligent, active reader of this outstanding book will have the best foundation at minimum cost for making meaningful contributions to mathematics, science, or engineering.” —Computing Reviews, November 2011
“When I used it for a course, students could not get enough … . The material is very well chosen and arranged, and teaching from Liebeck’s book has in many different ways been among my most rewarding teaching experiences during the last decades.” —Boris Hasselblatt, Tufts University Solutions manual available with qualifying course adoption
Catalog no. K11624, August 2010, 268 pp. Soft Cover ISBN: 978-1-4398-3598-2, $59.95
Based on the author’s course at the University of Pennsylvania, this book presents computational strategies and useful methods for dealing with a variety of situations involving contexts of strategic interaction. The author first introduces classical game theory and strategy selection, explaining how actual agents choose their strategies and the effects of these strategies on model systems. He then explores a number of basic games using models in which agents have fixed strategies. The text goes on to review core results and applications of agent-based models in which strategic interaction is present and for which design issues have genuine practical import. It also addresses miscellaneous topics in strategic interaction, including lying in negotiations, reasoning by backward induction, and evolutionary models. • Requires minimal mathematical requirements by providing the necessary math background in an appendix • Includes 12 easily used, documented NetLogo models to illustrate findings and support further exploration • Presents sample models that may be used to explore strategic decision making in a wide variety of contexts • Provides examples from many different fields, including business and economics, politics, philosophy, engineering, biology, and policy analysis • Links to “games in the wild,” not merely to stylized models of games • Details useful methods for dealing with strategic situations • Contains extensive study questions at the end of each chapter
Selected Contents: Starters. Mixed Motives. Markets and Applications. Topics in Strategic Analysis. Appendices. Bibliography. Index.
Catalog no. K11564, December 2011, 512 pp. ISBN: 978-1-4398-3470-1, $79.95 Also available as an eBook
Also available as an eBook
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Differential Equations and Nonlinearity
Second Edition
Solution Techniques for Elementary Partial Differential Equations
Denny Gulick
Second Edition
University of Maryland, College Park, USA
Christian Constanda
New!
Encounters with Chaos and Fractals
Revised and updated, this second edition provides an accessible introduction to chaotic dynamics and fractal geometry for students with a calculus background. It incorporates important mathematical concepts associated with these areas and backs up the definitions and results with motivation, examples, and applications. Laying the groundwork for later chapters, the text begins with examples of mathematical behavior exhibited by chaotic systems, first in one dimension and then in two and three dimensions. Focusing on fractal geometry, the author goes on to introduce famous infinitely complicated fractals. He analyzes them and explains how to obtain computer renditions of them. The book concludes with the famous Julia sets and the Mandelbrot set. With more than enough material for a one-semester course, this book gives students an appreciation of the beauty and diversity of applications of chaotic dynamics and fractal geometry. It shows how these subjects continue to grow within mathematics and in many other disciplines. • Provides an updated presentation of chaotic dynamics • Contains new and expanded material on fractals that illustrates how to obtain computer renderings of them • Includes a substantial number of new exercises at the end of each section and MATLAB® programs in the appendix, with selected solutions at the back of the book Solutions manual available with qualifying course adoption
Selected Contents: Periodic Points. One-Dimensional Chaos. TwoDimensional Chaos. Systems of Differential Equations. Introduction to Fractals. Creating Fractals Sets. Complex Fractals: Julia Sets and the Mandelbrot Set. Computer Programs. Answers to Selected Exercises. References. Index.
Catalog no. C5173, April 2012, 387 pp. ISBN: 978-1-58488-517-7, $79.95 Also available as an eBook
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University of Tulsa, Oklahoma, USA
“Each chapter has many problems for practice, with solutions for some of them provided at the very end. The book is well written, concise, has adequate examples and can be used as a textbook for beginners to learn the techniques of PDE solvers.” —MAA Reviews, January 2011
“… this is quite simply the best book of its kind that I have seen thus far. The book not only contains solution methods for some very important classes of PDEs, in an easy-to-read format, but is also student-friendly and teacher-friendly at the same time. It is definitely a textbook that should be adopted.” —From the Foreword by Peter Schiavone, University of Alberta
A 2002 CHOICE Outstanding Academic Title, this popular text contains many new worked examples and exercises as well as a new chapter on complex variable methods. This edition also includes new sections on Cauchy–Euler equations, Bessel functions, Legendre polynomials, spherical harmonics, applications of Fourier transformations, and general hyperbolic equations. Ancillary materials, including a solutions manual, are available with qualifying course adoption.
Selected Contents: Ordinary Differential Equations: Brief Revision. Fourier Series. Sturm–Liouville Problems. Some Fundamental Equations of Mathematical Physics. The Method of Separation of Variables. Linear Nonhomogeneous Problems. The Method of Eigenfunction Expansion. The Fourier Transformations. The Laplace Transformation. The Method of Green’s Functions. General Second-Order Linear Partial Differential Equations with Two Independent Variables. The Method of Characteristics. Perturbation and Asymptotic Methods. Complex Variable Methods. 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
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Mathematics for Finance New!
Monte Carlo Simulation with Applications to Finance Hui Wang
An Introduction to Exotic Option Pricing
Brown University, Providence, Rhode Island, USA
Peter Buchen
Developed from the author’s course on Monte Carlo simulation at Brown University, this text provides a self-contained introduction to Monte Carlo methods in financial engineering. It covers common variance reduction techniques, the cross-entropy method, and the simulation of diffusion process models.
In an easy-to-understand, nontechnical yet mathematically elegant manner, this book shows how to price exotic options, including complex ones, without performing complicated integrations or formally solving PDEs. It develops special pricing techniques based on the no-arbitrage principle and fully derives every price formula for the exotic options. The author incorporates a significant amount of original, previously unpublished material, such as the use of log-volutions and Mellin transforms to solve the Black–Scholes PDE. He also demystifies many esoteric issues underpinning the mathematical treatment of the subject. • Fully derives every price formula for the exotic options • Develops special pricing techniques based on the no-arbitrage principle • Contains a significant amount of original, previously unpublished material, such as the use of log-volutions and Mellin transforms to solve the Black–Scholes PDE • Demystifies many esoteric issues underpinning the mathematical treatment of the subject • Includes challenging problems at the end of each chapter to illustrate the special pricing techniques
Requiring minimal background in mathematics and finance, the book includes numerous examples of option pricing, risk analysis, and sensitivity analysis. It also provides many hand-and-paper and MATLAB® coding exercises at the end of every chapter. • Presents common variance reduction techniques as well as the cross-entropy method • Covers the simulation of diffusion process models • Requires minimal background in mathematics and finance • Contains numerous examples of option pricing, risk analysis, and sensitivity analysis • Includes many exercises at the end of every chapter
Selected Contents: Review of Probability. Brownian Motion. Arbitrage Free Pricing. Monte Carlo Simulation. Generating Random 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 Also available as an eBook
University of Sydney, Australia
Solutions manual available with qualifying course adoption
Selected Contents: TECHNICAL BACKGROUND: Financial Preliminaries. Mathematical Preliminaries. Gaussian Random Variables. APPLICATIONS TO EXOTIC OPTION PRICING: Simple Exotic Options. Dual Expiry Options. Two-Asset Rainbow Options. Barrier Options. Lookback Options. Asian Options. Exotic MultiOptions. References. Index.
Catalog no. C9100, February 2012, 296 pp. ISBN: 978-1-4200-9100-7, $79.95 Also available as an eBook
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Mathematics for Finance Option Valuation
New!
Computational Methods in Finance Ali Hirsa Caspian Capital Management, LLC, New York, USA
“A natural polymath, the author is at once a teacher, a trader, a quant, and now an author of a book for the ages. The content reflects the author’s vast experience teaching master’s level courses at Columbia and NYU, while simultaneously researching and trading on quantitative finance in leading banks and hedge funds.” —Peter Carr, Morgan Stanley and NYU Courant Institute of Mathematical Sciences
“A long-time expert in computational finance, Ali Hirsa brings his excellent expository skills to bear on not just one technique but the whole panoply, from finite difference solutions to PDEs/PIDEs through simulation to calibration and parameter estimation.” —Emanuel Derman, Columbia University and author of Models Behaving Badly
• Addresses key computational methods in finance, including transform techniques, the finite difference method, and Monte Carlo simulation • Shows how to accurately price a vast array of derivatives • 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 and Risk-Neutral Pricing. Derivatives Pricing via Transform Techniques. 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, August 2012, 436 pp. ISBN: 978-1-4398-2957-8, $89.95 Also available as an eBook
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A First Course in Financial Mathematics Hugo D. Junghenn The George Washington University, Washington, D.C., USA
Largely self-contained, this classroom-tested text provides a straightforward introduction to the mathematics and models used in the valuation of financial derivatives. It examines the principles of option pricing in detail via standard binomial and stochastic calculus models and develops the requisite mathematical background as needed. Numerous examples and exercises help students gain expertise with financial calculus methods and increase their general mathematical sophistication. • Offers a straightforward account of the principles and models of option pricing • Focuses on the (discrete time) binomial model and the (continuous time) Black-Scholes-Merton model • Develops probability theory and finance theory from first principles • Covers various types of financial derivatives, including currency forwards, put and call options, and path-dependent options • Uses the notion of variation of a function to illustrate the similarities and differences between classical calculus and stochastic calculus • Presents a martingale approach to option pricing • Contains many examples and end-of-chapter exercises Solutions manual available with qualifying course adoption
Selected Contents: Interest and Present Value. Probability Spaces. Random Variables. Options and Arbitrage. DiscreteTime Portfolio Processes. Expectation of a Random Variable. The Binomial Model. Conditional Expectation and Discrete-Time Martingales. The Binomial Model Revisited. Stochastic Calculus. The Black-Scholes-Merton Model. Continuous-Time Martingales. The BSM Model Revisited. Other Options. Appendices. Bibliography. Index.
Catalog no. K14090, November 2011, 266 pp. ISBN: 978-1-4398-8911-4, $59.95 Also available as an eBook
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Mathematics for Finance
Coming soon!
Stochastic Finance
Quantitative Finance
A Numeraire Approach
An Object-Oriented Approach in C++
Jan Vecer
Erik Schlogl
Columbia University, New York, New York, USA
University of Technology, Sydney, Australia
“… this book can be regarded as a wonderful application of stochastic analysis, as it includes not only detailed theoretical proofs but also practical illustrative examples. … Most importantly, the representation of prices as a pairwise relationship of two assets is the most novel characteristic of this book, which could lead to deeper understanding of derivative contracts.”
This practical resource builds a foundation in the key methods and models of quantitative finance from the perspective of their implementation in C++. It introduces computational finance in a pragmatic manner, focusing on practical implementation.
—Jian Ping Wan, Mathematical Reviews, 2012f
“Finally, we have a full volume with a systematic treatment of the change of numeraire techniques. Jan Vecer has taken years of teaching experience and practitioners’ feedback to unify a previously complicated topic into the most elegant and easily accessible numeraire textbook to come down the pike. …” —Uwe Wystup, MathFinance AG
With many examples and exercises, this classroomtested text provides a deep understanding of derivative contracts. It treats price as a number of units of one asset needed for an acquisition of a unit of another asset instead of expressing prices in dollar terms exclusively. This numeraire approach leads 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. Barrier Options. Lookback Options. American Options. Contracts on Three or More Assets: Quantos, Rainbows and “Friends.” Asian Options. Jump Models. Appendix. Solutions to Selected Exercises. References. Index.
Catalog no. K10632, January 2011, 342 pp. ISBN: 978-1-4398-1250-1, $69.95 Also available as an eBook
The author takes an object-oriented approach that starts from simple building blocks to assembling more complex and powerful models. He expresses models and algorithms of the industry-standard C++ language and includes working C++ source code on a CD-ROM that accompanies the book. • Presents quantitative finance in a pragmatic manner with a focus on practical implementation • Serves as a self-contained reference for the implementation of the key models and methods • Expresses models and algorithms in the de facto industry-standard programming language C++ • Takes an object-oriented approach, starting from simple building blocks to assembling more complex and powerful models • Provides working C++ source code on a CD-ROM
Selected Contents: A Brief Review of the C++ Programming Language. Basic Building Blocks. Portfolio Optimization and Asset Pricing. Lattice Models. The Black/Scholes World. Finite Difference Methods for Partial Differential Equations. Implied Volatility and Implied Distributions. Monte Carlo Simulation. The Heath/Jarrow/Morton Model. The Lognormal Forward Rate "Market Models." Case Studies of the Object-Oriented Approach.
Catalog no. C4797, January 2013, c. 506 pp. ISBN: 978-1-58488-479-8, $79.95 Also available as an eBook
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Mathematics for Finance
Coming soon!
Risk Management and Simulation Aparna Gupta Rensselaer Polytechnic University, Troy, New York, USA
This book presents the modeling techniques and methodologies used to solve problems of risk management that are relevant to market, credit, operational, and business risk. Topics covered include frameworks for risk management, regulations, building models of risk, credit risk management, asset-liability management, and strategic risk management. The author connects risk management with simulation to show how the tool can be used to minimize risk in an organization and then arrive at a solution. MATLAB® is used in the examples and exercises and the code is available on the author’s website. • Focuses on simulation modeling and analysis • Connects risk management and simulation • Discusses the range of tools used in risk management • Includes many applied examples, problems, and exercises • Provides support for students taking the CFA, GARP, and actuarial exams
Selected Contents: Defining Risk: What Is Risk? Types of Risk. Modeling Risk. Summary Frameworks for Risk Management: How to Handle Risk? Elements of the Framework. Example Contexts to Apply the Framework. Regulations and Risk Management: Regulations and Their Impact. Regulations and Banking. Regulations and Investment Banking. Regulations and Insurance. Principles of Simulation and Generating Random Variates: Principles of Simulation. Random Number Generation. Generation of Discrete Random Variates. Generation of Continuous Random Variates. Testing Random Variates. Validation of Model. Output Analysis. Modeling Risk Evolving over Time: Discrete-Time Evolution of Risk. Continuous-Time Evolution of Risk. Building and Solving Models of Risk: Defining New Integrals. Ito Calculus. Analytical Solutions. Solving the Model using Simulation. Evaluating Simulation Solutions. Estimating Parameters. Managing Equity Market Risk: Portfolio Optimization. Hedging Equity Risk. Optimal Hedging Strategy. Managing Interest Rates and Other Market Risks: Bond Pricing. Interest-Rate Derivatives. Managing Commodities Risk. Managing Foreign Exchange Risk. Value-at-Risk and its Use in Risk Management. Asset-Liability Management: Introduction to Asset-Liability Management. Gap Analysis. Cumulative Gap Analysis. Duration Gap Analysis. Long-Term Value at Risk Analysis. Scenario Analysis and Stress Testing. Credit Risk Management: Retail Credit Risk. Commercial Credit Risk. Credit Risk Hedging Instruments. Risk Management using Insurance: Principle behind Insurance. Types of Insurance. Risk Management Strategies. Securitization and Re-Insurance. Operational, Business and Strategic Risk Management: Operational Risk Management. Business Risk Management. Strategic Risk Management. Advanced Simulation Topics: Variance Reduction Techniques. Simulation-Based Optimization. Large-Scale Simulation. A summary appears at the end of each chapter.
Catalog no. K11622, December 2012, c. 416 pp., ISBN: 978-1-4398-3594-4, $99.95 Also available as an eBook
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Geometry and Topology
College Geometry A Unified Development David C. Kay University of North Carolina, Ashville, USA (Retired)
Differential Geometry of Manifolds Stephen T. Lovett Wheaton College, Illinois, USA
This text unifies Euclidean, elliptic, and hyperbolic geometry within an axiomatic framework. It covers topological shapes of geometric objects and includes more than 700 carefully crafted problems. Numerous examples show how geometry has real and far-reaching implications. The author approaches every topic as a fresh, new concept and carefully defines and explains geometric principles. He also offers instructions on specific experiments using the Geometer’s Sketchpad software. • Covers topological shapes of geometric objects • Includes “Moments for Reflection” sections that challenge students to think for themselves and encourage self-discovery • Offers instructions on specific experiments using the Geometer’s Sketchpad software • Contains more than 500 drawings and 80 examples to illustrate concepts and problem solving • Presents historical notes that point out the human aspects of geometric discovery • Incorporates research projects for undergraduate students • Provides more than 700 carefully crafted problems, with selected solutions at the back of the book
“Differential Geometry of Curves and Surfaces and Differential Geometry of Manifolds will certainly be very useful for many students. A distinguishing feature of the books is that many of the basic notions, properties and results are illustrated by a great number of examples and figures. Each section includes numerous interesting exercises … a nice addition to the existing literature … . I strongly recommend them to anyone wishing to enter into the beautiful world of the differential geometry.”
Solutions manual available with qualifying course adoption
Brown University, Providence, Rhode Island, USA
Selected Contents: Lines, Distance, Segments, and Rays. Angles, Angle Measure, and Plane Separation. Unified Geometry: Triangles and Congruence. Quadrilaterals, Polygons, and Circles. Three Geometries. Inequalities for Quadrilaterals: Unified Trigonometry. Beyond Euclid: Modern Geometry. Transformations in Modern Geometry. Non-Euclidean Geometry: Analytical Approach. Appendices. Solutions to Selected Problems. Bibliography. Index.
Catalog no. K11008, June 2011, 652 pp. ISBN: 978-1-4398-1911-1, $89.95 Also available as an eBook
—Velichka Milousheva, Journal of Geometry and Symmetry in Physics, 2012
Catalog no. K00383, June 2010, 440 pp. ISBN: 978-1-56881-457-5, $79.95
Differential Geometry of Curves and Surfaces Thomas F. Banchoff Stephen T. Lovett Wheaton College, Illinois, USA
“Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book … Some of the more interesting theorems explore relationships between local and global properties. A special feature is the availability of accompanying online interactive Java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena.” —L’Enseignement Mathématique (2) 57 (2011)
Catalog no. K00382, March 2010, 352 pp. ISBN: 978-1-56881-456-8, $51.95 Also available as an eBook
For more information and complete contents, visit www.crctextbooks.com
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Mathematics for Engineering
New!
Linear Algebra and Probability for Computer Science Applications Ernest Davis Based on the author's course at NYU, this book gives an introduction to two mathematical fields that are fundamental in many areas of computer science. The course and the text are addressed to students with a very weak mathematical background. Assuming as little mathematical background as possible, this classroom-tested text focuses on mathematical techniques that are most relevant to computer scientists. It covers applications from computer graphics, web search, machine learning, cryptography, and a host of other computer science areas. After an introductory chapter on MATLAB®, the text is divided into two sections, with the first focusing on linear algebra and the second discussing probability. MATLAB functions, MATLAB programming assignments, and problems are included in each chapter. MATLAB code is available on the author’s website. • Focuses on mathematical techniques that are most relevant to computer scientists • Assumes as little mathematical background as possible • 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 in each chapter • Offers MATLAB code on the author’s website
Selected Contents: MATLAB. LINEAR ALGEBRA: Vectors. Matrices. Vector Spaces. Algorithms. Geometry. Change of Basis, DFT, and SVD. PROBABILITY: Probability. Numerical Random Variables. Markov Models. Confidence Intervals. Monte Carlo Methods. Information and Entropy. Maximum Likelihood Estimation. References. Notation. Index.
Catalog no. K14397, May 2012, 431 pp. ISBN: 978-1-4665-0155-3, $59.95 Also available as an eBook
Advanced Mathematical Methods in Science and Engineering Second Edition S.I. Hayek The Pennsylvania State University, University Park, USA
This update of a best-selling text presents methods of applied mathematics that are particularly suited to address physical problems in science and engineering. This edition incorporates a new chapter on numerical methods and new appendices on vector algebra, calculus, and matrix algebra. The author provides a complete treatment of ODEs and PDEs and explores selfadjoint systems and orthogonal series. Numerous examples illustrate the various methods of solution and answers to end-of-chapter problems are included at the back of the book.
Catalog no. C1977, June 2010, 866 pp. ISBN: 978-1-4200-8197-8, $135.95
Advanced Engineering Mathematics with MATLAB® Third Edition Dean G. Duffy Former Instructor, US Naval Academy, Annapolis, Maryland, USA
“This third edition includes new examples, problems, projects, and, more significantly, new and improved coverage of Green’s functions and matrix exponential, numerical methods for solving differential equations, and probability and random processes. … The text accommodates two general tracks: the differential equations course and the engineering mathematics course. …” —SciTech Book News, February 2011 Solutions manual available with qualifying course adoption
Catalog no. K10835, October 2010, 1105 pp. ISBN: 978-1-4398-1624-0, $115.95 Also available as an eBook
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Mathematics for Biology and Medicine
Dynamics of Biological Systems
An Introduction to Stochastic Processes with Applications to Biology Second Edition
Michael Small
Linda J.S. Allen
Hong Kong Polytechnic University
Texas Tech University, Lubbock, USA
With exercises and projects in each chapter, this classroom-tested text shows how to apply a variety of mathematical and computational techniques to model and analyze the temporal and spatial phenomena of biological systems. The mathematical models and computer simulations offer insight into cardiac pacemakers, artificial electrical defibrillation, pandemics, pattern formation, flocking behavior, the interaction of autonomous agents, and hierarchical and structured network topologies. MATLAB® implementations of algorithms and case studies are available on the author’s website. • Uses complex systems, complex networks, and dynamics to derive models and computer simulations of various biological systems • Presents a wide range of models, from ECG signal processing to pandemic modeling to population dynamics • Requires no advanced knowledge of mathematics • Includes exercises as well as computational and research projects at the end of each chapter • Offers MATLAB implementations of many key algorithms and various case studies on the author’s website
“Instructors who are already teaching a stochastic processes course and want to introduce biological examples will find this book to be a gold mine of useful material. …”
Solutions manual available with qualifying course adoption
Ehud Lamm
Selected Contents:
Tel-Aviv University, Israel
Biological Systems and Dynamics. Population Dynamics of a Single Species. Observability of Dynamic Variables. Biomedical Signal Processing. Computational Neurophysiology. Mathematical Neurodynamics. 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 Also available as an eBook
—Kathy Temple, MAA Reviews, January 2012
“… a good introductory textbook for junior graduate students … the author has made a great effort to encourage the use of stochastic models in practice by providing many pieces of MATLAB® codes, which are usually unavailable in other books on stochastic processes. …” —Hongyu Miao, Mathematical Reviews, Issue 2011m
Catalog no. K10993, December 2010, 490 pp. ISBN: 978-1-4398-1882-4, $89.95 Also available as an eBook
Biological Computation Ron Unger Bar-Ilan University, Ramat-Gan, Israel
“Biological computing … is ready for our educational mainstream. This beautiful undergraduate text by Lamm and Unger may be the first step. This book expertly presents fundamental concepts of molecular biology in its first chapter, and then goes on to develop many computing classics from biology. … I enjoyed reading this text. The exercises flex the imagination, the definitions are clear and precise, and the explanations are unusually powerful. I have been searching for a text like this for years, and now I look forward to using it.” —Computing Reviews, August 2011
Catalog no. C7959, May 2011, 343 pp. ISBN: 978-1-4200-8795-6, $79.95
For more information and complete contents, visit www.crctextbooks.com
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Algebra
Universal Algebra Fundamentals and Selected Topics Clifford Bergman Iowa State University, Ames, USA
“… as far as I am concerned, the book under review, by Clifford Bergman, is most welcome: we need more of this sort of thing, both for potential universal algebraists and for people like me: fellow travelers to some degree, or mathematicians who both use and thoroughly adore algebra and its structural qualities, and find themselves growing more appreciative of this architectural elegance as they evolve in their work and studies. … it is clearly written and pleasant to read … the author provides motivation as well as examples and exercises galore. At first glance it looks to me like the exercises are well-structured and should do the job of bringing the student or reader along at a decent pace from ignorance to both an appreciation for the subject and some facility with it. It’s definitely an area worth pursuing for a graduate student with the right disposition.”
Advanced Linear Algebra Bruce Cooperstein University of California, Santa Cruz, USA
“The book is well written, and the examples are appropriate. … Each section contains relevant problems at the end. The ‘What You Need to Know’ feature at the beginning of each section outlining the knowledge required to grasp the material is useful. Recommended.” —CHOICE, January 2011
“… the material has been chosen in order to cover the material a beginning graduate student would be expected to know when taking a first course in group or field theory or functional analysis. …” —SciTech Book News, February 2011 Solutions manual available with qualifying course adoption
Catalog no. K11457, June 2010, 364 pp. ISBN: 978-1-4398-2966-0, $83.95
—Michael Berg, MAA Reviews, December 2011
• Emphasizes clones and varieties of algebras • Offers an extensive presentation of tame congruence theory • Uses a set of examples throughout the text to illustrate key concepts • Introduces tools and techniques as needed and links 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. SELECTED TOPICS: Congruence Distributive Varieties. Arithmetical Varieties. Maltsev Varieties. Finite Algebras and Locally Finite Varieties. Bibliography. Index.
Catalog no. K12346, September 2011, 320 pp. ISBN: 978-1-4398-5129-6, $99.95 Also available as an eBook
FiniteDimensional Linear Algebra Mark S. Gockenbach Michigan Technological University, Houghton, USA
This text provides a solid foundation for the study of advanced mathematics and covers many interesting applications of linear algebra, which show how linear algebra is essential in such diverse areas as combinatorics, differential equations, optimization, and approximation. The book discusses important concepts and methods from numerical linear algebra. It contains a range of exercises in each section and incorporates mini-projects that encourage students to develop topics not covered in the text. A solutions manual is available with qualifying course adoption.
Catalog no. K10803, May 2010, 672 pp. ISBN: 978-1-4398-1563-2, $99.95 Also available as an eBook
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Mathematical Computation An Introduction to Numerical Methods
New!
Abu Dhabi University, United Arab Emirates
Numerical and Analytical Methods with MATLAB® for Electrical Engineers
Ronald B. Guenther
William Bober
Oregon State University, Corvallis, USA
Florida Atlantic University, Boca Raton, USA
Praise for Previous Editions:
Andrew Stevens
“Kharab and Guenther offer an attractive, clear, error-free, and well-written introduction to numerical methods … Highly recommended.”
Electrical Science, Inc., Rye Brook, New York, USA
A MATLAB® Approach, Third Edition Abdelwahab Kharab
—J.H. Ellison, CHOICE
This popular text continues to present a wide range of useful and important algorithms for scientific and engineering applications. Along with MATLAB® GUIs throughout, this third edition incorporates a new chapter on the numerical solution of integral equations and a new section on nonlinear PDEs. The authors use MATLAB to illustrate each numerical method, providing full details of the computer results and supplying the MATLAB functions on a CD-ROM. • Covers the most common numerical methods encountered in science and engineering • Illustrates the methods using MATLAB • Presents numerous examples and exercises, with selected answers at the back of the book • Supplies MATLAB functions on an accompanying CD-ROM Solutions manual available with qualifying course adoption
Selected Contents: Introduction. Number System and Errors. Roots of Equations. System of Linear Equations. Interpolation. Interpolation with Spline Functions. The Method of Least Squares. Numerical Optimization. Numerical Differentiation. Numerical Integration. Numerical Methods for Linear Integral Equations. Numerical Methods for Differential Equations. Boundary-Value Problems. Eigenvalues and Eigenvectors. Partial Differential 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 Also available as an eBook
“I like the organization of the book and especially the early focus on matrix fundamentals … use of examples is excellent. …The end-of chapter problems are good … presents some excellent frameworks for computational methods—students should be able to build their programs more effectively by understanding the core components and following the directions…” —Michael R. Gustafson II, Duke University
“Numerical methods, algorithms, and implementations are well explained.” —Gleb V. Tcheslavski, Lamar University
This textbook presents basic programming techniques consistent with the MATLAB® software package. It also discusses numerical and analytical concepts applicable to electrical engineering. The text contains many sample MATLAB programs that provide guidance for students completing the assigned projects. In addition, case studies relate concepts presented in the chapters to engineering in practice. • Presents electrical and computer engineering examples, cases, and problems • Integrates MATLAB throughout the text and includes 50 MATLAB programs • Includes case studies related to engineering practice Solutions manual available with qualifying course adoption
Selected Contents: Numerical Modeling For Engineers. MATLAB Fundamentals. Matrices. Roots of Algebraic and Transcendental Equations. Numerical Integration. Numerical Integration of Ordinary Differential Equations. Simulink. Curve Fitting. Optimization. Partial Differential Equations. Laplace Transforms. Signal Processing. Control Systems.
Catalog no. K12515, August 2012, 288 pp. ISBN: 978-1-4398-5429-7, $109.95 Also available as an eBook
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Probability and Statistics with Applications / Set Theory and Logic
New!
Probability and Stochastic Modeling Vladimir I. Rotar San Diego State University, California, USA
“This is a superbly written text on probability and stochastic processes for students who have had two semesters of calculus and an introductory course in linear algebra. … Important and wellchosen examples illustrate the theory throughout, and a large body of exercises supplements the text. … an outstanding addition to the field requiring only a modest background in mathematics.” —Rabi Bhattacharya, University of Arizona
“… an ideal textbook for anyone interested in probability theory and its applications. The book will take a worthy place in the literature on probabilistic issues.”
Probability, Statistics, and Reliability for Engineers and Scientists Third Edition Bilal M. Ayyub and Richard H. McCuen University of Maryland, College Park, USA
The third edition of this best-selling text presents probability, statistics, reliability, and risk methods with an ideal balance of theory and applications. It places increased emphasis on simulation, particularly as a modeling tool, applying it progressively with projects that continue in each chapter. This edition also features expanded discussions of the analysis of variance and a thorough treatment of Monte Carlo simulation. A solutions manual and PowerPoint slides are available with qualifying course adoption.
Catalog no. K10476, April 2011, 663 pp. ISBN: 978-1-4398-0951-8, $119.95 Also available as an eBook
—Youri Davydov, Université des Sciences et Technologies de Lille
“This book is a welcome and attractive addition to the list of textbooks available for an upper division probability course and would even be suitable for a graduate-level introduction to non-measure-theoretic probability and stochastic processes.” —Patrick J. Fitzsimmons, University of California-San Diego Solutions manual and figure slides available with qualifying course adoption
Selected Contents: Basic Notions. Independence and Conditional Probability. Discrete Random Variables. Generating Functions. Branching Processes. Random Walk Revisited. Markov Chains. Continuous Random Variables. Distributions in the General Case. Simulation. Moment Generating Functions. The Central Limit Theorem for Independent Random Variables. Covariance Analysis. The Multivariate Normal Distribution. The Multivariate Central Limit Theorem. Maxima and Minima of Random Variables. Elements of Reliability Theory. Hazard Rate and Survival Probabilities. Stochastic Processes: Preliminaries. Counting and Queuing Processes. Birth and Death Processes: A General Scheme. …
Catalog no. K13311, September 2012, 508 pp. ISBN: 978-1-4398-7206-2, $79.95 Also available as an eBook
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Elements of Advanced Mathematics Third Edition Steven G. Krantz Washington University, St. Louis, Missouri, USA
This best-selling text provides a path for students to understand the rigor, axiomatics, set theory, and proofs of mathematics. This third edition adds four new chapters on point-set topology, theoretical computer science, the P/NP problem, and zeroknowledge proofs and RSA encryption. It also includes more exercise sets in each chapter, expanded treatment of proofs, and new proof techniques. A solutions manual is available with qualifying course adoption.
Catalog no. K14300, March 2012, 367 pp. ISBN: 978-1-4398-9834-5, $89.95 Also available as an eBook
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Applied Mathematics New!
Physical Oceanography A Mathematical Introduction with MATLAB®
Mathematics for the Environment
Reza Malek-Madani
Martin Walter
U.S. Naval Academy, Annapolis, Maryland, USA
University of Colorado, Boulder, USA
Accessible to advanced undergraduate students, this text demonstrates how to use the basic tenets of multivariate calculus to derive the governing equations of fluid dynamics in a rotating frame. It also explains how to use linear algebra and PDEs to solve basic initial-boundary value problems that have become the hallmark of physical oceanography. The book makes the most of MATLAB®’s matrix algebraic functions, differential equation solvers, and visualization capabilities. • Explores how mathematics plays a critical role in the investigation of geophysical fluid dynamics, wind-driven ocean circulation, shallow water, and other applications in physical oceanography • Reviews calculus, differential equations, linear algebra, and the basic use of MATLAB • Includes simple examples that introduce features of 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 who are making significant impacts on developing tools for modern physical oceanography • Contains end-of-chapter projects that incorporate MATLAB programming
“The book is heavily referenced … there are many detailed exercises designed to highlight how mathematics can be used to explain natural phenomena and human behavior and its consequences. … this book could serve as a text for courses in applied mathematics and a resource for study material in many other subject areas …”
Selected Contents:
John L. Crassidis
An Introduction to MATLAB. Matrix Algebra. Differential and Integral Calculus. Ordinary Differential Equations. Numerical Methods for ODEs. Equations of Fluid Dynamics. Equations of Geophysical Fluid Dynamics. Shallow Water Equations (SWE). Wind-Driven Ocean Circulation: The Stommel and Munk Models. Some Special Topics. Appendix.
Catalog no. C830X, April 2012, 456 pp. ISBN: 978-1-58488-830-7, $79.95 Also available as an eBook
—MAA Reviews, July 2011
This classroom-tested text shows how to employ simple mathematical tools, such as arithmetic, to uncover fundamental conflicts between the logic of human civilization and the logic of Nature. Slides are available with qualifying course adoption.
Catalog no. K11565, January 2011, 679 pp. ISBN: 978-1-4398-3472-5, $89.95 Also available as an eBook
Optimal Estimation of Dynamic Systems Second Edition State University of New YorkBuffalo, USA
John L. Junkins Texas A&M University, College Station, USA
This book highlights the importance of both physical and numerical modeling in solving dynamics-based estimation problems found in engineering systems, such as spacecraft attitude determination, GPS navigation, orbit determination, and aircraft tracking. With more than 100 pages of new material, this reorganized and expanded edition incorporates new theoretical results, a new chapter on advanced sequential state estimation, and additional examples and exercises. MATLAB® codes are available on the book’s website.
Catalog no. K11836, October 2011, 749 pp. ISBN: 978-1-4398-3985-0, $129.95 Also available as an eBook
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Mathematical Modeling / Operations Research Mathematical Modelling with Case Studies A Differential Equations Approach using Maple™ and MATLAB®, Second Edition Belinda Barnes Australian National University, Canberra, Australia
Glenn Robert Fulford University of Technology, Brisbane, Australia
“The book is written in a very lucid manner, with numerous case studies and examples thoroughly discussed. The material is very well organized, generously illustrated, and delightfully presented. … nicely designed exercises can be used for independent study. The book contains enough material to organize a new well-structured one-semester course or to complement the existing one with additional examples and problems and is highly recommended for either purpose.” —Zentralblatt MATH, 1168
“The book can be useful for students of mathematical modeling. They will find many skills for modeling and solving real problems. Useful sheets for Maple and MATLAB are included for numerical solution. … This is the best treasury of real case problems seen in a single book.” —EMS Newsletter, September 2009
Focusing on compartmental models, population models, and heat transfer problems, this textbook carefully details the process of constructing a model. Maple™ and MATLAB® codes are supplied in the text and online so results can be reproduced exactly. A solutions manual is available with qualifying course adoption.
Selected Contents: Compartmental Models. Models of Single Populations. Numerical Solution of Differential Equations. Interacting Population Models. PhasePlane Analysis. Linearization Analysis. Some Extended Population Models. Formulating Basic Heat Models. Solving Time-Dependent Heat Problems. Solving Heat Conduction Problems. Introduction to PDEs. Appendices. References. Index.
Catalog no. C8348, December 2008, 368 pp. ISBN: 978-1-4200-8348-4, $83.95 Also available as an eBook
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Value-Added Decision Making for Managers Kenneth Chelst Wayne State University, Detroit, Michigan, USA
Yavuz Burak Canbolat Abbott Laboratories, Abbott Park, Illinois, USA
Developed from the authors’ longstanding course on decision and risk analysis, this text explores the important interaction between decisions and management action and clarifies the barriers to rational decision making. The authors analyze strengths and weaknesses of the best alternatives, enabling decision makers to improve on these alternatives by adding value and reducing risk. They also discuss bias, negotiations, project/risk management, and ethical dilemmas. Numerous examples highlight real-world situations from everyday life, public policy, and industry. Software tutorials and other material are available on the book’s website. • Presents a wide range of realistic decision contexts for everyday life, public policy, and the oil, pharmaceutical, insurance, and biotech industries • Develops the concept of value-added decision making • Emphasizes the modeling of both multiobjective decisions and decisions in the presence of uncertainty • Provides a comprehensive review of diverse challenges to rational decision making, including forecasting bias and decision bias • Discusses alternate approaches to negotiations, project/risk management, and ethical dilemmas • Offers software tutorials, PowerPoint presentations, and solutions to numeric examples on the book’s website Figure slides available with qualifying course adoption
Selected Contents: Structuring Hard Decisions. Decisions with Multiple Objectives. Decisions and Management under Uncertainty. Challenges to “Rational” Decisions. Decisions with Multiple Perspectives. Appendices. Index.
Catalog no. C7572, October 2011, 578 pp. ISBN: 978-1-4200-7572-4, $129.95 Also available as an eBook
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A Solid Foundation for Teaching and Learning Mathematics • Show students how number theory and geometry are the essential components in mathematics • Help students understand how deep mathematical ideas grow from basic ideas • Get insight from highly trained educators who have worked with undergraduate students, advanced high school students, and public school K-8 teachers
Catalog no. K15328, October 2012, c. 528 pp. ISBN: 978-1-4665-5464-1, $69.95 Also available as an eBook
A Gentle, Hands-On Introduction to Cryptology • Clearly explain to students how fundamental mathematical concepts are the bases of cryptographic algorithms • Show students—even those with nontechnical backgrounds—how to complete complicated tasks with relative ease using student-friendly Maplets • Give students a real-world context of cryptology through examples such as the Enigma cipher machine and Navajo code
Catalog no. K13332, June 2012, 548 pp. ISBN: 978-1-4398-7241-3, $79.95 Also available as an eBook
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