Series: Graduate Texts in Mathematics , Vol. 24
2007, IX, 511 p. 11 illus., Hardcover
ISBN: 978-0-387-69903-
About this textbook
Provides an entry for graduate students into an active field of research
Each chapter includes exercises, examples, and figures
Will become a standard reference for researchers in the field
Contains descriptions of many known results and conjectures, together with an extensive bibliography
This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function.
A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs. As is typical in any subject combining Diophantine problems and geometry, a fundamental goal is to describe arithmetic properties, at least qualitatively, in terms of underlying geometric structures.
Key features:
- Provides an entry for graduate students into an active field of research
- Provides a standard reference source for researchers
- Includes numerous exercises and examples
- Contains a description of many known results and conjectures, as well as an extensive glossary, bibliography, and index
This graduate-level text assumes familiarity with basic algebraic number theory. Other topics, such as basic algebraic geometry, elliptic curves, nonarchimedean analysis, and the theory of Diophantine approximation, are introduced and referenced as needed. Mathematicians and graduate students will find this text to be an excellent reference.
Table of contents
Preface.- An Introduction to Classical Dynamics.- Dynamics over Local Fields: Good Reduction.- Dynamics over Global Fields.- Dynamics and Moduli.- Dynamics over Local Fields: Bad Reduction.- Dynamics with an Underlying Group.- Dynamics in Dimension Greater than One.
Series: Springer Texts in Statistics
1st ed. 2007. Corr. 2nd printing, 2008, XIII, 255 p., Hardcover
ISBN: 978-0-387-38979-0
About this textbook
This Bayesian modeling book is intended for practitioners and applied statisticians looking for a self-contained entry to computational Bayesian statistics. Focusing on standard statistical models and backed up by discussed real datasets available from the book website, it provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book.
Table of contents
Series: Geometry and Computing , Vol. 1
2008, XVI, 728 p. 204 illus. With Figure on back-endpaper (virtual) on p. 729.., Hardcover
ISBN: 978-3-540-73397-3
About this textbook
A comprehensive and self-contained treatment
Special features include an emphasis on the interplay of ideas from algebra and geometry and their historical origins
By virtue of their special algebraic structures, Pythagorean-hodograph (PH) curves offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and self-contained treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications. Special features include an emphasis on the interplay of ideas from algebra and geometry and their historical origins, detailed algorithm descriptions, and many figures and worked examples. The book will appeal, in whole or in part, to mathematicians, computer scientists, and engineers.
Table of contents
1 CD-ROM, 1 Hardback (ISBN-13: 9780521884075
This book/CD bundle of the greatly expanded third edition of Numerical Recipes now has wider coverage than ever before, many new, expanded and updated sections, and two completely new chapters. Co-authored by four leading scientists from academia and industry, Numerical Recipes starts with basic mathematics and computer science and proceeds to complete, working routines. The informal, easy-to-read style that made earlier editions so popular is kept throughout. Highlights of the new material include: a new chapter on classification and inference, Gaussian mixture models, HMMs, hierarchical clustering, and SVMs; a new chapter on computational geometry, covering KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres; interior point methods for linear programming; MCMC; an expanded treatment of ODEs with completely new routines; and many new statistical distributions. For support or further licence information please visit www.nr.com.
* Most comprehensive book available on scientific computing, now updated
* Now covers classification and inference HMMs, SVMs, computational geometry,
ODEs, MCMC and more * Over 600,000 Numerical Recipes products in print
Contents
1. Preliminaries; 2. Solution of linear algebraic equations; 3. Interpolation and extrapolation; 4. Integration of functions; 5. Evaluation of functions; 6. Special functions; 7. Random numbers; 8. Sorting and selection; 9. Root finding and nonlinear sets of equations; 10. Minimization or maximization of functions; 11. Eigensystems; 12. Fast Fourier transform; 13. Fourier and spectral applications; 14. Statistical description of data; 15. Modeling of data; 16. Classification and inference; 17. Integration of ordinary differential equations; 18. Two point boundary value problems; 19. Integral equations and inverse theory; 20. Partial differential equations; 21. Computational geometry; 22. Less-numerical algorithms; References.