Contents Algebra ..................................................................3 Discrete Mathematics/Combinatorics....................7 Differential Equations ..........................................12 Page 3

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Introductory Mathematics ..................................13 Mathematical Modeling ......................................16 Mathematics for Finance......................................17 Algebraic Geometry and Number Theory ..........20

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Real, Complex, and Functional Analysis ..............20 Mathematics for Engineering ..............................23 Mathematics for Biology/ Computational Biology ........................................28 Probability Theory and Applications ....................29

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Algebra

New!

Finite-Dimensional Linear Algebra Mark S. Gockenbach Michigan Technological University, Houghton, USA

Drawing on material from the author’s own course, this textbook gives students a strong theoretical understanding of linear algebra. It offers many illustrations of how linear algebra is used throughout mathematics in such diverse areas as combinatorics, differential equations, optimization, and approximation. The author takes students through an axiomatic development of vector spaces, linear operators, eigenvalues, norms, and inner products. In addition to discussing the special properties of symmetric matrices, he covers the Jordan canonical form, an important theoretical tool, and the singular value decomposition, a powerful tool for computation. The final chapters present introductions to numerical linear algebra and analysis in vector spaces.

Features • Provides a thorough foundation for the study of advanced mathematics • Contains a range of exercises in each section, including some that can be solved using a computer package such as MATLAB® • Incorporates mini-projects that encourage students to develop topics not covered in the text • Explores various applications of linear algebra, including polynomial interpolation, graph and coding theory, linear and integer programming, linear ordinary differential equations, Lagrange multipliers, and much more • Presents important concepts and methods from numerical linear algebra Solutions manual available for qualifying instructors

Contents Some Problems Posed on Vector Spaces Fields and Vector Spaces Linear Operators Determinants and Eigenvalues The Jordan Canonical Form The Spectral Theory of Symmetric Matrices The spectral theorem for symmetric matrices The spectral theorem for normal matrices Optimization and the Hessian matrix Lagrange multipliers Spectral methods for differential equations The Singular Value Decomposition The SVD for general matrices Solving least-squares problems using the SVD The SVD and linear inverse problems The Smith normal form of a matrix Matrix Factorizations and Numerical Linear Algebra The LU factorization Partial pivoting The Cholesky factorization Matrix norms The sensitivity of linear systems to errors Numerical stability The sensitivity of the least-squares problem The QR factorization Eigenvalues and simultaneous iteration The QR algorithm Analysis in Vector Spaces Analysis in Rn Infinite-dimensional vector spaces Functional analysis Weak convergence For more complete contents, visit www.crctextbooks.com

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

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Algebra Applied Algebra Codes, Ciphers and Discrete Algorithms, Second Edition Darel W. Hardy Colorado State University, Fort Collins, USA

Fred Richman Florida Atlantic University, Boca Raton, USA

Carol L. Walker New Mexico State University, Las Cruces, USA

Designed for an applied algebra course for students who have had prior classes in abstract or linear algebra, this text presents practical methods for solving problems in data security and data integrity. While the content has been reworked and improved, this edition continues to cover many algorithms that arise in cryptography and error-control codes.

New to the Second Edition • Double the number of exercises • New appendix that reviews prerequisite topics in algebra and number theory • A CD-ROM containing an interactive version of the book that is powered by Scientific Notebook® • Interactive examples

Contents Integers and Computer Algebra Codes Euclidean Algorithm Ciphers Error-Control Codes Chinese Remainder Theorem Theorems of Fermat and Euler Public Key Ciphers The Rivest–Shamir–Adleman Cipher System Electronic Signatures A System for Exchanging Messages Knapsack Ciphers Digital Signature Standard Finite Fields

• Computing hints

Error-Correcting Codes

• Self-tests

BCH Codes

• Some details of problem solutions beyond those in the printed text

A BCH Decoder

Explaining the mathematics as needed, this text thoroughly explores how mathematical techniques can be used to solve practical problems. It includes algorithms that offer common-sense approaches to problems, such as computing large powers, and explains the Rijndael algorithm to help students understand the data encryption standard.

Advanced Encryption Standard

Solutions manual available for qualifying instructors

Discrete Fourier Transforms

Reed–Solomon Codes Polynomial Algorithms and Fast Fourier Transforms Lagrange Interpolation Formula Kronecker’s Algorithm Neville’s Iterated Interpolation Algorithm Secure Multiparty Protocols Fast Fourier Interpolation Solutions to Odd Problems For more complete contents, visit www.crctextbooks.com

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

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Algebra

A Modern Introduction to Linear Algebra Henry Ricardo Medgar Evers College, Brooklyn, New York, USA

“This work is a sound presentation of linear algebra. … Each topic is carefully and thoroughly covered via the pedagogy … The volume includes more than 1,200 exercises, some to be completed manually and others intended to be solved using a computer algebra system. … The generality of approach makes this work appropriate for students in virtually any discipline. Summing Up: Recommended.” —CHOICE, June 2010

“The author of this text, Henry Ricardo, has identified several shortcomings of typical courses on linear algebra and provides an exciting offering, how to overcome them …” —Matthias Gobbert, University of Maryland, Baltimore, USA

Features • Provides a rigorous yet accessible matrixoriented introduction to the essential concepts of linear algebra • Follows the recommendations for a first course in linear algebra provided by the Linear Algebra Curriculum Study Group, Augmenting the Teaching of Linear Algebra through the use of Software Tools project, and the Linear Algebra Modules Project • Contains numerous exercises of varying levels of difficulty • Reviews basic mathematical tools in the appendices • Presents proofs for nearly all results • Includes a host of examples and various applications reflecting some of the many disciplines that use linear algebra Solutions manual available for qualifying instructors

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

Contents Vectors Systems of Equations Matrix Algebra Eigenvalues, Eigenvectors, and Diagonalization Vector Spaces Linear Transformations Linear Transformations The Range and Null Space of a Linear Transformation The Algebra of Linear Transformations Matrix Representation of a Linear Transformation Invertible Linear Transformations Isomorphisms Similarity Similarity Invariants of Operators Inner Product Spaces Complex Vector Spaces Inner Products Orthogonality and Orthonormal Bases The Gram–Schmidt Process Unitary Matrices and Orthogonal Matrices Schur Factorization and the Cayley–Hamilton Theorem The QR Factorization and Applications Orthogonal Complements Projections Hermitian Matrices and Quadratic Forms Linear Functionals and the Adjoint of an Operator Hermitian Matrices Normal Matrices Quadratic Forms Singular Value Decomposition The Polar Decomposition Answers/Hints to Odd-Numbered Problems For more complete contents, visit www.crctextbooks.com

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5

Algebra

Abstract Algebra

New!

An Interactive Approach

Advanced Linear Algebra

William Paulsen

Bruce Cooperstein

Arkansas State University, Jonesboro, USA

University of California, Santa Cruz, USA

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

Designed for advanced undergraduate and beginning graduate students, this textbook focuses on vector spaces and the maps between them that preserve their structure (linear transformations). Starting with familiar concepts and slowly building to deeper results, it shows students the beauty of linear algebra and prepares them for further study in mathematics. The author discusses the structure theory of an operator, various topics on inner product spaces, and the trace and determinant functions of a linear operator. He also covers bilinear forms with a full treatment of symplectic spaces and orthogonal spaces and explains the construction of tensor, symmetric, and exterior algebras.

—Gerhard Pfister, Zentralblatt MATH 1173

Features • Offers the option of using technology in the classroom by incorporating GAP and Mathematica® commands • Discusses topics not covered in similar texts, such as semi-direct products and skew fields • Includes many diagrams produced by Mathematica to help students visualize difficult concepts, such as homomorphisms and permutations • Contains numerous homework problems of both the interactive and standard types • Provides a CD-ROM with GAP packages and Mathematica notebooks Solutions manual available for qualifying instructors

Contents Understanding the Group Concept. The Structure within a Group. Patterns within the Cosets of Groups. Mappings between Groups. Permutation Groups. Building Larger Groups from Smaller Groups. The Search for Normal Subgroups. Solvable and Insoluble Groups. Introduction to Rings. The Structure within Rings. Integral Domains and Fields. Unique Factorization. Finite Division Rings. The Theory of Fields. Galois Theory. Bibliography. Answers to Odd Problems. Index. Catalog no. C4521, January 2010, 560 pp. ISBN: 978-1-4200-9452-7, $99.95

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Features • Takes a gentle approach that gradually builds from simple concepts to complex ideas and results • Begins each section with an outline of previously introduced concepts and results necessary for mastering the new material • Includes a wide variety of exercises and problems, with selected solutions in the appendices Solutions manual available for qualifying instructors

Contents Vector Spaces. Linear Transformations. Polynomials. Theory of a Single Linear Operator. Inner Product Spaces. Linear Operators on Inner Product Spaces. Trace and Determinant of a Linear Operator. Bilinear Maps and Forms. Tensor Products. Appendices. Index. Catalog no. K11457, June 2010, 364 pp. ISBN: 978-1-4398-2966-0, $79.95

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Discrete Mathematics/Combinatorics

New!

How to Count An Introduction to Combinatorics, Second Edition R.B.J.T. Allenby and Alan Slomson University of Leeds, UK

Completely revised, this textbook shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet’s pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises. Ideal for a first course in combinatorics, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Pólya’s counting theorem.

Contents Permutations and Combinations Occupancy Problems The Inclusion-Exclusion Principle Stirling and Catalan Numbers Partitions and Dot Diagrams Generating Functions and Recurrence Relations Partitions and Generating Functions Introduction to Graphs Trees Groups of Permutations

Features

Group Actions

• Explains how to solve various combinatorial problems

Counting Patterns

• Uses problems to introduce the theory • Contains enough material for a short course on graph theory

Pólya Counting Dirichlet’s Pigeonhole Principle Ramsey Theory

• Presents proofs of key results as well as numerous worked examples

Rook Polynomials and Matchings

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

Solutions to the A Exercises

• Lists suggestions for further reading

For more complete contents, visit www.crctextbooks.com

Solutions manual available for qualifying instructors

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

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Discrete Mathematics/Combinatorics

New!

Introduction to Cryptography with Mathematical Foundations and Computer Implementations Alexander Stanoyevitch California State University–Dominguez Hills, Carson, USA

From the exciting history of its development in ancient times to the present day, this self-contained introduction provides a focused tour of the central concepts of cryptography, suitable for a wide variety of mathematics and computer science courses. Rather than present an encyclopedic treatment of topics in cryptography, the text delineates cryptographic concepts in chronological order, developing the mathematics as needed. Written in an engaging yet rigorous style, each chapter introduces important concepts with clear definitions and theorems. Numerous examples explain key points while figures and tables help illustrate more difficult or subtle concepts. Each chapter is punctuated with “Exercises for the Reader;” complete solutions for these are included in an appendix. Carefully crafted exercise sets are also provided at the end of each chapter, and detailed solutions to most odd-numbered exercises can be found in a designated appendix. The computer implementation section at the end of every chapter guides students through the process of writing their own programs. A supporting website provides an extensive set of sample programs as well as downloadable platformindependent applet pages for some core programs and algorithms. Solutions manual available for qualifying instructors

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

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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 Elliptic Curves over the Real Numbers The Addition Operation for Elliptic Curves Groups Elliptic Curves over Zp The Variety of Sizes of Modular Elliptic Curves The Addition Operation for Elliptic Curves over Zp The Discrete Logarithm Problem on Modular Elliptic Curves An Elliptic Curve Version of the Diffie–Hellman Key Exchange Fast Integer Multiplication of Points on Modular Elliptic Curves Representing Plaintexts on Modular Elliptic Curves An Elliptic Curve Version of the El Gamal Cryptosystem A Factoring Algorithm Based on Elliptic Curves Exercises and Computer Implementations appear at the end of each chapter. Solutions and other material are available in the appendices. For more complete contents, visit www.crctextbooks.com

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Discrete Mathematics/Combinatorics

New!

Access Control, Security, and Trust A Logical Approach Shiu-Kai Chin and Susan Older Syracuse University, New York, USA

Developed from the authors’ courses at Syracuse University and the U.S. Air Force Research Laboratory, this book equips students with an access control logic they can use to specify and verify their security designs. Throughout the text, the authors use a single access control logic based on a simple propositional modal logic. Taking a logical, rigorous approach to access control, they show students how logic is a useful tool for analyzing security designs and spelling out the conditions upon which access control decisions depend. The first part of the book presents the syntax and semantics of access control logic, basic access control concepts, and an introduction to confidentiality and integrity policies. The second section covers access control in networks, delegation, protocols, and the use of cryptography. In the third section, the authors focus on hardware and virtual machines. The final part discusses confidentiality, integrity, and role-based access control.

Features

Contents Access Control, Security, Trust, and Logic PRELIMINARIES A Language for Access Control Reasoning about Access Control Basic Concepts Security Policies DISTRIBUTED ACCESS CONTROL Digital Authentication Delegation Networks: Case Studies ISOLATION AND SHARING A Primer on Computer Hardware Virtual Machines and Memory Protection

• Employs propositional modal logic to explain access control principles

Access Control Using Descriptors and Capabilities

• Shows how to perform derivations and calculations with mathematical precision and accuracy

Access Control Using Lists and Rings

• Presents numerous examples ranging from the control of physical memory in hardware to multilevel security policies

Confidentiality and Integrity Policies

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

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

• Offers HOL-4 implementation and slides for each chapter available for download on www.crctextbooks.com

For more complete contents, visit www.crctextbooks.com

ACCESS POLICIES

Role-Based Access Control

Solutions manual available for qualifying instructors

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

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Discrete Mathematics/Combinatorics

Discrete Mathematics Proofs, Structures, and Applications, Third Edition Rowan Garnier Surrey, UK

John Taylor University of Brighton, UK

“This is a textbook on discrete mathematics for undergraduate students in computer science and mathematics. … The style of exposition is very clear, step by step and the level is well adapted to undergraduates in computer science. The treatment is mathematically rigorous; therefore it is also suitable for mathematics students. Besides the theory, there are many concrete examples and exercises (with solutions!) to develop the routine of the student. So I can recommend warmly this book as a textbook for a course. It looks very attractive and has a nice typography. …” —H.G.J. Pijls, University of Amsterdam, The Netherlands

Contents Logic Mathematical Proof Sets Relations Functions Matrix Algebra Systems of Linear Equations Algebraic Structures Introduction to Number Theory Boolean Algebra Introduction

This third edition continues to provide a rigorous yet accessible exposition of discrete mathematics, including the core mathematical foundation of computer science. In the expanded first chapter, the text includes a new section on the formal proof of the validity of arguments in propositional logic before moving on to predicate logic. This edition also contains a new chapter on elementary number theory and congruences. This chapter explores groups that arise in modular arithmetic and RSA encryption, a widely used public key encryption scheme that enables practical and secure means of encrypting data. Solutions manual available for qualifying instructors

Properties of Boolean Algebras Boolean Functions Switching Circuits Logic Networks Minimization of Boolean Expressions Graph Theory Applications of Graph Theory Introduction Rooted Trees Sorting Searching Strategies Weighted Graphs The Shortest Path and Traveling Salesman Problems Networks and Flows Hints and Solutions to Selected Exercises For more complete contents, visit www.crctextbooks.com

Catalog no. K10650, January 2010, 843 pp. ISBN: 978-1-4398-1280-8, $89.95

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Discrete Mathematics/Combinatorics Coming soon!

Applied Combinatorics Second Edition

Introduction to Combinatorics

Fred S. Roberts

W.D. Wallis

Rutgers University, Piscataway, New Jersey, USA

Southern Illinois University, Carbondale, USA

Barry Tesman

J.C. George

Dickinson College, Carlisle, Pennsylvania, USA

Gordon College, Barnesville, Georgia, USA

“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. …”

This textbook is primarily for undergraduate students in mathematics taking an introductory course in combinatorics. It briefly discusses several examples of typical combinatorial problems and provides basic information on sets, proof techniques, enumeration, and graph theory. The next few chapters explore the pigeonhole principle, inclusion/exclusion, and enumerative functions and the relations between them. The authors describe generating functions and recurrences, important families of functions, and the theorems of Pólya and Redfield. They also present introductions to computer algebra and group theory, before considering graphs, codes, Latin squares, and experimental designs. The last chapter further illustrates the interaction between linear algebra and combinatorics.

—MAA Reviews, Dec. 2009

“The writing style is excellent. … The explanations are detailed enough that the students can follow the arguments readily. The motivating examples are a truly strong point for the text. No other text with which I am familiar comes even close to the number of applications presented here.” —John Elwin, San Diego State University, California, USA

“This book is a required textbook for my graduate course in discrete mathematics. … an excellent resource … clearly reinforces both the practical and theoretical understanding in a way students are able to correlate. …” —Dawit Haile, Virginia State University, Petersburg, USA

Now with solutions to selected problems

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

Features • Provides background material in the appendices on sets, induction, proof techniques, vectors, and matrices • Includes exercises and problems in each chapter, with some solutions at the back of the book • Discusses Maple™, Mathematica®, and other technological tools where appropriate

Contents Introduction. 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 c. 397 pp., ISBN: 978-1-4398-0622-7, $79.95

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Differential Equations New!

New!

Ordinary Differential Equations

Solution Techniques for Elementary Partial Differential Equations

Applications, Models, and Computing Charles E. Roberts, Jr. Indiana State University, Terre Haute, USA

Bringing the computer into the classroom, this text emphasizes the use of computer software in teaching linear and nonlinear differential equations and systems. Designed to be independent of any particular software package, the book includes a CD-ROM with the software used to generate the solutions and graphs for the examples. The appendices contain complete instructions for running the software.

Features • Provides an even balance between theory, computer solution, and application • Includes numerical case studies that highlight possible pitfalls when computing a numerical solution without first considering the appropriate theory

Second Edition Christian Constanda University of Tulsa, Oklahoma, USA

“This concise, well-written book, which includes a profusion of worked examples and exercises, serves as an excellent text in undergraduate and graduate learning … .” —Barbara Zubik-Kowal, Boise State University, Idaho, USA

“… In my opinion, 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 easyto-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, Edmonton, Canada

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

Winner of the 2002 CHOICE Outstanding Academic Title Award!

• Requires no prior knowledge of programming languages

Solutions manual available for qualifying instructors

Solutions manual available for qualifying instructors

Contents

Introduction. The Initial Value Problem y′ = f (x, y); y(c) =d. Applications of the Initial Value Problem y′ = f (x, y); y(c) =d. N-th Order Linear Differential Equations. The Laplace Transform Method. Applications of Linear Differential Equations with Constant Coefficients. Systems of First-Order Differential Equations. Linear Systems of First-Order Differential Equations. Applications of Linear Systems with Constant Coefficients. Applications of Systems of Equations. Appendices. Answers to Selected Exercises. References. Index.

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. K11006, April 2010, 600 pp. ISBN: 978-1-4398-1908-1, $99.95

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

Contents

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Introductory Mathematics New!

A Concise Introduction to Pure Mathematics Third Edition Martin Liebeck Imperial College, London, UK

“… 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, Medford, Massachusetts, USA

“… This book will give a student the understanding to go on in further courses in abstract algebra and analysis. The notion of a proof will no longer be foreign, but also mathematics will not be viewed as some abstract black box. …” —From the Foreword by Robert Guralnick, University of Southern California, Los Angeles, USA

A robust bridge between high school and higher level mathematics, this text presents some of the most fundamental and beautiful ideas in pure mathematics. It covers not only standard material but also many interesting topics not usually encountered at this level. This third edition contains three new chapters that provide an introduction to mathematical analysis. It also includes solutions to the odd-numbered exercises.

Features • Describes methods for writing proofs • Develops the theory of basic number systems, including integers, real numbers, and complex numbers, from first principles

Contents Sets and Proofs Number Systems Decimals Inequalities nth Roots and Rational Powers Complex Numbers Polynomial Equations Induction Euler’s Formula and Platonic Solids The Integers Prime Factorization More on Prime Numbers Congruence of Integers More on Congruence Secret Codes Counting and Choosing More on Sets Equivalence Relations

• Covers important topics, such as solving cubic equations, studying the five Platonic solids, coding secret information, and comparing the sizes of two infinite sets

Functions

• Contains new chapters on mathematical analysis that offer an introduction to the theory of limits and continuous functions

Introduction to Analysis: Bounds

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

Yet More Analysis: Continuity

• Requires only a solid foundation in high school mathematics Solutions manual available for qualifying instructors

Permutations Infinity More Analysis: Limits Solutions to Odd-Numbered Exercises Further Reading Index of Symbols Index

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

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Introductory Mathematics

Introduction to Mathematical Logic Fifth Edition Elliott Mendelson Queens College, Flushing, New York, USA

“Since its first edition, this fine book has been a text of choice for a beginner’s course on mathematical logic. … There are many fine books on mathematical logic, but Mendelson’s textbook remains a sure choice for a first course for its clear explanations and organization: definitions, examples and results fit together in a harmonic way, making the book a pleasure to read. …” —MAA Reviews, Dec. 2009

Retaining all the key features of its predecessors, this fifth edition of a long-established, bestselling text covers the basic topics of a solid first course in mathematical logic. This edition includes a new section covering basic ideas and results about nonstandard models of number theory, a second appendix that introduces modal propositional logic, an expanded bibliography, and additional exercises and selected answers. Continuing to expose students to natural proofs and set-theoretic methods, the author explores propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. He also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing.

Features • Provides a compact introduction to the principal topics of mathematical logic • Presents the fundamental assumptions and proof techniques that form the basis of mathematical logic • Includes many examples and exercises

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

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Contents The Propositional Calculus First-Order Logic and Model Theory Quantifiers First-Order Languages and Their Interpretations. Satisfiability and Truth. Models First-Order Theories Properties of First-Order Theories Additional Metatheorems and Derived Rules Rule C Completeness Theorems First-Order Theories with Equality Definitions of New Function Letters and Individual Constants Prenex Normal Forms Isomorphism of Interpretations. Categoricity of Theories Generalized First-Order Theories. Completeness and Decidability Elementary Equivalence. Elementary Extensions Ultrapowers: Nonstandard Analysis Semantic Trees Quantification Theory Allowing Empty Domains Formal Number Theory Axiomatic Set Theory An Axiom System Ordinal Numbers Equinumerosity. Finite and Denumerable Sets Hartogs’ Theorem. Initial Ordinals. Ordinal Arithmetic The Axiom of Choice. The Axiom of Regularity Other Axiomatizations of Set Theory Computability Algorithms. Turing Machines Diagrams Partial Recursive Functions. Unsolvable Problems The Kleene–Mostowski Hierarchy. Recursively Enumerable Sets Other Notions of Computability Decision Problems Answers to Selected Exercises For more complete contents, visit www.crctextbooks.com

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Introductory Mathematics Mathematics in Games, Sports, and Gambling The Games People Play

Introduction to Mathematical Proofs A Transition

Ronald J. Gould

Charles E. Roberts, Jr.

Emory University, Atlanta, Georgia, USA

Indiana State University, Terre Haute, USA

Presenting a fun and interesting way to teach an introductory mathematics course, this book shows students how discrete probability, statistics, and elementary discrete mathematics are used in games, sports, and gambling situations. It draws on numerous examples, questions, and problems to explain the application of mathematical theory to various real-life games. Only requiring high school algebra, the text offers flexibility in choosing what material to cover in a basic mathematics course. For each topic, the author includes exercises based on real games and sports data.

Written in a conversational style, yet maintaining the proper level of mathematical rigor, this accessible textbook teaches students how to reason logically, read proofs critically, and write valid mathematical proofs. It facilitates a smooth transition from courses designed to develop computational skills and problem solving abilities to courses that emphasize theorem proving. In the appendix, the author includes some basic guidelines to follow when writing proofs.

Features • Encourages students to think mathematically and apply the fundamentals to real gaming situations • Explores concepts, such as binomial distributions and combinatorics, through common games and sports, including backgammon, poker, roulette, baseball, football, and hockey

Features • Provides a thorough presentation of logic by including both formal and informal proofs • Explains how to develop integers from natural numbers, rational numbers from integers, and real numbers from rational numbers • Proves many theorems from different areas in mathematics • Illustrates how to write proofs and solve problems through numerous examples

• Discusses more unusual topics, such as mathematical card tricks and old TV shows

• Presents several biographical sketches and historical comments

• Contains many in-class group problems and homework exercises

• Defines numerous technical terms

Contents Basic Probability. The Game’s Afoot. Repeated Play. Card Tricks and More. Dealing with Data. Testing and Relationships. Games and Puzzles. Combinatorial Games. Appendix. References. Index. Catalog no. K10099, January 2010, 374 pp. ISBN: 978-1-4398-0163-5, $59.95

• Includes many exercises of varying difficulty at the end of each section Solutions manual available for qualifying instructors

Contents Logic. Deductive Mathematical Systems and Proofs. Set Theory. Relations. Functions. Mathematical Induction. Cardinalities of Sets. Proofs from Group Theory. Appendix. Answers to Selected Exercises. References. Index. Catalog no. C6955, 2009, 433 pp. ISBN: 978-1-4200-6955-6, $89.95

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

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Mathematical Modeling An Integrated Introduction to Computer Graphics and Geometric Modeling Ronald Goldman

Mathematical and Experimental Modeling of Physical and Biological Processes

Rice University, Houston, Texas, USA

H.T. Banks and H.T. Tran

“… this book may be the first book on geometric modeling that also covers computer graphics. In addition, it may be the first book on computer graphics that integrates a thorough introduction to ‘freedom’ curves and surfaces and to the mathematical foundations for computer graphics. … the book is well suited for an undergraduate course. … The entire book is very well presented and obviously written by a distinguished and creative researcher and educator. It certainly is a textbook I would recommend. …”

North Carolina State University, Raleigh, USA

—Computer-Aided Design, 42, 2010

“… The author has used his experiences of teaching and research to write a book that will, I am sure, become a valuable reference source for years to come. …” —International Statistical Review, 2010

Taking a novel, more appealing approach than current texts, this book focuses on graphics, modeling, and mathematical methods. The author also brings back the turtle from obscurity to introduce several major concepts in computer graphics. The text includes many exercises and programming projects as well as PowerPoint slides on a website.

Contents Two-Dimensional Computer Graphics: From Common Curves to Intricate Fractals. Mathematical Methods for Three-Dimensional Computer Graphics. Three-Dimensional Computer Graphics: Realistic Rendering. Geometric Modeling: Freedom Curves and Surfaces. Further Readings. Index. Catalog no. K10188, January 2010, 574 pp. ISBN: 978-1-4398-0334-9, $89.95

“ … The book can be recommended to advanced undergraduate students for whom mathematics is a bit more than just proving theorems. Teachers can find suggestions for motivations for introductory parts of lectures on ordinary differential equations and partial differential equations.” —EMS Newsletter, Sept. 2009

Integrating real-world applications into the traditional mathematics curriculum, this text provides students with a fundamental understanding of how mathematics is applied to problems in science and engineering. For each case study problem, the authors discuss why a model is needed and what goals can be achieved with the model. Exploring what mathematics can reveal about applications, the book focuses on the design of appropriate experiments to validate the development of mathematical models. It guides students through the modeling process, from empirical observations and formalization of properties to model analysis and interpretation of results. On the included CD-ROM, students can download real experimental data for projects presented as exercises in the book.

Contents Introduction: The Iterative Modeling Process. Modeling and Inverse Problems. Mathematical and Statistical Aspects of Inverse Problems. Mass Balance and Mass Transport. Heat Conduction. Structural Modeling: Force/Moments Balance. Beam Vibrational Control and Real-Time Implementation. Wave Propagation. SizeStructured Population Models. Appendices. Catalog no. C7337, 2009, 298 pp. ISBN: 978-1-4200-7337-9, $79.95

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Mathematics for Finance

New!

Portfolio Optimization Michael J. Best University of Waterloo, Ontario, Canada

Eschewing a more theoretical approach, Portfolio Optimization shows students how the mathematical tools of linear algebra and optimization can quickly and clearly formulate important ideas on the subject. This practical book extends the concepts of the Markowitz “budget constraint only” model to a linearly constrained model. Through reading the book, students see how the basic portfolio optimization problem helps in choosing profitable investments. The text includes MATLAB® to help with problem solving. Although the author clearly describes how to implement each technique by hand, he includes several MATLAB programs designed to implement the methods and offers these programs on the accompanying CD-ROM.

Features • Requires only elementary linear algebra • Uses MATLAB to help with problem solving • Includes exercises at the end of each chapter • Provides a CD-ROM with MATLAB programs • Explains how the basic portfolio optimization problem can help determine the optimal investment of an investor’s wealth in each asset owned • Develops the key ideas of portfolio optimization from the topics of optimization and linear algebra • Explores how quadratic programming is essential to solving practical portfolio optimization problems Solutions manual available for qualifying instructors

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

Contents Optimization Quadratic Minimization Nonlinear Optimization Extreme Points Computer Results The Efficient Frontier The Efficient Frontier Computer Results The Capital Asset Pricing Model The Capital Market Line The Security Market Line Computer Results Sharpe Ratios and Implied Risk-Free Returns Direct Derivation Optimization Derivation Free Solutions to Problems Computer Results Quadratic Programming Geometry Geometry of Quadratic Programs (QPs) The Geometry of QP Optimality Conditions The Geometry of Quadratic Functions Optimality Conditions for QPs A QP Solution Algorithm QPSolver: A QP Solution Algorithm Computer Results Portfolio Optimization with Linear Inequality Constraints An Example The General Case Computer Results Determination of the Entire Efficient Frontier PQPSolver: Generates the Entire Efficient Frontier Computer Results Sharpe Ratios under Constraints and Kinks Sharpe Ratios under Constraints Kinks and Sharpe Ratios Computer Results Appendix References Exercises appear at the end of each chapter.

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

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Mathematics for Finance

Stochastic Financial Models Douglas Kennedy Trinity College, Cambridge, UK

“This book is a superb beginning-level text for senior undergraduate/graduate mathematicians, which is based on lectures delivered by its author to many generations of appreciative Cambridge mathematicians. Many of my own Ph.D. and masters students have taken Dr. Kennedy’s course to uniformly good reviews; this readable book will make its material available to a worldwide audience. … the book contains 40 pages of fully worked out solutions … .” —M.A.H. Dempster, Centre for Financial Research, Statistical Laboratory, University of Cambridge, UK

Developed from the esteemed author’s advanced undergraduate and graduate courses at the University of Cambridge, this text provides a hands-on, sound introduction to mathematical finance. The author first presents the classical topics of utility and the mean-variance approach to portfolio choice. Focusing on derivative pricing, the text then covers the binomial model, the general discrete-time model, Brownian motion, the Black–Scholes model and various interest-rate models.

Features

Contents Portfolio Choice Introduction Utility Mean-variance analysis The Binomial Model One-period model Multi-period model A General Discrete-Time Model One-period model Multi-period model Brownian Motion Introduction Hitting-time distributions Girsanov’s theorem Brownian motion as a limit Stochastic calculus The Black–Scholes Model Introduction

• Presents a self-contained treatment of mathematical models in finance by including the relevant mathematical background • Takes a hands-on approach to calculations, enabling students to derive the prices of many common financial products

The Black–Scholes formula Hedging and the Black–Scholes equation Path-dependent claims Dividend-paying assets Interest-Rate Models

• Assumes no prior knowledge of stochastic calculus or measure-theoretic probability

Introduction

• Includes exercises in each chapter and solutions in an appendix

Gaussian random-field model

Survey of interest-rate models Appendix A: Mathematical Preliminaries Appendix B: Solutions to the Exercises Further Reading References

Catalog no. C3452, January 2010, 264 pp. ISBN: 978-1-4200-9345-2, $69.95

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Index Exercises appear at the end of each chapter.

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Mathematics for Finance Introduction to Financial Models for Management and Planning James R. Morris and John P. Daley University of Colorado, Denver, USA

This authoritative text provides graduate-level instruction on the development of models for financial management and planning. By working through the problems and models in the text, students learn how computer-based models should be structured to analyze a firm’s investment and financing. Emphasizing Monte Carlo simulation, the authors cover modeling problems related to financial management, firm valuation, forecasting, and security pricing. While the primary focus is on models related to corporate financial management, the book also introduces students to a variety of models related to security markets, stock and bond investments, portfolio management, and options.

Features • Covers all key aspects of financial modeling • Introduces powerful tools for the financial toolbox and shows how to use them to build successful models

Interest Rate Modeling Theory and Practice Lixin Wu University of Science & Technology, Kowloon, Hong Kong

“The book presents in a balanced way both theory and applications of interest rate modeling. … The book can serve as a textbook. It is selfcontained in mathematics and presents rigorous justifications for almost all results. Many exercises are provided which often require computer implementation. …” —Pavel Stoynov, Zentralblatt MATH 1173

Containing many results that are new or exist only in recent research articles, this text portrays the theory of interest rate modeling as a threedimensional object of finance, mathematics, and computation. It introduces all models with financial-economical justifications, develops options along the martingale approach, and handles option evaluations with precise numerical methods. Taking a top-down approach, the author shows students how to build and use models. The text includes exercises and real-world examples, along with code, tables, and figures accessible on the author’s website.

• Contains extensive exercises throughout the text

Solutions manual available for qualifying instructors

• Provides complementary access to the Monte Carlo simulation software @Risk

The Basics of Stochastic Calculus. The Martingale Representation Theorem. Interest Rates and Bonds. The Heath–Jarrow–Morton Model. ShortRate Models and Lattice Implementation. The LIBOR Market Model. Calibration of LIBOR Market Model. Volatility and Correlation Adjustments. Affine Term Structure Models. References. Index.

Solutions manual and PowerPoint slides available for qualifying instructors

Contents Tools for Financial Planning and Modeling: Financial Analysis. Tools for Financial Planning and Modeling: Simulation. Introduction to Forecasting Methods. A Closer Look at the Details of a Financial Model. Modeling Security Prices and Investment Portfolios. Optimization Models. References. Index.

Contents

Catalog no. C0569, 2009, 353 pp. ISBN: 978-1-4200-9056-7, $79.95

Catalog no. C0542, 2009, 754 pp. ISBN: 978-1-4200-9054-3, $89.95

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

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Algebraic Geometry and Number Theory

Advanced Number Theory with Applications Richard A. Mollin University of Calgary, Alberta, Canada

“When I was looking over books for my course, I was very pleased by yours, and look forward to teaching from it.” —David Barth-Hart, Associate Head, School of Mathematical Sciences, Rochester Institute of Technology, New York, USA

“… a wondrous book, successfully fulfilling the author’s purpose of effecting a bridge to modern number theory for the somewhat initiated. … it’s very nice to find in Mollin’s book a high quality and coherent treatment of this beautiful material and pointers in abundance to where to go next.” —Michael Berg, Loyola Marymount University, MAA Review, 2009

By covering a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory, this text provides the most up-to-date and comprehensive material for a second course in this field. It includes numerous examples and exercises and enables students to easily cross-reference and find the appropriate data.

Limits of Graphs in Group Theory and Computer Science Edited by

Goulnara Arzhantseva University of Geneva, Switzerland

Alain Valette University of Neuchatel, Switzerland

Covering the geometric, combinatorial, and computational aspects of group theory, this book focuses on the study of large families of finite graphs with certain expanding properties and their embeddings into Hilbert and Banach spaces. It investigates the structure of finitely generated groups giving rise to such graphs and explores new interactions with broad areas of theoretical computer science. Catalog no. N10060, 2009, 280 pp. ISBN: 978-1-4398-0400-1, $94.50

Real, Complex, and Functional Analysis Measure & Probability S.R. Athreya

Solutions manual available for qualifying instructors

Indian Academy of Sciences, Bangalore, India

Contents

V.S. Sunder

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

Institute of Mathematical Sciences, Chennai, India

Catalog no. C8328, January 2010, 440 pp. ISBN: 978-1-4200-8328-6, $89.95

“… The book is neatly written and can be recommended as an introduction to all students who intend to start courses on advanced modern probability.” —EMS Newsletter, Sept. 2009

This book begins with the construction of Lebesgue measure via Caratheodory’s outer measure approach and goes on to discuss integration and standard convergence theorems. It also presents the elements of probability theory, the law of large numbers, central limit theorem, discrete time Markov chains, stationary distributions, and limit theorems. Catalog no. N10021, 2009, 232 pp. ISBN: 978-1-4398-0126-0, $69.95

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Real, Complex, and Functional Analysis

New!

Applied Functional Analysis Second Edition J. Tinsley Oden and Leszek F. Demkowicz University of Texas at Austin, USA

Ideal for a two-semester course, this proven textbook teaches students how to prove theorems and prepares them for further study of more advanced mathematical topics. It helps them succeed in formulating research questions in a mathematically rigorous way. While retaining the structure of its bestselling predecessor, this second edition includes revisions of many original examples, along with new examples that often reflect the authors’ own vast research experiences and perspectives. The examples in the text motivate students to appreciate the value of mathematical rigor.

New to the Second Edition • Completely revised section on lim sup and lim inf • New discussions of connected sets, probability, Bayesian statistical inference, and the generalized (integral) Minkowski inequality • New sections on elements of multilinear algebra and determinants, the singular value decomposition theorem, the Cauchy principal value, and Hadamard finite part integrals • New example of a Lebesgue non-measurable set • Many more exercises This text presents the mathematical foundations that lead to classical results in functional analysis. It prepares students to learn the variational theory of partial differential equations, distributions and Sobolev spaces, and numerical analysis with an emphasis on finite element methods. Solutions manual available for qualifying instructors

Contents Preliminaries Elementary Logic and Set Theory Relations Functions Cardinality of Sets Foundations of Abstract Algebra Elementary Topology in Rn Elements of Differential and Integral Calculus Linear Algebra Vector Spaces—The Basic Concepts Linear Transformations Algebraic Duals Euclidean Spaces Lebesgue Measure and Integration Lebesgue Measure Lebesgue Integration Theory Topological and Metric Spaces Elementary Topology Theory of Metric Spaces Banach Spaces Topological Vector Spaces Hahn–Banach Extension Theorem Bounded (Continuous) Linear Operators on Normed Spaces Closed Operators Topological Duals. Weak Compactness Closed Range Theorem. Solvability of Linear Equations Hilbert Spaces Basic Theory Duality in Hilbert Spaces Elements of Spectral Theory References

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

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

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Real, Complex, and Functional Analysis

Real and Complex Analysis Christopher Apelian and Steve Surace Drew University, Madison, New Jersey, USA with

Akhil Mathew

Unlike other undergraduate-level texts, Real and Complex Analysis develops both the real and complex theory together. It takes a unified, elegant approach to the theory that is consistent with the recommendations of the MAA’s 2004 Curriculum Guide. By presenting real and complex analysis together, the authors illustrate the connections and differences between these two branches of analysis right from the beginning. This combined development also allows for a more streamlined approach to real and complex function theory. Enhanced by more than 1,000 exercises, the text covers all the essential topics usually found in separate treatments of real analysis and complex analysis. Consequently, students will no longer have to use two separate textbooks—one for real function theory and one for complex function theory. The book’s website offers hints and solutions to selected exercises as well as further reading suggestions.

Contents The Spaces R, Rk, and C. Point-Set Topology. Limits and Convergence. Functions: Definitions and Limits. Functions: Continuity and Convergence. The Derivative. Real Integration. Complex Integration. Taylor Series, Laurent Series, and the Residue Calculus. Complex Functions as Mappings. Bibliography. Index. Catalog no. C8067, January 2010, 567 pp. ISBN: 978-1-58488-806-2, $89.95

Essentials of Topology with Applications Steven G. Krantz Washington University, St. Louis, Missouri, USA

With examples, exercises, and illustrations to augment the teaching process, this text provides a clear, insightful, and thorough introduction to the basics of modern topology. It presents the traditional concepts of topological space, open and closed sets, separation axioms, and more, along with applications of the ideas in Morse, manifold, homotopy, and homology theories. The text contains material on graph theory and dynamical systems, both of which are insightful applications of topological ideas. Taking a fresh and accessible approach to a venerable subject, it gives students the foundation for further mathematical study in real analysis, abstract algebra, and beyond.

Features • Presents a thorough treatment of algebraic topology • Offers numerous examples, illustrations, and exercises to make learning the topic easier • Draws on examples in mathematics, physics, economics, engineering, and other disciplines • Includes several appendices that supply background information on logic, real variable theory, set theory, and algebraic structures

Contents Fundamentals. Advanced Properties of Topological Spaces. Basic Algebraic Topology. Manifold Theory. Moore–Smith Convergence and Nets. Function Spaces. Knot Theory. Graph Theory. Dynamical Systems. Appendices. Solutions of Selected Exercises. Bibliography. Index. Catalog no. C9749, January 2010, 420 pp. ISBN: 978-1-4200-8974-5, $89.95

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Mathematics for Engineering

Coming soon!

Advanced Engineering Mathematics with MATLAB® Third Edition Dean G. Duffy Former Instructor, US Naval Academy, Annapolis, Maryland, USA

Retaining the format and writing style that made previous editions so popular, this text builds a solid background in the mathematics required throughout the engineering disciplines. It covers complex variables, ordinary and partial differential equations, transform methods, vector algebra, and linear algebra. The third edition includes two new chapters: one on probability to introduce the topic along with Markov chains and a second on stochastic processes that introduces a stochastic modeling approach. This edition also places an increased emphasis on MATLAB® through additional examples, problems, and projects.

Features • Incorporates the use of MATLAB to help students visualize and understand the mathematics and solve problems requiring heavy computation • Brings relevance to the material through many examples, most drawn from the engineering and scientific literature • Introduces the z transform, which is of great importance in digital technologies • Includes a chapter on the Hilbert transform, crucial to work in communications • Contains an abundance of exercises that help build problem-solving skills Solutions manual available for qualifying instructors

Contents Complex Variables First-Order Ordinary Differential Equations Higher-Order Ordinary Differential Equations Fourier Series The Fourier Transform The Laplace Transform The Z-Transform The Hilbert Transform The Sturm-Liouville Problem The Wave Equation The Heat Equation Laplace’s Equation Vector Calculus Linear Algebra Answers to the Odd-Numbered Problems For more complete contents, visit www.crctextbooks.com

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

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

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Mathematics for Engineering

New!

Advanced Mathematical Methods in Science and Engineering Second Edition S.I. Hayek Pennsylvania State University, University Park, USA

An update of a classroom-tested bestseller, this second edition continues to give students the strong foundation needed to apply mathematical techniques to the physical phenomena encountered in scientific and engineering applications. Numerous examples illustrate the various methods of solution and answers to the end-of-chapter problems are included at the back of the book.

Contents Ordinary Differential Equations Series Solutions of Ordinary Differential Equations Special Functions

After introducing integration and solution methods of ODEs, the book presents Bessel and Legendre functions as well as the derivation and methods of solution of linear boundary value problems for physical systems in one spatial dimension governed by ODEs. It also covers complex variables, calculus, and integrals; linear PDEs in classical physics and engineering; the derivation of integral transforms; Green’s functions for ODEs and PDEs; asymptotic methods for evaluating integrals; and the asymptotic solution of ODEs.

Boundary Value Problems and Eigenvalue Problems

New to this edition, the final chapter offers an extensive treatment of numerical methods for solving non-linear equations, finite difference differentiation and integration, initial value and boundary value ODEs, and PDEs in mathematical physics. Chapters that cover boundary value problems and PDEs contain derivations of the governing differential equations in many fields of applied physics and engineering, such as wave mechanics, acoustics, heat flow in solids, diffusion of liquids and gases, and fluid flow.

Asymptotic Methods

Features

Appendix E: Plots of Special Functions

• Incorporates a new chapter on numerical methods

Appendix F: Vector Analysis

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

Appendix G: Matrix Algebra

• Provides a complete treatment of ODEs and PDEs

Functions of a Complex Variable Partial Differential Equations of Mathematical Physics Integral Transforms Green’s Functions

Numerical Methods Appendix A: Infinite Series Appendix B: Special Functions Appendix C: Orthogonal Coordinate Systems Appendix D: Dirac Delta Functions

References Answers

• Covers Green’s functions for unbounded and bounded media

Index

• Explores self-adjoint systems and orthogonal series

For more complete contents, visit www.crctextbooks.com

• Includes many solved examples and problems with answers Catalog no. C1977, June 2010, 866 pp. ISBN: 978-1-4200-8197-8, $129.95

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Mathematics for Engineering

Classical and Modern Numerical Analysis Theory, Methods, and Practice Azmy S. Ackleh, Edward James Allen, Ralph Baker Kearfott, and Padmanabhan Seshaiyer This advanced, graduate-level introduction to the theory and methods of numerical analysis provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It supplies the necessary background in numerical methods so that students can apply the techniques and understand the mathematical literature in this area. The authors illustrate the concepts with many examples as well as analytical and computational exercises at the end of each chapter. Although the book is independent of a specific computer program, MATLAB® code is used to illustrate various concepts.

Features • Provides a clear and solid introduction to the theory and application of computational methods for applied mathematics problems • Helps prepare students for doctoral examinations in numerical analysis • Presents the most important advanced aspects of numerical linear algebra, finite element theory, approximation theory, optimization, and integral equations • Covers interval computation methods in numerical analysis • Includes fully worked out solutions for selected problems • Offers the MATLAB files on the authors’ website Solutions manual available for qualifying instructors

Catalog no. C9157, January 2010, 628 pp. ISBN: 978-1-4200-9157-1, $99.95

Contents Mathematical Review and Computer Arithmetic Numerical Solution of Nonlinear Equations of One Variable Numerical Linear Algebra Approximation Theory Eigenvalue-Eigenvector Computation Numerical Differentiation and Integration Initial Value Problems for Ordinary Differential Equations Introduction Euler’s Method Single-Step Methods: Taylor Series and Runge–Kutta Error Control and the Runge–Kutta–Fehlberg Method Multistep Methods Predictor-Corrector Methods Stiff Systems Extrapolation Methods Application to Parameter Estimation in Differential Equations Numerical Solution of Systems of Nonlinear Equations Introduction and Fréchet Derivatives Successive Approximation (Fixed Point Iteration) and the Contraction Mapping Theorem Newton’s Method and Variations Multivariate Interval Newton Methods Quasi-Newton Methods (Broyden’s Method) Methods for Finding All Solutions Optimization Local Optimization Constrained Local Optimization Constrained Optimization and Nonlinear Systems Linear Programming Dynamic Programming Global (Non-Convex) Optimization Boundary Value Problems and Integral Equations Solutions to Selected Exercises Exercises appear at the end of each chapter. For more complete contents, visit www.crctextbooks.com

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

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Mathematics for Engineering Essentials of Control Techniques and Theory John Billingsley

New!

Introduction to the Simulation of Dynamics Using Simulink®

University of Southern Queensland, Toowoomba, Australia

Michael A. Gray

Carefully separating the essential from the ornamental, this book presents the nuts and bolts for designing a successful controller. It shows students how mathematics can help us understand the concepts that underpin the controller’s effects. It also provides software simulation examples and other material at www.esscont.com

Designed for undergraduate students in the general science, engineering, and mathematics community, this text shows how to use the powerful tool of Simulink to investigate and form intuitions about the behavior of dynamical systems. It clearly explains how to transition from physical models described by mathematical equations directly to executable Simulink simulations. PowerPoint slides and solutions to exercises are offered at http://nw08.american.edu/~gray/index.htm

Solutions manual available for qualifying instructors Catalog no. 91239, January 2010, 339 pp. ISBN: 978-1-4200-9123-6, $89.95

Advanced Linear Algebra for Engineers with MATLAB® Sohail A. Dianat and Eli S. Saber Rochester Institute of Technology, New York, USA

Designed to elevate the analytical and problemsolving skills of engineering students, this text provides systematic instruction that enables those students to make full use of the advanced capabilities that MATLAB® provides. Offering a broad selection of progressive exercises and MATLAB problems, each chapter features carefully chosen examples that demonstrate underlying ideas at work in practical scenarios. Solutions manual available for qualifying instructors Catalog no. 95234, 2009, 346 pp. ISBN: 978-1-4200-9523-4, $99.95

American University, Washington, D.C., USA

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

Linear and Nonlinear Programming with Maple™ An Interactive, Applications-Based Approach Paul E. Fishback Grand Valley State University, Allendale, Michigan, USA

Integrating a hands-on learning approach, a strong linear algebra focus, Maple™ software, and real-world applications, this book introduces undergraduate students to the mathematical concepts and principles underlying linear and nonlinear programming. It fills the gap between management science books lacking mathematical detail and rigor and graduate-level books on mathematical programming. Maple worksheets and code can be found on the book’s website. Solutions manual available for qualifying instructors Catalog no. C064X, January 2010, 413 pp. ISBN: 978-1-4200-9064-2, $89.95

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Mathematics for Engineering MATLAB® with Applications to Engineering, Physics and Finance David Baez-Lopez

Advanced Engineering Mathematics with Modeling Applications

Universidad de las Américas, Puebla, Mexico

S. Graham Kelly

This book explains how to perform complex mathematical tasks with MATLAB® programs. The author first describes simple functions such as differentiation, integration, and plotting. He then addresses advanced topics, including programming, producing executables, publishing results directly from MATLAB programs, and creating graphical user interfaces. The text also presents examples of Simulink for system modeling and simulation. It explores the use of MATLAB in digital signal processing, chemical and food engineering, astronomy, optics, financial derivatives, and much more.

Presenting mathematical theory at an understandable level, this graduate-level text explores topics from real and functional analysis, such as vector spaces, inner products, norms, and linear operators, to formulate mathematical models of engineering problems for both discrete and continuous systems. The author presents theorems and proofs, but without the full detail found in mathematical books, so that development of the theory does not obscure its application to engineering problems. He applies principles and theorems of linear algebra to derive solutions, including proofs of theorems when they are instructive. Tying mathematical theory to applications, this book provides engineering students with a strong foundation in mathematical terminology and methods.

Features • Brings together diverse applications of MATLAB in many areas • Provides a gradual introduction to MATLAB functions and programming • Covers the graphical user interfaces in MATLAB and Simulink • Presents Simulink for scientific and engineering system simulation • Contains more than 160 practical worked examples and numerous end-of-chapter exercises • Offers downloadable MATLAB examples and programs on the book’s website

University of Akron, Ohio, USA

Features • Emphasizes mathematical modeling, dimensional analysis, scaling, and their application to macroscale and nanoscale problems • Explores eigenvalue problems for discrete and continuous systems and many applications • Develops and applies approximate methods, such as Rayleigh–Ritz and finite element methods • Presents applications that use contemporary research in areas such as nanotechnology

Solutions manual available for qualifying instructors

Contents Introduction to MATLAB. Variables and Functions. Matrices and Linear Algebra. Calculus. Plotting with MATLAB. Programming in MATLAB. Graphical User Interfaces. Simulink. MATLAB Applications to Engineering. MATLAB Applications to Physics. MATLAB Applications to Finance. Index.

Solutions manual available for qualifying instructors

Contents Foundations of Mathematical Modeling. Linear Algebra. Ordinary Differential Equations. Variational Methods. Eigenvalue Problems. Partial Differential Equations. Index. Catalog no. 9533, 2009, 522 pp. ISBN: 978-0-8493-9533-8, $111.95

Catalog no. K10356, January 2010, 426 pp. ISBN: 978-1-4398-0697-5, $79.95

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

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Mathematics for Biology/Computational Biology Differential Equations and Mathematical Biology Second Edition D.S. Jones University of Dundee, Scotland

M.J. Plank University of Canterbury, Christchurch, New Zealand

B.D. Sleeman University of Leeds, UK

“… Where this text stands out is in its thoughtful organization and the clarity of its writing. This is a very solid book … The authors succeed because they do a splendid job of integrating their treatment of differential equations with the applications, and they don’t try to do too much. … Each chapter comes with a collection of well-selected exercises, and plenty of references for further reading.” —MAA Reviews, April 2010

Contents Linear Ordinary Differential Equations with Constant Coefficients Systems of Linear Ordinary Differential Equations Modelling Biological Phenomena First-Order Systems of Ordinary Differential Equations Mathematics of Heart Physiology

Ideal for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, this bestselling text introduces the fundamental modeling and analytical techniques used to understand biological phenomena. It discusses the modeling of biological behavior, including the heartbeat cycle, chemical reactions, nerve pulses, predator–prey models, and epidemics.

Mathematics of Nerve Impulse Transmission

New to the Second Edition

Numerical Bifurcation Analysis

• A section on spiral waves • Recent developments in tumor biology • More on the numerical solution of differential equations and numerical bifurcation analysis • MATLAB® files available for download online at www.crctextbooks.com • Many additional examples and exercises The book uses various differential equations to model biological behavior. It explains how bifurcation and chaotic behavior play key roles in fundamental problems of biological modeling. The authors also present a unique treatment of pattern formation in developmental biology based on Turing’s famous idea of diffusion-driven instabilities. Catalog no. C8357, January 2010, 462 pp. ISBN: 978-1-4200-8357-6, $79.95

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Chemical Reactions Predator and Prey Partial Differential Equations Evolutionary Equations Problems of Diffusion Bifurcation and Chaos Growth of Tumors Introduction Mathematical model I of tumor growth Spherical tumor growth based on model I Stability of tumor growth based on model I Mathematical model II of tumor growth Spherical tumor growth based on model II Stability of tumor growth based on model II Epidemics The Kermack–McKendrick model Vaccination An incubation model Spreading in space Answers to Selected Exercises For more complete contents, visit www.crctextbooks.com

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Mathematics for Biology/Computational Biology Coming soon!

Biological Computation

Algorithms in Bioinformatics

Ehud Lamm

A Practical Introduction

Tel-Aviv University, Israel

Ron Unger

Wing-Kin Sung

Bar-Ilan University, Ramat-Gan, Israel

National University of Singapore

“… an excellent guide. The book is appropriate for advanced undergraduates and graduates in mathematics or CS. … The 27-page introduction is the most efficient concept-building summary and explication of molecular biology that I have encountered. … This self-contained, welldesigned, and well-written book, with its many good exercises, bibliographic references, and photo-quality figures, is an ideal introduction to bioinformatics.” —George Hacken, Computing Reviews, March 2010

Solutions manual available for qualifying instructors Catalog no. C7033, January 2010, 407 pp. ISBN: 978-1-4200-7033-0, $79.95

Created for advanced undergraduate students, Biological Computation covers major themes of bio-inspired computing, including cellular automata, molecular computation, genetic algorithms, and neural networks. Providing theoretical and coding exercises, this self-contained text requires no previous knowledge of biology. It provides valuable insight to students from biomedical backgrounds looking to gain the computational skills needed to make entry into the fields of systems biology, biological modeling, and simulations. Catalog no. C7959, October 2010, c. 344 pp. ISBN: 978-1-4200-8795-6, $79.95

Probability Theory and Applications Introduction to Probability with Mathematica®

Stochastic Processes

Second Edition

Peter W. Jones and Peter Smith

Kevin J. Hastings

An Introduction, Second Edition

Knox College, Galesburg, Illinois, USA

Keele University, Staffordshire, UK

Updated to conform to Mathematica® 7.0, this second edition continues to show students how to easily create simulations from templates and solve problems using Mathematica. It also includes additional problems from Actuarial Exam P as well as new examples, exercises, and data sets. The accompanying CD-ROM contains updated Mathematica notebooks. Solutions manual available for qualifying instructors

Based on a highly popular, well-established course taught by the authors, this updated textbook makes the material accessible to students by avoiding specialized applications and instead highlighting simple applications and examples. It includes over 50 worked examples and more than 200 end-of-chapter problems with selected answers in the back of the book. The authors provide Mathematica® and R programs on the book’s website.

Catalog no. C7938, January 2010, 465 pp. ISBN: 978-1-4200-7938-8, $89.95

Solutions manual available for qualifying instructors via password on the book’s website Catalog no. K10004, January 2010, 232 pp. Soft Cover, ISBN: 978-1-4200-9960-7, $79.95

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