Includes bibliographical references and index.

Machine generated contents note: Preface xi1 Basic Counting Methods 11.1 The multiplication principle 11.2 Permutations 41.3 Combinations 61.4 Binomial coefficient identities 101.5 Distributions 191.6 The principle of inclusion and exclusion 231.7 Fibonacci numbers 311.8 Linear recurrence relations 331.9 Special recurrence relations 411.10 Counting and number theory 45Notes 502 Generating Functions 532.1 Rational generating functions 532.2 Special generating functions 632.3 Partition numbers 762.4 Labeled and unlabeled sets 802.5 Counting with symmetry 862.6 Cycle indexes 932.7 Polya's theorem 962.8 The number of graphs 982.9 Symmetries in domain and range 1022.10 Asymmetric graphs 103Notes 1053 The Pigeonhole Principle 1073.1 Simple examples 1073.2 Lattice points, the Gitterpunktproblem, and SET(r) 1103.3 Graphs 1153.4 Colorings of the plane 1183.5 Sequences and partial orders 1193.6 Subsets 124Notes 1264 Ramsey Theory 1314.1 Ramsey's theorem 1314.2 Generalizations of Ramsey's theorem 1354.3 Ramsey numbers, bounds, and asymptotics 1394.4 The probabilistic method 1434.5 Sums 1454.6 Van der Waerden's theorem 146Notes 1505 Codes 1535.1 Binary codes 1535.2 Perfect codes 1565.3 Hamming codes 1585.4 The Fano Configuration 162Notes 1686 Designs 1716.1 t-designs 171CONTENTS ix6.2 Block designs 1756.3 Projective planes 1806.4 Latin squares 1826.5 MOLS and OODs 1856.6 Hadamard matrices 1886.7 The Golay code and S(5, 8, 24) 1946.8 Lattices and sphere packings 1976.9 Leech's lattice 199Notes 201A Web Resources 205B Notation 207Exercise Solutions 211References 225Index 227.

Machine generated contents note: Part I. Principles and Techniques: 1. General principles and characteristics of optical magnetometers D. F. Jackson Kimball, E. B. Alexandrov and D. Budker; 2. Quantum noise in atomic magnetometers M. V. Romalis; 3. Quantum noise, squeezing, and entanglement in radio-frequency optical magnetometers K. Jensen and E. S. Polzik; 4. Mx and Mz magnetometers E. B. Alexandrov and A. K. Vershovskiy; 5. Spin-exchange-relaxation-free (serf) magnetometers I. Savukov and S. J. Seltzer; 6. Optical magnetometry with modulated light D. F. Jackson Kimball, S. Pustelny, V. V. Yashchuk and D. Budker; 7. Microfabricated atomic magnetometers S. Knappe and J. Kitching; 8. Optical magnetometry with nitrogen-vacancy centers in diamond V. M. Acosta, D. Budker, P. R. Hemmer, J. R. Maze and R. L. Walsworth; 9. Magnetometry with cold atoms W. Gawlik and J. M. Higbie; 10. Helium magnetometers R. E. Slocum, D. D. McGregor and A. W. Brown; 11. Surface coatings for atomic magnetometry S. J. Seltzer, M.-A. Bouchiat and M. V. Balabas; 12. Magnetic shielding V. V. Yashchuk, S.-K. Lee and E. Paperno; Part II. Applications: 13. Remote detection magnetometry S. M. Rochester, J. M. Higbie, B. Patton, D. Budker, R. Holzlöhner and D. Bonaccini Calia; 14. Detection of nuclear magnetic resonance with atomic magnetometers M. P. Ledbetter, I. Savukov, S. J. Seltzer and D. Budker; 15. Space magnetometry B. Patton, A. W. Brown, R. E. Slocum and E. J. Smith; 16. Detection of biomagnetic fields A. Ben-Amar Baranga, T. G. Walker and R. T. Wakai; 17. Geophysical applications M. D. Prouty, R. Johnson, I. Hrvoic and A. K. Vershovskiy; Part III. Broader Impact: 18. Tests of fundamental physics with optical magnetometers D. F. Jackson Kimball, S. K. Lamoreaux and T. E. Chupp; 19. Nuclear magnetic resonance gyroscopes E. A. Donley and J. Kitching; 20. Commercial magnetometers and their application D. C. Hovde, M. D. Prouty, I. Hrvoic and R. E. Slocum; Index.

"Featuring chapters written by leading experts in magnetometry, this book provides comprehensive coverage of the principles, technology and diverse applications of optical magnetometry, from testing fundamental laws of nature to detecting biomagnetic fields and medical diagnostics. Readers will find a wealth of technical information, from antirelaxation-coating techniques, microfabrication and magnetic shielding to geomagnetic-field measurements, space magnetometry, detection of biomagnetic fields, detection of NMR and MRI signals and rotation sensing. The book includes an original survey of the history of optical magnetometry and a chapter on the commercial use of these technologies. The book is supported by extensive online material, containing historical overviews, derivations, sideline discussion, additional plots and tables, available at www.cambridge.org/9781107010352. As well as introducing graduate students to this field, the book is also a useful reference for researchers in atomic physics"-- Provided by publisher.