Series: Developments in Mathematics, Vol. 18
1st Edition., 2010, VII, 345 p. 47 illus., Hardcover
ISBN: 978-1-4419-6210-2
Due: May 29, 2010
This volume of invited works collects the most recent research and developments in quadratic forms, linear algebraic groups, and cohomology; topics that are each at the intersection of algebra, number theory and algebraic geometry. The contributions to this volume are the work of renowned experts and present new results related to the research of Raman Parimala, to whom this collection is dedicated. Some specific topics presented in this volume include, Iwasawa theory, Witt groups and sheafs, Chow motives, quaternion algebras, p-adic curves, and progress on the Kato conjecture as well as topics of recent interest such as field patching and a proof of the Serre's Conjecture II for function fields of complex surfaces. This volume is intended for researchers and graduate students specializing in algebra, number theory, and algebraic geometry and may be suitable for supplementary use in an advanced graduate course.
Content Level ≫ Research
Keywords ≫ Algebraic Geometry - Algebraic Number Theory - Cohomology - Field Patching - Iwasawa Theory - K-Theory - Linear Algebraic Groups - Quadratic Forms - Serre's Conjecture - p-adic Curves
Foreword.- Surveys.- Multiples of forms (Eva Bayer-Fluckiger).- On Saltman’s p-adic curves papers (Eric Brussel).- Serre’s Conjecture II: a survey (Philippe Gille).- Field patching, factorization, and local-global principles (Daniel Krashen).- Deformation theory and rational points on rationally connected varieties (Max Lieblich).- Recent progress on the Kato Conjecture (Shuji Saito).- Elliptic curves and Iwasawa’s μ=0 conjecture (R. Sujatha).- Cohomological invariants of central simple algebras with involution (Jean-Pierre Tignol).- Witt groups of varieties and the purity problem (Kirill Zainoulline).- Invited articles.- Some extensions and applications of Eisenstein irreducibility criterion (Anuj Bishnoi and Sudesh K. Khanduja).- On the kernel of the Rost invariant for E8 modulo 3 (V. Chernousov).- Une version du theoreme d'Amer et Brumer pour les zero-cycles (Jean-Louis Colliot-Thelene and Marc Levine).- Quaternion algebras with the same subfields (Skip Garibaldi and David J. Saltman).- Lifting of coefficients for Chow motives of quadrics (Olivier Haution).- Upper motives of outer algebraic groups (Nikita Karpenko).- Triality and etale algebras (Max-Albert Knus and Jean-Pierre Tignol).- Vector bundles generated by sections and morphisms to Grassmannians (F. Laytimi and D.S. Nagaraj).- Adams operations and the Brown-Gersten-Quillen spectral sequence (Alexander Merkurjev).- Remarks on unimodular rows (N. Mohan Kumar and M. Pavaman Murthy).- Non-self-dual stably free modules (Madhav V. Nori, Ravi A. Rao, and Richard G. Swan).- Homotopy invariance of the sheaf WNis and of its cohomology (I. Panin).- Imbedding quasi-split groups in isotropic groups (M.S. Raghunathan).
Series: Springer Undergraduate Mathematics Series, Vol. 53
1st Edition., 2010, XX, 180 p. 112 illus., 56 in color., Softcover
ISBN: 978-1-84996-250-6
Due: May 29, 2010
MathematicaR: A Problem-Centered Approach introduces the vast array of features and powerful mathematical functions of Mathematica using a multitude of clearly presented examples and worked- out problems. Each section starts with a description of a new topic and some basic examples. The author then demonstrates the use of new commands through three categories of problems
- the first category highlights those essential parts of the text that demonstrate the use of new commands in Mathematica whilst solving each problem presented;
- the second comprises problems that further demonstrate the use of commands previously introduced to tackle different situations; and
- the third presents more challenging problems for further study.
The intention is to enable the reader to learn from the codes, thus avoiding long and exhausting explanations.
While based on a computer algebra course taught to undergraduate students of mathematics, science, engineering and finance, the book also includes chapters on calculus and solving equations, and graphics, thus covering all the basic topics in Mathematica. With its strong focus upon programming and problem solving, and an emphasis on using numerical problems that do not need any particular background in mathematics, this book is also ideal for self-study and as an introduction to researchers who wish to use Mathematica as a computational tool.
1. Introduction.- 1.1 Mathematica as a calculator.- 1.2 Numbers.- 1.3 Algebraic computations.- 1.4 Trigonometric computations.- 1.5 Variables.- 1.6 Equalities =, :=, ==.- 1.7 Dynamic variables.- 2. Defining functions.- 2.1 Formulas as functions.- 2.2 Anonymous functions.- 3. Lists.- 3.1 Functions producing lists.- 3.2 Listable functions.- 3.3 Selecting from a list.- 4. Changing heads!.- 5. A bit of logic and set theory.- 5.1 Being logical.- 5.2 Handling sets.- 5.3 Decision making, If and Which.- 6. Sums and products.- 6.1 Sum.- 6.2 Product.- 7. Loops and repetitions.- 7.1 Do, For a While.- 7.2 Nested loops.- 7.3 Nest, NestList and more.- 7.4 Fold and FoldList.- 7.5 Inner and Outer.- 8. Substitution, Mathematica rules.- 9. Pattern matching.- 10. Functions with multiple definitions.- 10.1 Functions with local variables.- 10.2 Functions with conditions.- 11. Recursive functions.- 12. Linear algebra.- 12.1 Vectors.- 12.2 Matrices.- 13. Graphics.- 13.1 Two-dimensional graphs.- 13.2 Three-dimensional graphs.- 14. Calculus and equations.- 14.1 Solving equations.- 14.2 Calculus.- 15. Solutions to the Exercises
Series: Springer Monographs in Mathematics, Vol. 151
1st Edition., 2010, 275 p. 20 illus., 10 in color., Hardcover
ISBN: 978-1-84996-298-8
Due: May 29, 2010
Recent years have seen a significant rise of interest in max-linear theory and techniques. In addition to providing the linear-algebraic background in the field of tropical mathematics, max-algebra provides mathematical theory and techniques for solving various nonlinear problems arising in areas such as manufacturing, transportation, allocation of resources and information processing technology. It is, therefore, a significant topic spanning both pure and applied mathematical fields.
A welcome introduction to the subject of max-plus (tropical) linear algebra, and in particular algorithmic problems, Max-linear Systems: Theory and Algorithms offers a consolidation of both new and existing literature, thus filling a much-needed gap. Providing the fundamentals of max-algebraic theory in a comprehensive and unified form, in addition to more advanced material with an emphasis on feasibility and reachability, this book presents a number of new research results. Topics covered range from max-linear systems and the eigenvalue-eigenvector problem to periodic behavior of matrices, max-linear programs, linear independence, and matrix scaling.
This book assumes no prior knowledge of max-algebra and much of the theoryis illustrated with numerical examples, complemented by exercises, and accompanied by both practical and theoretical applications. Open problems are also demonstrated.
A fresh and pioneering approach to the topic of Max-linear Systems, this book will hold a wide-ranging readership, and will be useful for:
* anyone with basic mathematical knowledge wishing to learn essential max-algebraic ideas and techniques
* undergraduate and postgraduate students of mathematics or a related degree
* mathematics researchers
* mathematicians working in industry, commerce or management
Introduction.- Max-algebra: Two Special Features.- One-sided Max-linear Systems and Max-algebraic Subspaces.- Eigenvalues and Eigenvectors.- Maxpolynomials. The Characteristic Maxpolynomial.- Linear Independence and Rank. The Simple Image Set.- Two-sided Max-linear Systems.- Reachability of Eigenspaces.- Generalized Eigenproblem.- Max-linear Programs.- Conclusions and Open Problems
1st Edition., 2010, 350 p., Hardcover
ISBN: 978-1-4419-6204-1
Due: August 29, 2010
The 20 papers contained in this volume span the areas of mathematical physics, dynamical systems, and probability. Yakov Sinai is one of the most important and influential mathematicians of our time, having won the Boltzmann Medal (1986), the Dirac Medal (1992), Dannie Heinemann Prize for Mathematical Physics (1989), Nemmers Prize (2002), and the Wolf Prize in Mathematics (1997). He is well-known as both a mathematician and a physicist, with numerous theorems and proofs bearing his name in both fields, and this book should be of interest to researchers from all fields of the physical sciences.This volume follows Volume I.
Content Level ≫ Research
Related subjects ≫ Dynamical Systems & Diff. Equations - Physics - Probability Theory
Probability Theory.-Statistical Mechanics.-Mathematical Physics.-Mathematical Fluid Dynamics
Series: Lecture Notes in Mathematics, Vol. 1998
Subseries: Fondazione C.I.M.E., Firenze
1st Edition., 2010, XII, 348 p., Softcover
ISBN: 978-3-642-13170-7
Due: July 14, 2010
The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. This volume collects the Lectures held at the 2008 CIME session on "Holomorphic Dynamical Systems" held in Cetraro, Italy. This CIME Course focused on a number of important topics in the study of discrete and continuous dynamical systems, including both local and global aspects, providing a fascinating introduction to many key problems in current research. The contributions provide an ample description of the phenomena occurring in central themes of holomorphic dynamics such as automorphisms and meromorphic self-maps of projective spaces, of entire maps on complex spaces and holomorphic foliations in surfaces and higher dimensional manifolds, elaborating on the different techniques used and familiarizing readers with the latest findings on current research topics.
Content Level ≫ Research
Keywords ≫ 37Fxx,32Axx,32Qxx,32H50,30Dxx,31Bxx - Discrete holomorphic local dynamical systems - Dynamics of entire functions - Dynamics of rational surface automorphisms - Holomorphic endomorphisms, polynomial-like maps - Uniformisation of foliations by curves
Related subjects ≫ Analysis - Dynamical Systems & Diff. Equations