Bela Bollobas
Trinity College, Cambridge

The Art of Mathematics
Coffee Time in Memphis

Hardback (ISBN-13: 9780521872287 | ISBN-10: 0521872286)
Paperback (ISBN-13: 9780521693950 | ISBN-10: 0521693950)

available from August 2006

Can a Christian escape from a lion? How quickly can a rumour spread? Can you fool an airline into accepting oversize baggage? Recreational mathematics is full of frivolous questions where the mathematician's art can be brought to bear. But play often has a purpose, In mathematics, it can sharpen skills, provide amusement, or simply surprise, and books of problems have been the stock-in-trade of mathematicians for centuries. This collection is designed to be sipped from, rather than consumed in one sitting. The questions range in difficulty: the most challenging offer a glimpse of deep results that engage mathematicians today; even the easiest are prompt readers to think about mathematics. All come with solutions, many with hints, and most with illustrations. Whether you are an expert, or a beginner or an amateur mathematician, this book will delight for a lifetime.

* Aimed at a broad audience ranging from professional mathematicians to interested amateur * Entertaining mix of problems ranging from the frivolous to others that show how mathematicians discover new ideas * Inspired by two of the twentieth century's leading mathematicians, Paul Erdos and J. E. Littlewood, who were both inveterate problem posers and solvers

Contents

Preface: Part I. The Problems: Part II. The Hints; Part III. The Solutions.

Katrin Becker / University of Utah
Melanie Becker / University of Maryland, College Park
John Schwarz / California Institute of Technology

String Theory and M-Theory
A Modern Introduction

Hardback (ISBN-13: 9780521860697 | ISBN-10: 0521860695)
available from November 2006

String theory is one of the most exciting and challenging areas of modern theoretical physics. This book guides the reader from the basics of string theory to recent developments. It introduces the basics of perturbative string theory, world-sheet supersymmetry, space-time supersymmetry, conformal field theory and the heterotic string, before describing modern developments, including D-branes, string dualities and M-theory. It then covers string geometry and flux compactifications, applications to cosmology and particle physics, black holes in string theory and M-theory, and the microscopic origin of black-hole entropy. It concludes with Matrix theory, the AdS/CFT duality and its generalizations. This book is ideal for graduate students and researchers in modern string theory, and will make an excellent textbook for a one-year course on string theory. It contains over 120 exercises with solutions, and over 200 homework problems with solutions available on a password protected website for lecturers at www.cambridge.org/9780521860697.

* Comprehensive coverage of topics from basics of string theory to recent developments * Ideal textbook for a one-year course in string theory * Includes over 100 exercises with solutions * Contains over 200 homework problems with solutions available to lecturers on-line

Contents
1. Introduction; 2. The bosonic string; 3. Conformal field theory and string interactions; 4. Strings with world-sheet supersymmetry; 5. Strings with space-time supersymmetry; 6. T-duality and D-branes; 7. The heterotic string; 8. M-theory and string duality; 9. String geometry; 10. Flux compactifications; 11. Black holes in string theory; 12. Gauge theory/string theory dualities; References; Index.

Cliff Burgess / McGill University, Montreal
Guy More / McGill University, Montreal

The Standard Model
A Primer

Hardback (ISBN-13: 9780521860369 | ISBN-10: 0521860369)
available from November 2006

The standard model brings together two theories of particle physics in order to describe the interactions of subatomic particles, except those due to gravity. This book uses the standard model as a vehicle for introducing quantum field theory. In doing this the book also introduces much of the phenomenology on which this model is based. The book uses a modern approach, emphasizing effective field theory techniques, and contains brief discussions of some of the main proposals for going beyond the standard model, such as seesaw neutrino masses, supersymmetry, and grand unification. Requiring only a minimum of background material, this book is ideal for graduate students in theoretical and experimental particle physics. It concentrates on getting students to the level of being able to use this theory by doing real calculations with the minimum of formal development, and contains several problems. Password protected solutions are available to lecturers at www.cambridge.org/9780521860369.

* Introduces students to phenomena of current interest and practices computational techniques * Contains a modern and up-to-date discussion of neutrino masses and oscillations * Has an extensive discussion of the main proposals for physics beyond the Standard Model

Contents

Part I. Theoretical Framework: 1. Field theory review; 2. The standard model: general features; 3. Cross sections and lifetimes; Part II. Applications: Leptons: 4. Elementary boson decays; 5. Leptonic weak interactions: decays; 6. Leptonic weak interactions: collisions; 7. Effective Lagrangians; Part III. Applications: Hadrons: 8. Hadrons and QCD; 9. Hadronic interactions; Part IV. Beyond the Standard Model: 10. Neutrino masses; 11. Open questions, proposed solutions; Appendix A. Experimental values for the parameters; Appendix B. Symmetries and group theory review; Appendix C. Lorentz group and the Dirac algebra; Appendix D. E-gauge Feynman rules; Appendix E. Metric convention conversion table; Appendix F. Bibliography; Index.

Jacob Kogan
University of Maryland, Baltimore

Clustering Large and High Dimensional Data

Hardback (ISBN-13: 9780521852678 | ISBN-10: 0521852676)
Paperback (ISBN-13: 9780521617932 | ISBN-10: 0521617936)
available from January 2007

There is a growing need for a more automated system of partitioning data sets into groups, or clusters. For example, digital libraries and the World Wide Web continue to grow exponentially, the ability to find useful information increasingly depends on the indexing infrastructure or search engine. Clustering techniques can be used to discover natural groups in data sets and to identify abstract structures that might reside there, without having any background knowledge of the characteristics of the data. Clustering has been used in a variety of areas, including computer vision, VLSI design, data mining, bio-informatics (gene expression analysis), and information retrieval, to name just a few. This book focuses on a few of the most important clustering algorithms, providing a detailed account of these major models in an information retrieval context. The beginning chapters introduce the classic algorithms in detail, while the later chapters describe clustering through divergences and show recent research for more advanced audiences.

* Rather than providing comprehensive coverage of the area, the book focuses on a few important clustering algorithms * A detailed and elementary description of the algorithms is provided in the beginning chapters, to be easily absorbed by undergraduates * Recent research results involving sophisticated mathematics are of interest for graduate students and research experts

Contents

1. Introduction and motivation; 2. Quadratic k-means algorithm; 3. BIRCH; 4. Spherical k-means algorithm; 5. Linear algebra techniques; 6. Information-theoretic clustering; 7. Clustering with optimization techniques; 8. k-means clustering with divergence; 9. Assessment of clustering results; 10. Appendix: Optimization and Linear Algebra Background; 11. Solutions to selected problems.

Mark Srednicki
University of California, Santa Barbara

Quantum Field Theory

Hardback (ISBN-13: 9780521864497 | ISBN-10: 0521864496)
available from January 2007

Quantum theory is used to describe the physics of elementary particles, and has applications in many areas of particle and condensed matter physics. This textbook is a complete and essential introduction to the theory of elementary particles. It is written in a modular format, and each chapter is self-contained. The prerequisite material needed for each chapter is listed, giving the book great flexibility. It covers all the key theories necessary to understand the standard model and contains treatments of modern topics, including the renormalization group, spinor-helicity, methods for quark and gluon scattering, magnetic monopoles, instantons, supersymmetry, and unification forces. Assuming an undergraduate knowledge of quantum mechanics and special relativity, this book is ideal for graduate students studying quantum field theory and elementary particle theory. It is based on a year long course given by the author and contains extensive problems, with password protected solutions available to lecturers at www.cambridge.org/9780521864497.

* A complete treatment of elementary particle theory from basics to advanced topics * Contains 250 excercises with solutions available to lecturers at www.cambridge.org/9780521864497 * Presented in a logical sequence ? Written in a flexible, modular format with fully self-contained chapters

Contents

Preface for students; Preface for instructors; Acknowledgements; Part I. Spin Zero: 1. Attempts at relativistic quantum mechanics; 2. Lorentz invariance; 3. Canonical quantization of scalar fields; 4. The spin-statistics theorem; 5. The LSZ reduction formula; 6. Path integrals in quantum mechanics; 7. The path integral for the harmonic oscillator; 8. The path integral for free field theory; 9. The path integral for interacting field theory; 10. Scattering amplitudes and the Feynman rules; 11. Cross sections and decay rates; 12. Dimensional analysis with ?=c=1; 13. The Lehmann-Kallen form; 14. Loop corrections to the propagator; 15. The one-loop correction in Lehmann-Kallen form; 16. Loop corrections to the vertex; 17. Other 1PI vertices; 18. Higher-order corrections and renormalizability; 19. Perturbation theory to all orders; 20. Two-particle elastic scattering at one loop; 21. The quantum action; 22. Continuous symmetries and conserved currents; 23. Discrete symmetries: P, T, C, and Z; 24. Nonabelian symmetries; 25. Unstable particles and resonances; 26. Infrared divergences; 27. Other renormalization schemes; 28. The renormalization group; 29. Effective field theory; 30. Spontaneous symmetry breaking; 31. Broken symmetry and loop corrections; 32. Spontaneous breaking of continuous symmetries; Part II. Spin One Half: 33. Representations of the Lorentz Group; 34. Left- and right-handed spinor fields; 35. Manipulating spinor indices; 36. Lagrangians for spinor fields; 37. Canonical quantization of spinor fields I; 38. Spinor technology; 39. Canonical quantization of spinor fields II; 40. Parity, time reversal, and charge conjugation; 41. LSZ reduction for spin-one-half particles; 42. The free fermion propagator; 43. The path integral for fermion fields; 44. Formal development of fermionic path integrals; 45. The Feynman rules for Dirac fields; 46. Spin sums; 47. Gamma matrix technology; 48. Spin-averaged cross sections; 49. The Feynman rules for majorana fields; 50. Massless particles and spinor helicity; 51. Loop corrections in Yukawa theory; 52. Beta functions in Yukawa theory; 53. Functional determinants; Part III. Spin One: 54. Maxwell?s equations; 55. Electrodynamics in coulomb gauge; 56. LSZ reduction for photons; 57. The path integral for photons; 58. Spinor electrodynamics; 59. Scattering in spinor electrodynamics; 60. Spinor helicity for spinor electrodynamics; 61. Scalar electrodynamics; 62. Loop corrections in spinor electrodynamics; 63. The vertex function in spinor electrodynamics; 64. The magnetic moment of the electron; 65. Loop corrections in scalar electrodynamics; 66. Beta functions in quantum electrodynamics; 67. Ward identities in quantum electrodynamics I; 68. Ward identities in quantum electrodynamics II; 69. Nonabelian gauge theory; 70. Group representations; 71. The path integral for nonabelian gauge theory; 72. The Feynman rules for nonabelian gauge theory; 73. The beta function for nonabelian gauge theory; 74. BRST symmetry; 75. Chiral gauge theories and anomalies; 76. Anomalies in global symmetries; 77. Anomalies and the path integral for fermions; 78. Background field gauge; 79. Gervais-Neveu gauge; 80. The Feynman rules for N x N matrix fields; 81. Scattering in quantum chromodynamics; 82. Wilson loops, lattice theory, and confinement; 83. Chiral symmetry breaking; 84. Spontaneous breaking of gauge symmetries; 85. Spontaneously broken abelian gauge theory; 86. Spontaneously broken nonabelian gauge theory; 87. The standard model: Gauge and Higgs sector; 88. The standard model: Lepton sector; 89. The standard model: Quark sector; 90. Electroweak interactions of hadrons; 91. Neutrino masses; 92. Solitons and monopoles; 93. Instantons and theta vacua; 94. Quarks and theta vacua; 95. Supersymmetry; 96. The minimal supersymmetric standard model; 97. Grand unification; Bibliography.