Series: Mathematical Sciences Research Institute Publications
Hardback (ISBN-13: 9780521191678)
Page extent: 452 pages
Size: 234 x 156 mm
Appearance of singularities is pervasive in many problems in topology, differential geometry, and algebraic geometry. This book concerns the study of singular spaces using techniques from a variety of areas of geometry and topology and the interactions among them. Expository chapters by well-known experts cover intersection homology, L2 cohomology and differential operators, topology of algebraic varieties, signatures and characteristic classes, mixed Hodge theory, and elliptic genera of singular complex and real algebraic varieties. The book concludes with a list of open problems.
* This volume offer expository papers on the topology of stratified spaces as opposed to new research * Provides an interdisciplinary discussion within the world of stratified space research * Collect special introductory papers written by experts from the field
1. An introduction to L2 cohomology Xianzhe Dai; The almost closed range condition Gilles Carron; 2. Rigidity of differential operators and Chern numbers of singular varieties Robert Waelder; 3. Hodge theory meets the minimal model program: a survey of log canonical and du Bois singularities Sandor J. Kovacs and Karl Schwede; 4. Elliptic genera, real algebraic varieties and quasi-Jacobi forms Anatoly Libgober; 5. The weight filtration for real algebraic varieties Clint McCrory and Adam Parusinski; 6. On the Milnor classes of complex hypersurfaces Laurentiu Maxim; 7. An introduction to intersection homology with general perversity functions Greg Friedman; 8. The signature of singular spaces and its refinements to generalized homology theories Markus Banagl; 9. Intersection homology Wang sequence Filipp Levikov; 10. An exponential history of functions with logarithmic growth Matt Kerr and Gregory Pearlstein; 11. Motivic characteristic classes Shoji Yokura; 12. Characteristic classes of mixed Hodge modules Jorg Schurmann.
Series: Carus Mathematical Monographs
Hardback (ISBN-13: 9780883850435)
Page extent: 260 pages
Size: 208 x 148 mm
Randomness and Recurrence in Dynamical Systems makes accessible, at the undergraduate or beginning graduate level, results and ideas on averaging, randomness and recurrence that traditionally require measure theory. Assuming only a background in elementary calculus and real analysis, new techniques of proof have been developed, and known proofs have been adapted, to make this possible. The book connects the material with recent research, thereby bridging the gap between undergraduate teaching and current mathematical research. The various topics are unified by the concept of an abstract dynamical system, so there are close connections with what may be termed 'Probabilistic Chaos Theory' or 'Randomness'. The work is appropriate for undergraduate courses in real analysis, dynamical systems, random and chaotic phenomena and probability. It will also be suitable for readers who are interested in mathematical ideas of randomness and recurrence, but who have no measure theory background.
* An emphasis on possible interpretations of certain results and concepts, and their connections to other areas of inquiry, gives the reader a depth of understanding * Includes both 'Exercises' and 'Investigations': the former emphasise more technical questions concerning the ideas, while the latter are more open, allowing scope for student initiative and further research * Notes at the end of each part set the mathematical ideas in their historical background
Introduction: 1. Origins, approach and aims of the work; 2. Dynamical systems
and the subject matter; 3. Using this book; Part I. Background Ideas and
Knowledge: 4. Dynamical systems, iteration, and orbits; 5. Information
loss and randomness in dynamical systems; 6. Assumed knowledge and notations;
Appendix: mathematical reasoning and proof; Exercises; Investigations;
Notes; Bibliography; Part II. Irrational Numbers and Dynamical Systems:
7. Introduction: irrational numbers and the infinite; 8. Fractional parts
and points on the unit circle; 9. Partitions and the pigeon-hole principle;
10. Kronecker's theorem; 11. The dynamical systems approach to Kronecker's
theorem; 12. Kronecker and chaos in the music of Steve Reich; 13. The ideas
in Weyl's theorem on irrational numbers; 14. The proof of Weyl's theorem;
15. Chaos in Kronecker systems; Exercises; Investigations; Notes; Bibliography;
Part III. Probability and Randomness: 16. Introduction: probability, coin
tossing and randomness; 17. Expansions to a base; 18. Rational numbers
and periodic expansions; 19. Sets, events, length and probability; 20.
Sets of measure zero; 21. Independent sets and events; 22. Typewriters,
recurrence, and the Prince of Denmark; 23. The Rademacher functions; 24.
Randomness, binary expansions and a law of averages; 25. The dynamical
systems approach; 26. The Walsh functions; 27. Normal numbers and randomness;
28. Notions of probability and randomness; 29. The curious phenomenon of
the leading significant digit; 30. Leading digits and geometric sequences;
31. Multiple digits and a result of Diaconis; 32. Dynamical systems and
changes of scale; 33. The equivalence of Kronecker and Benford dynamical
systems; 34. Scale invariance and the necessity of Benford's law; Exercises;
Investigations; Notes; Bibliography; Part IV. Recurrence: 35. Introduction:
random systems and recurrence; 36. Transformations that preserve length;
37. Poincare recurrence; 38. Recurrent points; 39. Kac's result on average
recurrence times; 40. Applications to the Kronecker and Borel dynamical
systems; 41. The standard deviation of recurrence times; Exercises; Investigations;
Notes; Bibliography; Part V. Averaging in Time and Space: 42. Introduction:
averaging in time and space; 43. Outer measure; 44. Invariant sets; 45.
Measurable sets; 46. Measure-preserving transformations; 47. Poincare recurrence
… again!; 48. Ergodic systems; 49. Birkhoff's theorem: the time average
equals the space average; 50. Weyl's theorem from the ergodic viewpoint;
51. The Ergodic Theorem and expansions to an arbitrary base; 52. Kac's
recurrence formula: the general case; 53. Mixing transformations and an
example of Kakutani; 54. Luroth transformations and continued fractions;
Exercises; Investigations; Notes; Bibliography; Index.
Donald E. Knuth has been making foundational contributions to the field of computer science for as long as computer science has been a field. His award-winning textbooks are often given credit for shaping the field, and his scientific papers are widely referenced and stand as milestones of development over a wide variety of topics. The present volume, the seventh in a series of his collected papers, is devoted to his work on the design of new algorithms. Nearly thirty of Knuth's classic papers are collected in this book and brought up to date with extensive revisions and notes on subsequent developments. The papers cover numerous discrete problems, such as assorting, searching, data compression, theorem proving, and cryptography, as well as methods for controlling errors in numerical computations.
Donald E. Knuth is the Fletcher Jones Professor of Computer Science emeritus at Stanford University.
March 2010
ISBN (Paperback): 9781575865829
ISBN (Cloth): 9781575865836
Logic and Pragmatism features a number of the key writings of Giovanni Vailati (1863*1909), the Italian mathematician and philosopher renowned for his work in mechanics, geometry, logic, and epistemology. The selections in this book*many of which are available here for the first time in English*focus on Vailati's significant contributions to the field of pragmatism. Accompanying these pieces are introductory essays by the volume's editors that outline the traits of Vailati's pragmatism and provide insights into the scholar's life.
Claudia Arrighi is an independent researcher. Paola Cantu is a postdoctoral researcher at the University of Nancy. Mauro De Zan teaches philosophy and history in Crema, Italy and is the president of the Centro Studi Giovanni Vailati. Patrick Suppes is the Lucie Stern Professor of Philosophy emeritus at Stanford University.
April 2010
ISBN (Paperback): 978157586-590-4
ISBN (Cloth): 978157586-591-1
In Modal Logic for Open Minds, Johan van Benthem provides an introduction to the field of modal logic, outlining its major ideas and exploring the numerous ways in which various academic fields have adopted it. Van Benthem begins with the basic theories of modal logic, examining its relationship to language, semantics, bisimulation, and axiomatics, and then covers more advanced topics, such as expressive power, computational complexity, and intelligent agency. Many of the chapters are followed by exercises, making this volume ideal for undergraduate and graduate students in philosophy, computer science, symbolic systems, cognitive science, and linguistics.
Johan van Benthem is University Professor of pure and applied logic at the University of Amsterdam, the Henry Waldgrave Stuart Professor of Philosophy at Stanford University, and the Weilun Visiting Professor of Humanities at Tsinghua University in Beijing.
April 2010
ISBN (Paperback): 978157586-598-0
ISBN (Cloth): 978157586-599-7
This original study considers the effects of language and meaning on the brain. Jens Erik Fenstad*an expert in the fields of recursion theory, nonstandard analysis, and natural language semantics*combines current formal semantics with a geometric structure in order to trace how common nouns, properties, natural kinds, and attractors link with brain dynamics.
Jens Erik Fenstad is professor emeritus in the Department of Mathematics at the University of Oslo and a member of the Norwegian Academy of Letters and Science and of Academia Europaea.
April 2010
ISBN (Paperback): 978157586-592-8
ISBN (Cloth): 978157586-593-5
This review is devoted to the differential-geometric theory of homogenous forms and other different homogenous structures (mainly Poisson and symplectic structures) on loop spaces of smooth manifolds, their natural generalizations and applications in mathematical physics and field theory.
Pb 204pp 2009
978-1-904868-72-9
Multidimensional Monge-Ampere Equation by A.V.Pogorelov presents a detailed exposition of the results concerning the existence and uniqueness of the solutions of the general Monge-Ampere multidimensional equations of elliptic type. This division of the theory of partial differential equations is closely connected with geometry. This review is intended for students, postgraduates and researchers in geometry and differential equations.
2009 110pp Pb
978-1-904868-81-1