Series: Sources and Studies in the History of Mathematics and Physical Science
2011, XXX, 598 p. 173 illus., 167 in color., Hardcover
ISBN: 978-0-85729-035-9
Due: November 9, 2010
Tantrasangraha, composed by the renowned Kerala astronomer Nilakantha Somayaji (c. 1444-1545 CE) ranks along with Aryabhatiya of Aryabhata and Siddhantasiromani of Bhaskaracarya as one of the major works that significantly influenced further work on astronomy in India. One of the distinguishing features of this text is the introduction of a major revision of the traditional planetary models which includes a unified theory of planetary latitudes and a better formulation of the equation of centre for the interior planets (Mercury and Venus) than was previously available.
Several important innovations in mathematical technique are also to be found in Tantrasangraha, especially related to the computation of accurate sine tables, the use of series for evaluating the sine and cosine functions, and a systematic treatment of the problems related to the diurnal motion of the celestial objects. The spherical trigonometry relations presented in the text?applied to a variety of problems such as the computation eclipses, elevation of the moon’s cusps and so forthare also exact.
In preparing the translation and explanatory notes, the authors have used authentic Sanskrit editions of Tantrasangraha by Suranad Kunjan Pillai and K V Sarma. The text consists of eight chapters?mean londitudes, true longitues, gnomonic shadow, lunar eclipse, solar eclipse, vyat?p?ta, reduction to observation and elevation of the moon’s cusps?and 432 verses. All the verses have been translated into English and are supplemented with detailed explanations including all mathematical relations, figures and tables using modern mathematical notation.
This edition of Tantrasangraha will appeal to historians of astronomy as well as those who are keen to know about the actual computational procedures employed in Indian astronomy. It is a self-contained text with several appendices included, enabling the reader to comprehend the subject matter without the need for further research.
Mean longitudes of planets.- True longitudes of planets.- Gnomonic shadow.- Lunar eclipse.- Solar eclipse.- Vyat?p?ta.- Reduction to observation.- Elevation of lunar horns.- Appendices.
Series: Universitext
2011, XXII, 838 p. 150 illus., 75 in color., Softcover
ISBN: 978-3-642-15626-7
Due: December 2010
The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphic images of them) are characterized in this book by simple local axioms on points and lines. Simple point-line characterizations of Lie incidence geometries allow one to recognize Lie incidence geometries and their automorphism groups. These tools could be useful in shortening the enormously lengthy classification of finite simple groups. Similarly, recognizing ruled manifolds by axioms on light trajectories, offers a way for a physicist to recognize the action of a Lie group in a context where it is not clear what Hamiltonians or Casimir operators are involved. The presentation is self-contained in the sense that proofs proceed step-by-step from elementary first principals without further appeal to outside results. Several chapters have new heretofore unpublished research results. On the other hand, certain groups of chapters would make good graduate courses. All but one chapter provide exercises for either use in such a course, or to elicit new research directions.
I.Basics.- 1 Basics about Graphs.- 2 .Geometries: Basic Concepts.- 3 .Point-line Geometries.-4.Hyperplanes, Embeddings and Teirlinck's Eheory.- II.The Classical Geometries.- 5 .Projective Planes.-6.Projective Spaces.- 7.Polar Spaces.- 8.Near Polygons.- III.Methodology.- 9.Chamber Systems and Buildings.- 10.2-Covers of Chamber Systems.- 11.Locally Truncated Diagram Geometries.-12.Separated Systems of Singular Spaces.- 13 Cooperstein's Theory of Symplecta and Parapolar Spaces.- IV.Applications to Other Lie Incidence Geometries.- 15.Characterizing the Classical Strong Parapolar Spaces: The Cohen-Cooperstein Theory Revisited.- 16.Characterizing Strong Parapolar Spaces by the Relation between Points and Certain Maximal Singular Subspaces.- 17.Point-line Characterizations of the “Long Root Geometries”.- 18.The Peculiar Pentagon Property.
Series: Probability and Its Applications
2011, XIV, 416 p., Hardcover
ISBN: 978-3-642-15006-7
Due: November 2010
Since its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology.
Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume contains thorough coverage of the method’s fundamentals, includes a large number of recent developments in both theory and applications, and will help accelerate the appreciation, understanding, and use of Stein's method by providing the reader with the tools needed to apply it in new situations. It addresses researchers as well as graduate students in Probability, Statistics and Combinatorics.
Preface.- 1.Introduction.- 2.Fundamentals of Stein's Method.- 3.Berry-Esseen Bounds for Independent Random Variables.- 4.L^1 Bounds.- 5.L^1 by Bounded Couplings.- 6 L^1: Applications.- 7.Non-uniform Bounds for Independent Random Variables.- 8.Uniform and Non-uniform Bounds under Local Dependence.- 9.Uniform and Non-Uniform Bounds for Non-linear Statistics.- 10.Moderate Deviations.- 11.Multivariate Normal Approximation.- 12.Discretized normal approximation.- 13.Non-normal Approximation.- 14.Extensions.- References.- Author Index .- Subject Index.- Notation.
Series: Springer Monographs in Mathematics
2011, X, 290 p., Hardcover
ISBN: 978-3-642-15127-9
Due: October 18, 2010
Assuming only basic algebra and Galois theory, the book develops the method of "algebraic patching" to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "ample fields". Among others, it leads to the solution of two central results in "Field Arithmetic": (a) The absolute Galois group of a countable Hilbertian pac field is free on countably many generators; (b) The absolute Galois group of a function field of one variable over an algebraically closed field C is free of rank equal to the cardinality of C.
1. Algebraic Patching.- 2. Normed Rings.- 3. Several Variables.- 4. Constant Split Embedding Problems over Complete Fields.- 5. Ample Fields.- 6. Non-Ample Fields.- 7. Split Embedding Problems over Complete Fields.- 8. Split Embedding Problems over Ample Fields.- 9. The Absolute Galois Group of C(t).- 10. Semi-Free Profinite Groups.- 11. Function Fields of One Variable over PAC Fields.- 12. Complete Noetherian Domains.- Open Problems.- References.- Glossary of Notation.- Index.
Series: Texts in Applied Mathematics, Vol. 25
2011, 440 p., Hardcover
ISBN: 978-1-4419-7253-8
Due: October 29, 2010
Detailed calculations of a number of concrete examples Written for mathematicians who want to see something of the applications of topology and geometry to modern physics Also aimed at physicists who want to see the foundations of their subject treated with mathematical rigor
This is a book on topology and geometry, and like any book on subjects as vast as these, it has a point of view that guided the selection of topics. The author’s point of view is that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The goal is to weave together rudimentary notions from the classical gauge theories of physics and the topological and geometrical concepts that became the mathematical models of these notions. The reader is assumed to have a minimal understanding of what an electromagnetic field is, a willingness to accept a few of the more elementary pronouncements of quantum mechanics, and a solid background in real analysis and linear algebra with some of the vocabulary of modern algebra.
To such a reader we offer an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2)-connections on S4 with instanton number -1. This second edition of the book includes a new chapter on singular homology theory and a new appendix outlining Donaldson’s beautiful application of gauge theory to the topology of compact, simply connected , smooth 4-manifolds with definite intersection form.
Preface.- Physical and geometrical motivation 1 Topological spaces.- Homotopy groups.- Principal bundles.- Differentiable manifolds and matrix Lie groups.- Gauge fields and Instantons. Appendix. References. Index.