Series: Mathematical Sciences Research Institute Publications
Hardback (ISBN-13: 9780521861342)
Paperback (ISBN-13: 9780521678544)
This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, on impartial games such as Chomp and Wythoff’s Nim, and on aspects of games with infinitesimal values, plus analyses of the complexity of some games and puzzles and surveys on algorithmic game theory, on playing to lose, and on coping with cycles. The volume is rounded out with an up-to-date bibliography by Fraenkel and, for readers eager to get their hands dirty, a list of unsolved problems by Guy and Nowakowski. Highlights include some of Siegel’s groundbreaking work on loopy games, the unveiling by Friedman and Landsberg of the use of renormalization to give very intriguing results about Chomp, and Nakamura’s “Counting Liberties in Capturing Races of Go.” Like its predecessors, this book should be on the shelf of all serious games enthusiasts.
* Offers an up to date bibliography by Aviezri Fraenkel * Includes a list
of unsolved problems by Guy and Nowakowski * Updates on standard games
such as Go and Hex, on impartial games such as Chomp and Wythoff’s Nim,
and on aspects of games with infinitesmal values
Part I. Surveys: 1. Playing games with algorithms: algorithmic combinatorial game theory Erik D. Demaine and Robert A. Hearn; 2. Advances in losing Thane E. Plambeck; 3. Coping with cycles Aaron N. Siegel; 4. On day N David Wolfe; Part II. Standards: 5. Goal threats, temperature and Monte-Carlo Go Tristan Cazenave; 6. A puzzling hex primer Ryan B. Hayward; 7. Tigers and goats is a draw Lim Yew Jin and Jurg Nievergelt; 8. Counting liberties in Go capturing races Teigo Nakamura; 9. Backsliding toads and frogs Aaron N. Siegel; 10. Loopy games Aaron N. Siegel; 11. A library of eyes in Go, I: a life-and-death definition consistent with bent-4 Thomas Wolf; 12. A library of eyes in Go, II: monolithic eyes Thomas Wolf and Matthew Pratola; Part III. Complexity: 13. The complexity of Dyson telescopes Erik D. Demaine, Martin L. Demaine, Rudolf Fleischer, Robert A. Hearn, and Timo von Oertzen; 14. Amazons, konane, and cross purposes are PSPACE-complete Robert A. Hearn; Part IV. Impartial: 15. Monotonic sequence games M. H. Albert, R. E. L. Aldred, M. D. Atkinson, C. C. Handley, D. A. Holton, D. J. Mccaughan, and B. E. Sagan; 16. The game of end-wythoff Aviezri S. Fraenkel and Elnatan Reisner; 17. On the geometry of combinatorial games: a renormalization approach Eric J. Friedman and Adam S. Landsberg; 18. More on the sprague*grundy function for wythoff's game Gabriel Nivasch; Part V. Theory of the Small: 19. Yellow-brown hackenbush Elwyn Berlekamp; 20. Ordinal partizan end nim Adam Duffy, Garrett Kolpin, and David Wolfe; 21. Reductions of partizan games J. P. Grossman and Aaron N. Siegel; 22. Partizan Splittles G. A. Mesdal III; Part VI. Columns: 23. Unsolved problems in combinatorial games Richard K. Guy and Richard J. Nowakowski; 24. Bibliography of combinatorial games Aviezri S. Fraenkel.
Series: Acta Numerica (No. 18)
Hardback (ISBN-13: 9780521192118)
Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide ‘state of the art’ techniques and analysis.
* High impact survey volume * Contributors are leading researchers * Covers
topics of current interest and presents state-of-the-art overviews of them
1. Recent trends in the numerical solution of retarded functional differential equations A. Bellen, N. Guglielmi, S. Maset and M. Zennaro; 2. Adaptivity with moving grids Chris J. Budd, Weizhang Huang and Robert D. Russell; 3. Fast direct solvers for integral equations in complex three-dimensional domains L. Greengard, D. Gueyffier, P.-G. Martinsson and V. Rokhlin; 4. Blow-up or no blow-up* A unified computational and analytic approach to 3D incompressible Euler and Navier-Stokes equations Thomas Y. Hou.
A. Bellen, N. Guglielmi, S. Maset, M. Zennaro, Chris J. Budd, Weizhang Huang, Robert D. Russell, L. Greengard, D. Gueyffier, P.-G. Martinsson, V. Rokhlin, Thomas Y. Hou
Hardback (ISBN-13: 9780521867566)
This clear and lively introduction to probability theory concentrates on the results that are the most useful for applications, including combinatorial probability and Markov chains. Concise and focused, it is designed for a one-semester introductory course in probability for students who have some familiarity with basic calculus. Reflecting the author’s philosophy that the best way to learn probability is to see it in action, there are more than 350 problems and 200 examples. The examples contain all the old standards such as the birthday problem and Monty Hall, but also include a number of applications not found in other books, from areas as broad ranging as genetics, sports, finance, and inventory management.
* Over 350 exercises and 200 examples * Can be used by students who do
not know much calculus * Covers Markov chains
1. Basic concepts; 2. Combinatorial probability; 3. Conditional probability; 4. Markov chains; 5. Continuous distributions; 6. Limit theorems; 7. Option pricing.
‘The book has a nice interplay between probability modeling and scientific applications, whether from biology, sports, or discussions of China's one-child policy. Many of the examples are thought provoking, including ones on DNA samples for paternity cases and others about the O. J. Simpson trial. As an instructor, I enjoy digging into these examples in class. And the large selection of interesting problems builds basic skills and deepens or extends the main ideas.’ Professor Michael Phelan, University of California, Irvine
Hardback (ISBN-13: 9780898716726)
Symmetry suggests order and regularity whilst chaos suggests disorder and randomness. Symmetry in Chaos is an exploration of how combining the seemingly contradictory symmetry and chaos can lead to the construction of striking and beautiful images. This book is an engaging look at the interplay of art and mathematics, and between symmetry and chaos. The underlying mathematics involved in the generation of the images is described. This second edition has been updated to include the Faraday experiment, a classical experiment from fluid dynamics which illustrates that increasing the vibration amplitude of a container of liquid causes the liquid to form surface waves, instead of moving as a solid body. This second edition also includes updated methods for numerically determining the symmetry of higher dimensional analogues of the images. As well as this, it contains new and improved quality images.
* A stunning collection of mathematically generated full colour images
* Describes how a chaotic process can eventually lead to symmetric patterns
* A classic in the interdisciplinary field of art and mathematics
1. Introduction to symmetry and chaos; 2. Planar symmetries; 3. Patterns everywhere; 4. Chaos and symmetry creation; 5. Symmetric icons; 6. Quilts; 7. Symmetric fractals; Appendix A. Picture parameters; Appendix B. Icon mappings; Appendix C. Planar lattices; Bibliography; Index.
‘An impressive and beautiful exploration of an impressive and beautiful
area of mathematics * the interplay between order and chaos. The images
are breathtaking, the mathematics fundamental. Symmetry in Chaos is an
important book, a work of art, and a joy to read.’ Ian Stewart, author
of Why Beauty is Truth
‘A classic in the interdisciplinary field of art and mathematics, this very well written book takes the ingenious idea of combining symmetry with chaos to construct stunning images that anyone can enjoy, in particular mathematicians, who can also appreciate the underlying mathematics. Beautiful art cannot be the result of just clever computer graphics. The artist must also have a keen sense of color and that intangible artistic sensibility, which is present in Symmetry in Chaos. Anyone interested in the relationship of art and mathematics should read this book.’ Nat Friedman, Director, International Society of the Arts, Mathematics and Architecture
Series: London Mathematical Society Lecture Note Series (No. 364)
Paperback (ISBN-13: 9780521125123)
Recent years have seen considerable research activity at the interface of mathematics and fluid mechanics, particularly partial differential equations. The 2007 workshop at the University of Warwick was organised to consolidate, survey and further advance the subject. This volume is an outgrowth of that workshop. It consists of a number of reviews and a selection of more traditional research articles. The result is an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. The book serves as both a helpful overview for graduate students new to the area and a useful resource for more established researchers.
* Covers a wide range of active research topics within the area and includes
exciting new results * Serves as both an accessible overview for graduate
students and a valuable resource for established researchers in the field
* Authored by leaders in their respective fields
Preface; List of contributors; 1. Shear flows and their attractors M. Boukrouche and G. Lukaszewicz; 2. Mathematical results concerning unsteady flows of chemically reacting incompressible fluids M. Buli*ek, J. Malek and K. R. Rajagopal; 3. The uniqueness of Lagrangian trajectories in Navier*Stokes flows M. Dashti and J. C. Robinson; 4. Some controllability results in fluid mechanics E. Fernandez-Cara; 5. Singularity formation and separation phenomena in boundary layer theory F. Gargano, M. C. Lombardo, M. Sammartino and V. Sciacca; 6. Partial regularity results for solutions of the Navier*Stokes system I. Kukavica; 7. Anisotropic Navier*Stokes equations in a bounded cylindrical domain M. Paicu and G. Raugel; 8. The regularity problem for the three-dimensional Navier*Stokes equations J. C. Robinson and W. Sadowski; 9. Contour dynamics for the surface quasi-geostrophic equation J. L. Rodrigo; 10. Theory and applications of statistical solutions of the Navier*Stokes equations R. M. Rosa.
M. Boukrouche, G. Lukaszewicz, M. Buli*ek, J. Malek, K. R. Rajagopal, M.
Dashti, J. C. Robinson, E. Fernandez-Cara, F. Gargano, M. C. Lombardo,
M. Sammartino, V. Sciacca, I. Kukavica, M. Paicu, G. Raugel, W. Sadowski,
J. L. Rodrigo, R. M. Rosa
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