Hardback (ISBN-13: 9780521881715)
Information theory lies at the heart of modern technology, underpinning all communications, networking, and data storage systems. This book sets out, for the first time, a complete overview of both classical and quantum information theory. Throughout, the reader is introduced to key results without becoming lost in mathematical details. Opening chapters present the basic concepts and various applications of Shannon’s entropy, moving on to the core features of quantum information and quantum computing. Topics such as coding, compression, error-correction, cryptography and channel capacity are covered from classical and quantum viewpoints. Employing an informal yet scientifically accurate approach, Desurvire provides the reader with the knowledge to understand quantum gates and circuits. Highly illustrated, with numerous practical examples and end-of-chapter exercises, this text is ideal for graduate students and researchers in electrical engineering and computer science, and practitioners in the telecommunications industry. Further resources and instructor-only solutions are available at www.cambridge.org/9780521881715.
* A first-time complete overview of both classical and quantum information theory * Employs an informal yet scientifically accurate approach * Highly illustrated with numerous practical examples and end-of-chapter exercises
1. Probabilities basics; 2. Probability distributions; 3. Measuring information; 4. Entropy; 5. Mutual information and more entropies; 6. Differential entropy; 7. Algorithmic entropy and Kolmogorov complexity; 8. Information coding; 9. Optimal coding and compression; 10. Integer, arithmetic and adaptive coding; 11. Error correction; 12. Channel entropy; 13. Channel capacity and coding theorem; 14. Gaussian channel and Shannon-Hartley theorem; 15. Reversible computation; 16. Quantum bits and quantum gates; 17. Quantum measurments; 18. Qubit measurements, superdense coding and quantum teleportation; 19. Deutsch/Jozsa alorithms and quantum fourier transform; 20. Shor’s factorization algorithm; 21. Quantum information theory; 22. Quantum compression; 23. Quantum channel noise and channel capacity; 24. Quantum error correction; 25. Classical and quantum cryptography; Appendix A. Boltzmann’s entropy; Appendix B. Shannon’s entropy; Appendix C. Maximum entropy of discrete sources; Appendix D. Markov chains and the second law of thermodynamics; Appendix E. From discrete to continuous entropy; Appendix F. Kraft-McMillan inequality; Appendix G. Overview of data compression standards; Appendix H. Arithmetic coding algorithm; Appendix I. Lempel-Ziv distinct parsing; Appendix J. Error-correction capability of linear block codes; Appendix K. Capacity of binary communication channels; Appendix L. Converse proof of the Channel Coding Theorem; Appendix M. Block sphere representation of the qubit; Appendix N. Pauli matrices, rotations and unitary operators; Appendix O. Heisenberg Uncertainty Principle; Appendix P. Two qubit teleportation; Appendix Q. Quantum Fourier transform circuit; Appendix R. Properties of continued fraction expansion; Appendix S. Computation of inverse Fourier transform in the factoring of N=21 through Shor’s algorithm; Appendix T. Modular arithmetic and Euler’s Theorem; Appendix U. Klein’s inequality; Appendix V. Schmidt decomposition of joint pure states; Appendix W. State purification; Appendix X. Holevo bound; Appendix Y. Polynomial byte representation and modular multiplication.
ISBN: 978-0-470-45798-6
Paperback
284 pages
July 2009
The previous editions have proven to be successful guides for choosing and using the right techniques. Common Errors is consistently coherent and provides a consistent level throughout. The Third Edition elaborates on many key topics such as response variables, errors in testing hypothesis, higher order experimental design, curve fitting and magic beans, Poisson and negative binomial regression, correcting for confounding variables, dynamic models, factor analysis, general linear models, decision trees, etc. One new chapter has been added on "Statistical Analysis" and includes sections on data quality assessment, data review, and design review. Modifications have been included throughout the book, and many new figures have also been added. Topics covered include creating a research plan, collecting data, formulating and testing a hypothesis, estimating coefficients, specifying sample size, checking assumptions, interpreting p-values and confidence intervals, building a model, reporting results, data mining, Bayes' Theorem, the bootstrap, and many others.
Preface.
PART I: FOUNDATIONS.
1. Sources of Error.
2. Hypotheses: The Why of Your Research.
3. Collecting Data.
PART II: STATISTICAL ANALYSIS.
4. Data Quality Assessment.
5. Estimation.
6. Testing Hypotheses: Choosing a Test Statistic.
7. Miscellaneous Statistical Procedures.
PART III: REPORTS.
8. Reporting Results.
9. Interpreting Reports.
10. Graphics.
PART IV: BUILDING A MODEL.
11. Univariate Regression.
12. Alternate Modeling Methods.
13. Multivariate Regression.
14. Modeling Correlated Data.
15. Validation.
Advanced studies in pure mathematics, Volume 52
I. Expository Articles
S´ergio R. Fenley*Asymptotic geometry of foliations and pseudo-Anosov
flows * a survey 1
Kiyoshi Igusa * Pontrjagin classes and higher torsion of sphere bundles
21
Teruaki Kitano and Takayuki Morifuji * L2-torsion invariants and the Magnus
representation of the mapping class group 31
H*ong-V*an L*e and Kaoru Ono * Parameterized Gromov-Witten invariants and
topology of symplectomorphism groups 51
Robert C. Penner * Mapping class actions on surface group completions 77
Takuya Sakasai * Johnson’s homomorphisms and the rational cohomology of
subgroups of the mapping class group 93
II. Research Articles
Toshiyuki Akita*Onmod p Riemann-Roch formulae for mapping class groups
111
Joan S. Birman, Tara E. Brendle and Nathan Broaddus*Calculating the image
of the second Johnson-Morita representation 119
Joan S. Birman, Dennis Johnson and Andrew Putman * Symplectic Heegaard
splittings and linked abelian groups 135
Dmitri Burago, Sergei Ivanov and Leonid Polterovich*Conjugation- invariant
norms on groups of geometric origin 221
Hisaaki Endo * A generalization of Chakiris’ fibrations 251
Koji Fujiwara * Subgroups generated by two pseudo-Anosov elements in a
mapping class group. I. Uniform exponential growth 283
Kiyonori Gomi * Differential characters and the Steenrod squares 297
Richard Hain * Relative weight filtrations on completions of mapping class
groups 309
Yasushi Kasahara * Remarks on the faithfulness of the Jones representations
369
Nariya Kawazumi*On the stable cohomology algebra of extended mapping class
groups for surfaces 383
Dieter Kotschick * Stable length in stable groups 401
Yoshihiko Mitsumatsu and Elmar Vogt * Foliations and compact leaves on
4-manifolds I. Realization and self-intersection
of compact leaves 415
Shigeyuki Morita*Symplectic automorphism groups of nilpotent quotients
of fundamental groups of surfaces 443
Graeme Segal and Ulrike Tillmann * Mapping configuration spaces to moduli
spaces 469
Masaaki Suzuki * New examples of elements in the kernel of the Magnus representation
of the Torelli group 479
Takashi Tsuboi * On the simplicity of the group of contactomorphisms 491
Takashi Tsuboi * On the uniform perfectness of diffeomorphism groups 505
Series: Universitext
2009, XIV, 212 p., Softcover
ISBN: 978-0-387-87574-3
Key topics and features of this second edition:
- Approaches Galois theory from the linear algebra point of view, following Artin;
- Presents a number of applications of Galois theory, including symmetric functions, finite fields, cyclotomic fields, algebraic number fields, solvability of equations by radicals, and the impossibility of solution of the three geometric problems of Greek antiquity.
Review from the first edition:
"The text offers the standard material of classical field theory and Galois theory, though in a remarkably original, unconventional and comprehensive manner … . the book under review must be seen as a highly welcome and valuable complement to existing textbook literature … . It comes with its own features and advantages … it surely is a perfect introduction to this evergreen subject. The numerous explaining remarks, hints, examples and applications are particularly commendable … just as the outstanding clarity and fullness of the text." (Zentralblatt MATH, Vol. 1089 (15), 2006)
Steven H. Weintraub is a Professor of Mathematics at Lehigh University and the author of seven books. This book grew out of a graduate course he taught at Lehigh. He is also the author of Algebra: An Approach via Module Theory (with W. A. Adkins).
Introduction to Galois Theory.- Field Theory and Galois Theory.- Development and Applications of Galois Theory.- Extensions of the Field of Rational Numbers.- Further Topics in Field Theory.- Transcendental Extensions.- A. Some Results from Group Theory.- B. A Lemma on Constructing Fields.- C. A Lemma from Elementary Number Theory.- References.- Index.