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Mathematics Textbooks from Cambridge

Roger AstleyExecutive Publisher, Mathematical Sciences [email protected]

Mathematics Textbooks

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Contents

Logic, Categories and Sets

1 Set Theory

2 How to Prove It - Second Edition

3 An Introduction to Mathematical Reasoning

Algebra

4 Matrix Analysis

5 Linear Algebra

6 Classical Mechanics

Real and Complex Analysis

7 Numbers and Functions

8 A First Course in Mathematical Analysis

9 Calculus – Third Edition

Topology and Geometry

10 Geometry from a Differentiable Viewpoint

11 Geometry

12 Elementary Differential Geometry

13 Algebraic Topology

SUPPLEMENTARY READING

24 A Concise Text on Advanced Linear Algebra

A Course in Mathematical Analysis Volume 1



Differential and Integral Equations, Dynamical Systems and Control

14 Introduction to Dynamical Systems

15 Differential Equations and Linear Algebra

16 Linear Partial Differential Equations and Fourier Theory

Mathematical Modelling and Methods

17 Applied Complex Variables for Scientists and Engineers

18 Introduction to Linear Algebra – Fourth Edition

19 Mathematics for Economics and Finance

Mathematical Finance

20 An Elementary Introduction to Mathematical Finance

Computational Science

21 A Guide to MATLAB

Optimization, OR and Risk Analysis

22 Chance, Strategy, and Choice

23 A Gentle Introduction to Optimization


1 LOGIC, CATEGORIES AND SETS

Set TheoryA First Course

Daniel W. CunninghamUniversity at Buffalo, State University of New York

Mathematicians have shown that virtually all mathematical concepts and results can be formalized within set theory. This textbook covers the fundamentals of abstract sets and develops these theories within the framework of axiomatic set theory. The proofs presented are rigorous, clear, and suitable for undergraduate and graduate students.• Accessible to students without a background in logic and logical notation

• Clear, detailed proofs written for students who are still learning how to compose a proof

• Usable by instructors who are not experts in axiomatic set theory

Contents1. Introduction; 2. Basic set building axioms and operations; 3. Relations and functions; 4. The natural numbers; 5. On the size of sets; 6. Transfinite recursion; 7. The axiom of choice (revisited); 8. Ordinals; 9. Cardinals.

2016 228 x 152 mm 222pp 13 b/w illus.

9781107120327 | c. £39.99 / c. US$60.00 HB

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Cambridge Mathematical Textbooks

e-sample is available for inspection


2LOGIC, CATEGORIES AND SETS LOGIC, CATEGORIES AND SETS

How to Prove ItA Structured ApproachSecond edition

Daniel J. VellemanAmherst College, Massachusetts

Daniel J. Velleman’s lively text prepares students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. This new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.• Systematic and thorough, shows how several techniques can be combined to

construct a complex proof

• Selected solutions and hints now provided, plus over 200 exercises some using Proof Designer software to help students learn to construct their own proofs

• Covers logic, set theory, relations, functions and cardinality

Contents1. Sentential logic; 2. Quantificational logic; 3. Proofs; 4. Relations; 5. Functions; 6. Mathematical induction; 7. Infinite sets.2006 400pp 10 tables 536 exercises

9780521861243 | £64.99 / US$125.00 HB

9780521675994 | £23.99 / US$39.99 PB

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The book begins with the basic concepts of logic and theory … These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. No background standard in high scholl mathematics is assumed.”

L’Enseignement Mathématique



3

An Introduction to Mathematical ReasoningNumbers, Sets and Functions

Peter J. EcclesUniversity of Manchester

This book introduces the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. Over 250 problems include questions to interest and challenge the most able student and plenty of routine exercises to help familiarize the reader with the basic ideas.• Provides an introduction to the key notion of mathematical proof

• Fully class-tested by the author

• Makes use of a large number of fully worked examples

ContentsPart I. Mathematical Statements and Proofs: 1. The language of mathematics; 2. Implications; 3. Proofs; 4. Proof by contradiction; 5. The induction principle; Part II. Sets and Functions: 6. The language of set theory; 7. Quantifiers; 8. Functions; 9. Injections, surjections and bijections; Part III. Numbers and Counting: 10. Counting; 11. Properties of finite sets; 12. Counting functions and subsets; 13. Number systems; 14. Counting infinite sets; Part IV. Arithmetic: 15. The division theorem; 16. The Euclidean algorithm; 17. Consequences of the Euclidean algorithm; 18. Linear diophantine equations; Part V. Modular Arithmetic: 19. Congruences of integers; 20. Linear congruences; 21. Congruence classes and the arithmetic of remainders; 22. Partitions and equivalence relations; Part VI. Prime Numbers: 23. The sequence of prime numbers; 24. Congruence modulo a prime; Solutions to exercises.

1997 228 x 152 mm 364pp

9780521592697 | £89.99 / US$160.00 HB

9780521597180 | £29.99 / US$64.9 PB

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LOGIC, CATEGORIES AND SETS

The book is written with understanding of the needs of students …”

European Mathematical Society



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Matrix AnalysisRoger A. HornUniversity of Utah

and Charles R. JohnsonThe thoroughly revised and updated second edition of this acclaimed text for a second course on linear algebra has more than 1,100 problems and exercises, along with new sections on the singular value and CS decompositions and the Weyr canonical form, expanded treatments of inverse problems and of block matrices and much more.• Comprehensive coverage of core advanced linear algebra topics, using canonical forms

as a unifying theme

• More than 1,100 problems and exercises, many with detailed hints, including theme-based problems that develop throughout the text

• 2-by-2 examples illustrate concepts throughout the book

Contents 1. Eigenvalues, eigenvectors, and similarity; 2. Unitary similarity and unitary equivalence; 3. Canonical forms for similarity, and triangular factorizations; 4. Hermitian matrices, symmetric matrices, and congruences; 5. Norms for vectors and matrices; 6. Location and perturbation of eigenvalues; 7. Positive definite and semi-definite matrices; 8. Positive and nonnegative matrices; Appendix A. Complex numbers; Appendix B. Convex sets and functions; Appendix C. The fundamental theorem of algebra; Appendix D. Continuous dependence of the zeroes of a polynomial on its coefficients; Appendix E. Continuity, compactness, and Weierstrass’ theorem; Appendix F. Canonical pairs.

2012 253 x 177 mm 662pp 1175 exercises

9780521839402 | £84.99 / US$145.00 HB

9780521548236 | £34.99 / US$59.99 PB

2ND EDITION

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LOGIC, CATEGORIES AND SETS ALGEBRA

The presentation is straightforward and extremely readable. The authors’ enthusiasm pervades the book, and the printing is what we expect from this publisher. This will doubtless be the standard text for years to come.”

American Scientist



5 ALGEBRA

Linear Algebra Concepts and Methods

Martin AnthonyLondon School of Economics and Political Science

and Michele HarveyLondon School of Economics and Political Science

This thorough, yet concise, textbook covers key topics in first- and second-year university courses and includes many examples and exercises with solutions to help students practise and master the relevant methods. Crucially, it fully develops the underlying theory so that students can understand how these methods really work.• Suitable as a course text and also ideal for self-study

• Hundreds of exercises and solutions provide plenty of hands-on practice

• Easier to navigate than other lengthy texts

ContentsPreface; Preliminaries: before we begin; 1. Matrices and vectors; 2. Systems of linear equations; 3. Matrix inversion and determinants; 4. Rank, range and linear equations; 5. Vector spaces; 6. Linear independence, bases and dimension; 7. Linear transformations and change of basis; 8. Diagonalisation; 9. Applications of diagonalisation; 10. Inner products and orthogonality; 11. Orthogonal diagonalisation and its applications; 12. Direct sums and projections; 13. Complex matrices and vector spaces; 14. Comments on exercises; Index.

2012 247 x 174 mm 527pp 20 b/w illus. 150 exercises

9780521279482 | £34.99 / US$74.99 PB

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Linear Algebra: Concepts and Methods is bound to be a very successful book in today’s market. I for one intend to use it the next time I’m at bat in the linear algebra line-up.”

Michael Berg, MAA Reviews



6ALGEBRA

Classical MechanicsR. Douglas GregoryUniversity of Manchester

Gregory’s Classical Mechanics is a thorough, self-contained and highly readable account of a subject many students find difficult. The author’s clear and systematic style promotes a good understanding of the subject: each concept is motivated and illustrated by worked examples, while problem sets provide ample practice for understanding and technique.• Suitable for a wide range of undergraduate mechanics courses given in mathematics and

physics departments: no prior knowledge of the subject is assumed

• Profusely illustrated and thoroughly class-tested, with a clear direct style that makes the subject easy to understand: all concepts are motivated and illustrated by the many worked examples included

• Good, accurately set problems, with answers in the book: computer assisted problems and projects are also provided. Model solutions for problems available to teachers from www.cambridge.org/9780521534093

ContentsPart I. Newtonian Mechanics of a Single Particle: 1. The algebra and calculus of vectors; 2. Velocity, acceleration and scalar angular velocity; 3. Newton’s laws of motion and the law of gravitation; 4. Problems in particle dynamics; 5. Linear oscillations; 6. Energy conservation; 7. Orbits in a central field; 8. Non-linear oscillations and phase space; Part II. Multi-particle Systems: 9. The energy principle; 10. The linear momentum principle; 11. The angular momentum principle; Part III. Analytical mechanics: 12. Lagrange’s equations and conservation principle; 13. The calculus of variations and Hamilton’s principle; 14. Hamilton’s equations and phase space; Part IV. Further Topics: 15. The general theory of small oscillations; 16. Vector angular velocity and rigid body kinematics; 17. Rotating reference frames; 18. Tensor algebra and the inertia tensor; 19. Problems in rigid body dynamics; Appendix: centres of mass and moments of inertia; Answers to the problems; Bibliography; Index.

2006 247 x 174 mm 607pp 193 b/w illus. 3 tables 348 exercises

9780521534093 | £39.99 / US$74.99 PB

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The writing here is a picture of clarity and directness … The exercises include plenty of interesting and challenging problems … an attractive and well-written exposition of classical mechanics. I wish it had been my textbook when I was a student.”

Mathematical Association of America



7 REAL AND COMPLEX ANALYSIS

Numbers and FunctionsSteps into Analysis

R. P. BurnUniversity of Exeter

In this updated edition of Numbers and Functions, the reader is invited to tackle each of the key concepts of mathematical analysis in turn, progressing from experience through a structured sequence of over 800 problems to concepts, definitions and proofs of classical real analysis.• The third edition has been revised and updated

• Helps students transition from school-level calculus to undergraduate mathematical analysis

• Contains more than 800 exercises with brief answers and hints

Contents Preface to first edition; Preface to second edition; Preface to third edition; Glossary; Part I. Numbers: 1 Mathematical induction; 2. Inequalities; 3. Sequences: a first bite at infinity; 4. Completeness: what the rational numbers lack; 5. Series: infinite sums; Part II. Functions: 6. Functions and continuity: neighbourhoods, limits of functions; 7. Continuity and completeness: functions on intervals; 8. Derivatives: tangents; 9. Differentiation and completeness: mean value theorems, Taylor’s Theorem; 10. Integration: the fundamental theorem of calculus; 11. Indices and circle functions; 12. Sequences of functions; Appendix 1. Properties of the real numbers; Appendix 2. Geometry and intuition; Appendix 3. Questions for student investigation and discussion; Bibliography; Index.


9781107444539 | £34.99 / US$69.99 PB

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3RD EDITION This third edition of Numbers and Functions continues the author’s long-term commitment to support every reader in making sense of mathematics by responding to a succession of well-chosen questions that encourage personal reflection and discussion with others. Groups of questions are followed by a summary to build the bigger picture. Every chapter includes details of the historical development and ends with a full list of solutions. The author is aware of the difficulties that students encounter with the complexity of the limit concept and begins with a pragmatic approach to null sequences. This broadens into a full study of limits of sequences, completeness, and a full range of tests for convergence of infinite series … This latest edition maintains the original chapters of the original, while benefiting from detailed improvements that have arisen from the experience of many readers. Thoroughly recommended.” David Tall, University of Warwick



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Contents Preface to first edition; Preface to second edition; Preface to third edition; Glossary; Part I. Numbers: 1 Mathematical induction; 2. Inequalities; 3. Sequences: a first bite at infinity; 4. Completeness: what the rational numbers lack; 5. Series: infinite sums; Part II. Functions: 6. Functions and continuity: neighbourhoods, limits of functions; 7. Continuity and completeness: functions on intervals; 8. Derivatives: tangents; 9. Differentiation and completeness: mean value theorems, Taylor’s Theorem; 10. Integration: the fundamental theorem of calculus; 11. Indices and circle functions; 12. Sequences of functions; Appendix 1. Properties of the real numbers; Appendix 2. Geometry and intuition; Appendix 3. Questions for student investigation and discussion; Bibliography; Index.

REAL AND COMPLEX ANALYSIS

A First Course in Mathematical AnalysisDavid Alexander BrannanThe Open University, Milton Keynes

A down-to-earth advanced calculus text. It has a large number of diagrams and helpful margin notes; and uses many graded examples and exercises, often with complete solutions, to guide students through the tricky points. Suitable for self-study or use in parallel with a standard university course on the subject.• A sequential approach to continuity, differentiability and integration to make it easier to

understand the subject

• Many graded examples and exercises, with large numbers of complete solutions, to guide students through the tricky points

• Suitable for self-study or use in parallel with a standard university course; unlike other textbooks in the subject, should be intelligible to students on their own, offering considerable study help

ContentsPreface; Introduction: calculus and analysis; 1. Numbers; 2. Sequences; 3. Series; 4. Continuity; 5. Limits and continuity; 6. Differentiation; 7. Integration; 8. Power series; Appendix 1. Sets, functions and proofs; Appendix 2. Standard derivatives and primitives; Appendix 3. The first 1,000 decimal places of the square root of 2, e and pi; Appendix 4. Solutions to the problems; Index.

2006 246 x 189 mm 468pp 211 b/w illus. 1 table 207 exercises

9780521684248 | £34.99 / US$69.99 PB

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9 REAL AND COMPLEX ANALYSIS

CalculusThird edition

Michael SpivakPublish or Perish Inc, Houston, Texas

Spivak’s celebrated Calculus combines leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Ideal for honours students and mathematics majors seeking an alternative to doorstop textbooks and more formidable introductions to real analysis.• One of the most celebrated texts of its type now readily available outside of the US:

combines the rigor of more formidable books with the leisurely explanations, profusion of examples, exercises and illustrations associated with ‘doorstops’

• Ideal for students; clear, crisp explanations of what analysis and mathematics are really about

• Full range of exercises, from the straightforward to the challenging that deepen understanding; solutions available in book form via http://www.mathpop.com/bookhtms/cal.htm

ContentsPreface; Part I. Prologue: 1. Basic properties of numbers; 2. Numbers of various sorts; Part II. Foundations: 3. Functions; 4. Graphs; 5. Limits; 6. Continuous functions; 7. Three hard theorems; 8. Least upper bounds; Part III. Derivatives and Integrals: 9. Derivatives; 10. Differentiation; 11. Significance of the derivative; 12. Inverse functions; 13. Integrals; 14. The fundamental theorem of calculus; 15. The trigonometric functions; 16. Pi is irrational; 17. Planetary motion; 18. The logarithm and exponential functions; 19. Integration in elementary terms; Part IV. Infinite Sequences and Infinite Series: 20. Approximation by polynomial functions; 21. e is transcendental; 22. Infinite sequences; 23. Infinite series; 24. Uniform convergence and power series; 25. Complex numbers; 26. Complex functions; 27. Complex power series; Part V. Epilogue: 28. Fields; 29. Construction of the real numbers; 30. Uniqueness of the real numbers; Suggested reading; Answers (to selected problems); Glossary of symbols; Index.

2006 252 x 225 mm 681pp 700 b/w illus.

9780521867443 | £39.99 / US$69.99 HB

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3RD EDITION



10TOPOLOGY AND GEOMETRY

Geometry from a Differentiable ViewpointJohn McClearyVassar College, New York

This text, for a first course in differential or modern geometry, introduces methods within a historical context that is familiar to students from high school. The thoroughly revised second edition has been reorganized for greater clarity and includes numerous new exercises and topics such as Euclid’s geometry of space.• Takes historical approach discussing the discovery and construction of non-Euclidean

geometry and significant events like Huygens’s clock, the mathematics of cartography and Clairaut’s relation for geodesics

• Offers various intertwining approaches to geometry: students begin with the high school synthetic approach and, with development of the differential approach, learn how elementary ideas are related in the new setting

• Chapter 4 gives a thorough treatment of non-Euclidean geometry, as developed by Lobachevsky and Bolyai, while Chapter 14 parallels this treatment in the differential geometric manner

ContentsPart I. Prelude and Themes: Synthetic Methods and Results: 1. Spherical geometry; 2. Euclid; 3. The theory of parallels; 4. Non-Euclidean geometry; Part II. Development: Differential Geometry: 5. Curves in the plane; 6. Curves in space; 7. Surfaces; 8. Curvature for surfaces; 9. Metric equivalence of surfaces; 10. Geodesics; 11. The Gauss–Bonnet theorem; 12. Constant-curvature surfaces; Part III. Recapitulation and Coda: 13. Abstract surfaces; 14. Modeling the non-Euclidean plane; 15. Epilogue: where from here?


9780521116077 | £74.99 / US$125.00 HB

9780521133111 | £34.99 / US$59.99 PB

2ND EDITION

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… an unusual and interesting account of two subjects and their close historical interrelation.”

The Mathematical Gazette



11 TOPOLOGY AND GEOMETRY

GeometryDavid A. BrannanThe Open University, Milton Keynes

Matthew F. EsplenThe Open University, Milton Keynes

and Jeremy J. GrayThe Open University, Milton Keynes

Popular with students and instructors alike, this accessible and highly readable undergraduate textbook has now been revised to include end-of-chapter summaries, more challenging exercises, new results and a list of further reading. Complete solutions to all of the exercises are also provided in a new Instructors’ Manual available online.• Students respond to the authors’ modern, easy-to-read writing style

• Assumes basic knowledge of group theory and linear algebra but a rapid review of both topics is given in appendices

• Historical notes, teaching comments and diagrams feature in the margins


9781107647831 | £39.99 / US$69.99 PB

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ContentsPreface; Introduction: geometry and geometries; 1. Conics; 2. Affine geometry; 3. Projective geometry: lines; 4. Projective geometry: conics; 5. Inversive geometry; 6. Hyperbolic geometry: the disc model; 7. Elliptic geometry: the spherical model; 8. The Kleinian view of geometry; Special symbols; Further reading; Appendix 1. A primer of group theory; Appendix 2. A primer of vectors and vector spaces; Appendix 3. Solutions to the problems; Index.

This is a textbook that demonstrates the excitement and beauty of geometry … richly illustrated and clearly written.”


2ND EDITION



12TOPOLOGY AND GEOMETRY

Elementary Differential GeometryChristian BärUniversität Potsdam, Germany

This easy-to-read, generously illustrated textbook is an elementary introduction to differential geometry with emphasis on geometric results, preparing students for more advanced study. Clearly developed arguments and proofs, colour illustrations, and over 100 exercises and solutions make this book ideal for courses and self-study.• Assumes only one year of undergraduate calculus and linear algebra

• Equips the reader for further study in mathematics as well as other fields such as physics and computer science

• Over 100 exercises and solutions

ContentsPreface; Notation; 1. Euclidean geometry; 2. Curve theory; 3. Classical surface theory; 4. The inner geometry of surfaces; 5. Geometry and analysis; 6. Geometry and topology; 7. Hints for solutions to (most) exercises; Formulary; List of symbols; References; Index.

2010 247 x 174 mm 330pp 147 b/w illus. 4 colour illus. 125 exercises

9780521721493 | £39.99 / US$69.99 PB

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The book under review presents a detailed and pedagogically excellent study about differential geometry of curves and surfaces by introducing modern concepts and techniques so that it can serve as a transition book between classical differential geometry and contemporary theory of manifolds. the concepts are discussed through historical problems as well as motivating examples and applications. Moreover, constructive examples are given in such a way that the reader can easily develop some understanding for extensions, generalizations and adaptations of classical differential geometry to global differential geometry.”

Zentralblatt MATHe-sample is available for inspection


13 TOPOLOGY AND GEOMETRY

Algebraic TopologyAllen HatcherCornell University, New York

This introductory textbook is suitable for use in a first-year graduate course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises. Along with the basic material on fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory, the book includes many optional topics for which elementary expositions are hard to find.• Broad, readable coverage of the subject

• Geometric emphasis gives students better intuition

• Includes many examples and exercises

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ContentsPart I. Some Underlying Geometric Notions: 1. Homotopy and homotopy type; 2. Deformation retractions; 3. Homotopy of maps; 4. Homotopy equivalent spaces; 5. Contractible spaces; 6. Cell complexes definitions and examples; 7. Subcomplexes; 8. Some basic constructions; 9. Two criteria for homotopy equivalence; 10. The homotopy extension property; Part II. Fundamental Group and Covering Spaces: 11. The fundamental group, paths and homotopy; 12. The fundamental group of the circle; 13. Induced homomorphisms; 14. Van Kampen’s theorem of free products of groups; 15. The van Kampen theorem; 16. Applications to cell complexes; 17. Covering spaces lifting properties; 18. The classification of covering spaces; 19. Deck transformations and group actions; 20. Additional topics: graphs and free groups; 21. K(G,1) spaces; 22. Graphs of groups; Part III. Homology: 23. Simplicial and singular homology delta-complexes; 24. Simplicial homology; 25. Singular homology; 26. Homotopy invariance; 27. Exact sequences and excision; 28. The equivalence of simplicial and singular homology; 29. Computations and applications degree; 30. Cellular homology; 31. Euler characteristic; 32. Split exact sequences; 33. Mayer–Vietoris sequences; 34. Homology with coefficients; 35. The formal viewpoint axioms for homology; 36. Categories and functors; 37. Additional topics homology and fundamental group; 38. Classical applications; 39. Simplicial approximation and the Lefschetz fixed point theorem; Part IV. Cohomology: 40. Cohomology groups: the universal coefficient theorem; 41. Cohomology of spaces; 42. Cup product the cohomology ring; 43. External cup product; 44. Poincaré duality orientations; 45. Cup product; 46. Cup product and duality; 47. Other forms of duality; 48. Additional topics the universal coefficient theorem for homology; 49. The Kunneth formula; 50. H-spaces and Hopf algebras; 51. The cohomology of SO(n); 52. Bockstein homomorphisms; 53. Limits; 54. More about ext; 55. Transfer homomorphisms; 56. Local coefficients; Part V. Homotopy Theory: 57. Homotopy groups; 58. The long exact sequence; 59. Whitehead’s theorem; 60. The Hurewicz theorem; 61. Eilenberg–MacLane spaces; 62. Homotopy properties of CW complexes cellular approximation; 63. Cellular models; 64. Excision for homotopy groups; 65. Stable homotopy groups; 66. Fibrations the homotopy lifting property; 67. Fiber bundles; 68. Path fibrations and loopspaces; 69. Postnikov towers; 70. Obstruction theory; 71. Additional topics: basepoints and homotopy; 72. The Hopf invariant; 73. Minimal cell structures; 74. Cohomology of fiber bundles; 75. Cohomology theories and omega-spectra; 76. Spectra and homology theories; 77. Eckmann-Hilton duality; 78. Stable splittings of spaces; 79. The loopspace of a suspension; 80. Symmetric products and the Dold–Thom theorem; 81. Steenrod squares and powers; Appendix: topology of cell complexes; The compact-open topology.

2002 253 x 177 mm 556pp

9780521795401 | £28.99 / US$49.99 PB

… this is a marvellous tome, which is indeed a delight to read. This book is destined to become very popular amongst students and teachers alike.”

Bulletin of the Belgian Mathematical Society



14DIFFERENTIAL AND INTEGRAL EQUATIONS, DYNAMICAL SYSTEMS AND CONTROLIntroduction to Dynamical SystemsMichael BrinUniversity of Maryland, College Park

and Garrett StuckUniversity of Maryland, College Park

This introduction to the subject of dynamical systems is ideal for a one-year graduate course. From chapter one, the authors use examples to motivate, clarify and develop the theory. The book rounds off with beautiful and remarkable applications to such areas as number theory, data storage, and Internet search engines.• Broad-ranging graduate text, covering a variety of viewpoints

• Perfectly paced for a one-year course

• Includes exciting new applications to areas such as number theory, data storage, and Internet search engines

ContentsIntroduction; 1. Examples and basic concepts; 2. Topological dynamics; 3. Symbolic dynamics; 4. Ergodic theory; 5. Hyperbolic dynamics; 6. Ergodicity of Anosov diffeomorphisms; 7. Low-dimensional dynamics; 8. Complex dynamics; 9. Measure-theoretic entropy; Bibliography; Index.


9781107538948 | £34.99 / US$59.99 PB

9780521808415 | £49.99 / US$84.99 HB

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ContentsPart I. Some Underlying Geometric Notions: 1. Homotopy and homotopy type; 2. Deformation retractions; 3. Homotopy of maps; 4. Homotopy equivalent spaces; 5. Contractible spaces; 6. Cell complexes definitions and examples; 7. Subcomplexes; 8. Some basic constructions; 9. Two criteria for homotopy equivalence; 10. The homotopy extension property; Part II. Fundamental Group and Covering Spaces: 11. The fundamental group, paths and homotopy; 12. The fundamental group of the circle; 13. Induced homomorphisms; 14. Van Kampen’s theorem of free products of groups; 15. The van Kampen theorem; 16. Applications to cell complexes; 17. Covering spaces lifting properties; 18. The classification of covering spaces; 19. Deck transformations and group actions; 20. Additional topics: graphs and free groups; 21. K(G,1) spaces; 22. Graphs of groups; Part III. Homology: 23. Simplicial and singular homology delta-complexes; 24. Simplicial homology; 25. Singular homology; 26. Homotopy invariance; 27. Exact sequences and excision; 28. The equivalence of simplicial and singular homology; 29. Computations and applications degree; 30. Cellular homology; 31. Euler characteristic; 32. Split exact sequences; 33. Mayer–Vietoris sequences; 34. Homology with coefficients; 35. The formal viewpoint axioms for homology; 36. Categories and functors; 37. Additional topics homology and fundamental group; 38. Classical applications; 39. Simplicial approximation and the Lefschetz fixed point theorem; Part IV. Cohomology: 40. Cohomology groups: the universal coefficient theorem; 41. Cohomology of spaces; 42. Cup product the cohomology ring; 43. External cup product; 44. Poincaré duality orientations; 45. Cup product; 46. Cup product and duality; 47. Other forms of duality; 48. Additional topics the universal coefficient theorem for homology; 49. The Kunneth formula; 50. H-spaces and Hopf algebras; 51. The cohomology of SO(n); 52. Bockstein homomorphisms; 53. Limits; 54. More about ext; 55. Transfer homomorphisms; 56. Local coefficients; Part V. Homotopy Theory: 57. Homotopy groups; 58. The long exact sequence; 59. Whitehead’s theorem; 60. The Hurewicz theorem; 61. Eilenberg–MacLane spaces; 62. Homotopy properties of CW complexes cellular approximation; 63. Cellular models; 64. Excision for homotopy groups; 65. Stable homotopy groups; 66. Fibrations the homotopy lifting property; 67. Fiber bundles; 68. Path fibrations and loopspaces; 69. Postnikov towers; 70. Obstruction theory; 71. Additional topics: basepoints and homotopy; 72. The Hopf invariant; 73. Minimal cell structures; 74. Cohomology of fiber bundles; 75. Cohomology theories and omega-spectra; 76. Spectra and homology theories; 77. Eckmann-Hilton duality; 78. Stable splittings of spaces; 79. The loopspace of a suspension; 80. Symmetric products and the Dold–Thom theorem; 81. Steenrod squares and powers; Appendix: topology of cell complexes; The compact-open topology.

… an ideal choice for a graduate course on dynamical systems … warmly recommended …”

Acta Scientiarum Mathematicarum



15 DIFFERENTIAL AND INTEGRAL EQUATIONS, DYNAMICAL SYSTEMS AND CONTROLDifferential Equations and Linear AlgebraGilbert StrangMassachusetts Institute of Technology

An innovative textbook that allows differential equations to be taught alone, or in parallel with linear algebra, affording extra flexibility to instructors. It covers the fundamental undergraduate topics in differential equations and linear algebra, revealing connections between these two essential subjects, and applications to the physical sciences, engineering and economics.• An innovative new textbook that allows two crucial subjects to be

taught together or separately

• Solutions and videos are provided on an accompanying website

• Applications are drawn from the physical sciences, engineering and economics

ContentsPreface; 1. First order equations; 2. Second order equations; 3. Graphical and numerical methods; 4. Linear equations and inverse matrices; 5. Vector spaces and subspaces; 6. Eigenvalues and eigenvectors; 7. Applied mathematics and ATA; 8. Fourier and Laplace transforms; Matrix factorizations; Properties of determinants; Index; Linear algebra in a nutshell.

2015 231 x 184 mm 510pp

9780980232790 | £44.00 / US$73.50 HB

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This title is available from Cambridge to customers outside of North America; customers in North America should contact Wellesley-Cambridge Press e-sample is available for inspection


16DIFFERENTIAL AND INTEGRAL EQUATIONS, DYNAMICAL SYSTEMS AND CONTROL

ContentsPreface; 1. First order equations; 2. Second order equations; 3. Graphical and numerical methods; 4. Linear equations and inverse matrices; 5. Vector spaces and subspaces; 6. Eigenvalues and eigenvectors; 7. Applied mathematics and ATA; 8. Fourier and Laplace transforms; Matrix factorizations; Properties of determinants; Index; Linear algebra in a nutshell.

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DIFFERENTIAL AND INTEGRAL EQUATIONS, DYNAMICAL SYSTEMS AND CONTROL

Linear Partial Differential Equations and Fourier TheoryMarcus PivatoTrent University, Peterborough, Ontario

This highly visual introductory textbook presents an in-depth treatment suitable for undergraduates in mathematics and physics, gradually introducing abstraction while always keeping the link to physical motivation. Designed for lecturers as well as students, downloadable files for all figures, exercises, and practice problems are available online, as are solutions.• Online resources include full-colour and three-dimensional illustrations, practice problems

and complete solutions for instructors

• Includes a suggested twelve-week syllabus and lists recommended prerequisites for each section

• Contains nearly 400 challenging theoretical exercises

ContentsPreface; Notation; What’s good about this book?; Suggested twelve-week syllabus; Part I. Motivating Examples and Major Applications: 1. Heat and diffusion; 2. Waves and signals; 3. Quantum mechanics; Part II. General Theory: 4. Linear partial differential equations; 5. Classification of PDEs and problem types; Part III. Fourier Series on Bounded Domains: 6. Some functional analysis; 7. Fourier sine series and cosine series; 8. Real Fourier series and complex Fourier series; 9. Mulitdimensional Fourier series; 10. Proofs of the Fourier convergence theorems; Part IV. BVP Solutions Via Eigenfunction Expansions: 11. Boundary value problems on a line segment; 12. Boundary value problems on a square; 13. Boundary value problems on a cube; 14. Boundary value problems in polar coordinates; 15. Eigenfunction methods on arbitrary domains; Part V. Miscellaneous Solution Methods: 16. Separation of variables; 17. Impulse-response methods; 18. Applications of complex analysis; Part VI. Fourier Transforms on Unbounded Domains: 19. Fourier transforms; 20. Fourier transform solutions to PDEs; Appendices; References; Index.


9780521199704 | £89.99 / US$160.00 HB

9780521136594 | £39.99 / US$74.99 PB

I love this bare-handed approach to PDEs. Pivato has succeeded in creating a deeply engaging introductory PDE text; confidence building hands-on work and theory are woven together in a way that appeals to the intuition. Add to that the truly reasonable price, and you have the hands down winner in the field of introductory PDE books. The next time I teach introductory PDEs, I will use Pivato’s new text.”

Kevin R. Vixie, Washington State Universitye-sample is available for inspection


17 MATHEMATICAL MODELLING AND METHODS

Applied Complex Variables for Scientists and EngineersYue Kuen KwokHong Kong University of Science and Technology

An introduction to complex variable methods for scientists and engineers, with a high proportion of the book devoted to applications to physical problems. Now containing even more exercises with solutions, it is highly suitable for those wishing to learn the elements of complex analysis in an applied context.• Treats applications in detail and uses them to illustrate mathematical points and techniques

• Does not get bogged down in proofs

• This new edition includes many more stimulating exercises and examples

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Contents Preface; 1. Complex numbers; 2. Analytic functions; 3. Exponential, logarithmic and trigonometric functions; 4. Complex integration; 5. Taylor and Laurent series; 6. Singularities and calculus of residues; 7. Boundary value problems and initial-boundary value problems; 8. Conformal mappings and applications; Answers to problems; Index.


9780521701389 | £49.99 / US$84.99 PB

2ND EDITION

This text achieves a mixture of rigour and application that is not found in many books on complex variable theory. I think this is an advantage, allowing one to acquire the best of both mathematical precision alongside applications to physics and engineering … This must surely appeal to a wide range of learning styles and ensure a greater understanding for anyone who chooses to read this text.”

W. Joyce, Contemporary Physics



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MATHEMATICAL MODELLING AND METHODS

Introduction to Linear AlgebraGilbert StrangMassachusetts Institute of Technology

A leading textbook for first courses in linear algebra. Instead of teaching students by repetitive drill, Gilbert Strang encourages students to real mathematical thinking; an approach that has been successful over many years at MIT. The book is supported by online lectures and learning material via http://web.mit.edu/18.06/www/.• Strang’s online lectures and learning resources freely available via http://web.mit.edu/18.06/www/

• Gives MATLAB code to implement the key algorithms

• Teaches by inspiration not repetition

Contents1. Introduction to Vectors: 1.1 Vectors and linear combinations; 1.2 Lengths and dot products; 1.3 Matrices; 2. Solving Linear Equations: 2.1 Vectors and linear equations; 2.2 The idea of elimination; 2.3 Elimination using matrices; 2.4 Rules for matrix operations; 2.5 Inverse matrices; 2.6 Elimination = factorization: A = LU; 2.7 Transposes and permutations; 3. Vector Spaces and Subspaces: 3.1 Spaces of vectors; 3.2 The nullspace of A: solving Ax = 0; 3.3 The rank and the row reduced form; 3.4 The complete solution to Ax = b; 3.5 Independence, basis and dimension; 3.6 Dimensions of the four subspaces; 4. Orthogonality: 4.1 Orthogonality of the four subspaces; 4.2 Projections; 4.3 Least squares approximations; 4.4 Orthogonal bases and Gram-Schmidt; 5. Determinants: 5.1 The properties of determinants; 5.2 Permutations and cofactors; 5.3 Cramer’s rule, inverses, and volumes; 6. Eigenvalues and Eigenvectors: 6.1 Introduction to eigenvalues; 6.2 Diagonalizing a matrix; 6.3 Applications to differential equations; 6.4 Symmetric matrices; 6.5 Positive definite matrices; 6.6 Similar matrices; 6.7 Singular value decomposition (SVD); 7. Linear Transformations: 7.1 The idea of a linear transformation; 7.2 The matrix of a linear transformation; 7.3 Diagonalization and the pseudoinverse; 8. Applications: 8.1 Matrices in engineering; 8.2 Graphs and networks; 8.3 Markov matrices, population, and economics; 8.4 Linear programming; 8.5 Fourier series: linear algebra for functions; 8.6 Linear algebra for statistics and probability; 8.7 Computer graphics; 9. Numerical Linear Algebra: 9.1 Gaussian elimination in practice; 9.2 Norms and condition numbers; 9.3 Iterative methods for linear algebra; 10. Complex Vectors and Matrices: 10.1 Complex numbers; 10.2 Hermitian and unitary matrices; 10.3 The fast Fourier transform; Solutions to selected exercises; Matrix factorizations; Conceptual questions for review; Glossary: a dictionary for linear algebra; Index; Teaching codes.

2009 235 x 191 mm 585pp

9780980232714 | £64.99 / US$89.99 HB

This title is available from Cambridge to customers outside of North America; customers in North America should contact Wellesley-Cambridge Press

4TH EDITION



19 MATHEMATICAL MODELLING AND METHODS

Mathematics for Economics and FinanceMethods and Modelling

Martin AnthonyLondon School of Economics and Political Science

and Norman BiggsLondon School of Economics and Political Science

An introduction to mathematical modelling in economics and finance for students of both economics and mathematics. Throughout, the stress is firmly on how the mathematics relates to economics, illustrated with copious examples and exercises that will foster depth of understanding.• Authors have been teaching this at LSE for several years

• Very broad coverage of topics

• No mathematical fudging yet clear presentation

• Suitable for both maths and economics backgrounds

Contents1. Mathematical models in economics; 2. Mathematical terms and notations; 3. Sequences, recurrences and limits; 4. Elements of finance; 5. The cobweb model; 6. Introduction to calculus; 7. Some special functions; 8. Introduction to optimisation; 9. The derivative in economics I; 10. The derivative in economics II; 11. Partial derivatives; 12. Applications of partial derivatives; 13. Optimisation in two variables; 14. Vectors, preferences and convexity; 15. Matrix algebra; 16. Linear equations I; 17. Linear equations II; 18. Inverse matrices; 19. The input output model; 20. Determinants; 21. Constrained optimisation; 22. Lagrangians and the consumer; 23. Second-order recurrence equations; 24. Macroeconomic applications; 25. Areas and integrals; 26. Techniques of integration; 27. First-order differential equations; 28. Second-order differential equations; Selected solutions.

1996 228 x 152 mm 407pp

9780521559133 | £39.99 / US$74.99 PB

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Throughout, the stress is firmly on how the mathematics relates to economics, and this is illustrated with copious examples and exercises that will foster depth of understanding.”




20MATHEMATICAL FINANCE

Contents1. Probability; 2. Normal random variables; 3. Geometric Brownian motion; 4. Interest rates and present value analysis; 5. Pricing contracts via arbitrage; 6. The Arbitrage Theorem; 7. The Black–Scholes formula; 8. Additional results on options; 9. Valuing by expected utility; 10. Stochastic order relations; 11. Optimization models; 12. Stochastic dynamic programming; 13. Exotic options; 14. Beyond geometric motion models; 15. Autoregressive models and mean reversion.


9780521192538 | £39.99 / US$74.99 HB

… an excellent introduction to the subject … the book is ideally suited for self-study and provides a very accessible entry point to this fascinating field.”

ISI Short Book Reviews

3RD EDITION

An Elementary Introduction to Mathematical FinanceSheldon M. RossUniversity of Southern California

This textbook on the basics of option pricing is accessible to readers with limited mathematical training. It is for both professional traders and undergraduates studying the basics of finance. This third edition includes three new chapters, along with expanded sets of exercises and references for all the chapters.• This book combines accuracy and easy to understand mathematical arguments

• Assumes almost no technical knowledge, but presents all needed preliminary material

• The third edition is completely revised with two new chapters of material and additional exercises

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21 COMPUTATIONAL SCIENCE

A Guide to MATLAB®For Beginners and Experienced Users

Brian R. HuntUniversity of Maryland, College Park

Ronald L. LipsmanUniversity of Maryland, College Park

and Jonathan M. RosenbergUniversity of Maryland, College Park

Now in its third edition, this outstanding textbook explains everything you need to get started using MATLAB®. It contains concise explanations of essential MATLAB commands, as well as easily understood instructions for using MATLAB’s programming features, graphical capabilities, simulation models, and rich desktop interface.• Fully updated edition covering all of the new features of MATLAB 8

• Focuses first on the essentials, then develops finer points through numerous examples

• Suitable for novices, occasional users and experienced users wishing to update their skills

ContentsPreface; 1. Getting started; 2. MATLAB basics; 3. Interacting with MATLAB; Practice Set A. Algebra and arithmetic; 4. Beyond the basics; 5. MATLAB graphics; 6. MATLAB programming; 7. Publishing and M-books; Practice Set B. Math, graphics, and programming; 8. MuPAD; 9. Simulink; 10. GUIs; 11. Applications; Practice Set C. Developing your MATLAB skills; 12. Troubleshooting; Solutions to the practice sets; Glossary; Index.


9781107662223 | £39.99 / US$74.99 PB

Major highlights of the book are completely transparent examples of classical yet always intriguing mathematical, statistical, engineering, economics, and physics problems. In addition, the book explains a seamless use with Microsoft Word for integrating MATLAB® outputs with documents, reports, presentations, or other on-line processes. Advanced topics with examples include: Monte Carlo simulation, population dynamics, and linear programming. Overall, it is an outstanding textbook, and, likewise, should be an integral part of the technical reference shelf for most IT professionals. It is a great resource for wherever MATLAB® is available!”

ACM Ubiquity

3RD EDITION

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22OPTIMIZATION, OR AND RISK ANALYSIS

Chance, Strategy, and ChoiceAn Introduction to the Mathematics of Games and Elections

Samuel Bruce SmithSt Joseph’s University, Philadelphia

This classroom-tested undergraduate textbook is intended for a general education course in game theory at the freshman or sophomore level. While it starts off with the basics and introduces the reader to mathematical proofs, this text also presents several advanced topics, including accessible proofs of the Sprague–Grundy theorem and Arrow’s impossibility theorem.

Contents1. Introduction; 2. Games and elections; 3. Chance; 4. Strategy; 5. Choice; 6. Strategy and choice; 7. Choice and chance; 8. Chance and strategy; 9. Nash equilibria; 10. Proofs and counterexamples; 11. Laws of probability; 12. Fairness in elections; 13. Weighted voting; 14. Gambling games; 15. Zero-sum games; 16. Partial conflict games; 17. Take-away games; 18. Fairness and impossibility; 19. Paradoxes and puzzles in probability; 20. Combinatorial games; 21. Borda versus Condorcet; 22. The Sprague–Grundy theorem; 23. Arrow’s impossibility theorem.


9781107084520 | £29.99 / US$49.99 HB

Cambridge Mathematical Textbooks

Sam Smith’s book offers an intriguing juxtaposition of chance, strategy, and elections. The mathematical analysis is rigorous without being too formal or forbidding. The applications to topics in economics and political science – including auctions, power, and voting – as well as to parlor games like poker will engage both students and professionals.”

Steven Brams, New York University

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23 OPTIMIZATION, OR AND RISK ANALYSIS

A Gentle Introduction to OptimizationB. GueninUniversity of Waterloo, Ontario

J. KönemannUniversity of Waterloo, Ontario

and L. TunçelUniversity of Waterloo, Ontario

Assuming only basic linear algebra, this textbook is the perfect starting point for a wide range of undergraduate students from across the mathematical sciences (computer science, engineering, economics, and so on). The authors focus on the fundamental ideas in optimization and motivate the theory with real-world examples and exercises.• Course-tested material from authors with 40 years of teaching experience

• Self-contained chapters make it suitable for independent study

• Prepares the reader for more advanced courses in optimization

ContentsPreface; 1. Introduction; 2. Solving linear programs; 3. Duality through examples; 4. Duality theory; 5. Applications of duality; 6. Solving integer programs; 7. Nonlinear optimization; Appendix A. Computational complexity; References; Index.

2014 247 x 174 mm 282pp 55 b/w illus. 25 colour illus. 20 tables 140 exercises

9781107053441 | £59.99 / US$89.99 HB

9781107658790 | £28.99 / US$44.99 PB

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24SUPPLEMENTARY READING - ALSO AVAILABLE FOR INSPECTION

A Concise Text on Advanced Linear AlgebraYisong YangPolytechnic School of Engineering, New York University

This engaging, well-motivated textbook helps advanced undergraduate students to grasp core concepts and reveals applications in mathematics and beyond. Selected solutions are provided.

2014 228 x 152 mm 334pp 390 exercises

9781107087514 | £70.00 / US$115.00 HB

9781107456815 | £29.99 / US$55.00 PB

A Course in Mathematical AnalysisVolume 1: Foundations and Elementary Real Analysis

D. J. H. GarlingUniversity of Cambridge

The first volume of three providing a full and detailed account of undergraduate mathematical analysis.2013 247 x 174 mm 318pp 21 b/w illus. 340 exercises

9781107032026 | £79.99 / US$140.00 HB

9781107614185 | £29.99 / US$54.99 PB

A Course in Mathematical AnalysisVolume 3: Complex Analysis, Measure and Integration


The third volume of three providing a full and detailed account of undergraduate mathematical analysis.2014 247 x 174 mm 332pp 20 b/w illus. 270 exercises

9781107032040 | £79.99 / US$135.00 HB

9781107663305 | £34.99 / US$54.99 PB

A Course in Mathematical AnalysisVolume 2: Metric and Topological Spaces, Functions of a Vector Variable


The second volume of three providing a full and detailed account of undergraduate mathematical analysis.2014 247 x 174 mm 336pp 15 b/w illus. 280 exercises

9781107032033 | £79.99 / US$135.00 HB

9781107675322 | £34.99 / US$54.99 PB

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25 SUPPLEMENTARY READING - ALSO AVAILABLE FOR INSPECTION

Understanding Probability3rd Edition

Henk TijmsVrije Universiteit, Amsterdam

The third edition of Understanding Probability is a unique and stimulating approach to a first course in probability and includes new sections on Bayesian inference, Markov chain Monte-Carlo simulation, and more. 2012 229 x 152 x 30 mm 574pp 60 b/w illus. 520 exercises

9781107658561 | £29.99 / US$59.99 PB

Vectors, Pure and Applied A General Introduction to Linear Algebra

T. W. KörnerUniversity of Cambridge

This text explains both the how and the why of linear algebra and enables students to begin thinking like mathematicians. Selected solutions are available.2012 255 x 173 x 24 mm 452pp 3 b/w illus. 730 exercises

9781107033566 | £79.99 / US$125.00 HB

9781107675223 | £34.99 / US$59.99 PB

A Comprehensive Course in Number TheoryAlan BakerUniversity of Cambridge

Developed from the author’s popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. 2012 228 x 152 x 15 mm 264pp 7 b/w illus. 195 exercises

9781107019010 | £69.99 / US$99.99 HB

9781107019010 | £26.99 / US$39.99 PB

Essentials of Programming in Mathematica®Paul Wellin

Suitable for readers with little or no background in the language as well as for those with some experience using programs such as C or Java, this example-driven text covers the language from first principles, as well as including material from natural language processing, bioinformatics, and many other applied areas. Supplementary resources are available.2016 253 x 197 x 23 mm 436pp 45 b/w illus. 190 colour illus. 350 exercises

9781107116665 | £39.99 / US$59.99 HB

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SUPPLEMENTARY READING - ALSO AVAILABLE FOR INSPECTION

2009 254 x 195 x 19 mm 274pp

ISBN: 9780521719780

£22.99 I $39.99 PB

How to Think Like a Mathematician A Companion to Undergraduate Mathematics

KE VIN HOUSTONAffiliation: University of Leeds

Looking for a head start in your undergraduate degree in mathematics? Maybe you’ve already started your degree and feel bewildered by the subject you previously loved? Don’t panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively.

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