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Author :
Publisher : Academic Press
ISBN 13 : 9780080873695
Total Pages : 446 pages
Book Rating : 4.93/5 ( download)
Download or read book Differential Algebra & Algebraic Groups written by and published by Academic Press. This book was released on 1973-06-15 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Algebra & Algebraic Groups
Author : Alexandru Buium
Publisher : Springer
ISBN 13 : 3540467645
Total Pages : 160 pages
Book Rating : 4.49/5 ( download)
Download or read book Differential Algebraic Groups of Finite Dimension written by Alexandru Buium and published by Springer. This book was released on 2006-11-15 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential algebraic groups were introduced by P. Cassidy and E. Kolchin and are, roughly speaking, groups defined by algebraic differential equations in the same way as algebraic groups are groups defined by algebraic equations. The aim of the book is two-fold: 1) the provide an algebraic geometer's introduction to differential algebraic groups and 2) to provide a structure and classification theory for the finite dimensional ones. The main idea of the approach is to relate this topic to the study of: a) deformations of (not necessarily linear) algebraic groups and b) deformations of their automorphisms. The reader is assumed to possesssome standard knowledge of algebraic geometry but no familiarity with Kolchin's work is necessary. The book is both a research monograph and an introduction to a new topic and thus will be of interest to a wide audience ranging from researchers to graduate students.
Author :
Publisher : Academic Press
ISBN 13 : 9780080874333
Total Pages : 272 pages
Book Rating : 4.39/5 ( download)
Download or read book Differential Algebraic Groups written by and published by Academic Press. This book was released on 1985-01-25 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Algebraic Groups
Author : Teresa Crespo
Publisher : American Mathematical Soc.
ISBN 13 : 082185318X
Total Pages : 242 pages
Book Rating : 4.84/5 ( download)
Download or read book Algebraic Groups and Differential Galois Theory written by Teresa Crespo and published by American Mathematical Soc.. This book was released on 2011 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Galois theory has seen intense research activity during the last decades in several directions: elaboration of more general theories, computational aspects, model theoretic approaches, applications to classical and quantum mechanics as well as to other mathematical areas such as number theory. This book intends to introduce the reader to this subject by presenting Picard-Vessiot theory, i.e. Galois theory of linear differential equations, in a self-contained way. The needed prerequisites from algebraic geometry and algebraic groups are contained in the first two parts of the book. The third part includes Picard-Vessiot extensions, the fundamental theorem of Picard-Vessiot theory, solvability by quadratures, Fuchsian equations, monodromy group and Kovacic's algorithm. Over one hundred exercises will help to assimilate the concepts and to introduce the reader to some topics beyond the scope of this book. This book is suitable for a graduate course in differential Galois theory. The last chapter contains several suggestions for further reading encouraging the reader to enter more deeply into different topics of differential Galois theory or related fields.
Author : Ellis Robert Kolchin
Publisher :
ISBN 13 : 9780124176409
Total Pages : 271 pages
Book Rating : 4.02/5 ( download)
Download or read book Pure and Applied Mathematics written by Ellis Robert Kolchin and published by . This book was released on 1985 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ellis Robert Kolchin
Publisher :
ISBN 13 : 9780124176508
Total Pages : 446 pages
Book Rating : 4.0X/5 ( download)
Download or read book Differential Algebra and Algebraic Groups written by Ellis Robert Kolchin and published by . This book was released on 1973 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Li Guo
Publisher : World Scientific
ISBN 13 : 9814490504
Total Pages : 320 pages
Book Rating : 4.04/5 ( download)
Download or read book Differential Algebra and Related Topics written by Li Guo and published by World Scientific. This book was released on 2002-05-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential algebra explores properties of solutions to systems of (ordinary or partial, linear or nonlinear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration, and symmetry analysis of differential equations. This volume includes tutorial and survey papers presented at workshop. Contents:The Ritt–Kolchin Theory for Differential Polynomials (W Y Sit)Differential Schemes (J J Kovacic)Differential Algebra — A Scheme Theory Approach (H Gillet)Model Theory and Differential Algebra (T Scanlon)Inverse Differential Galois Theory (A R Magid)Differential Galois Theory, Universal Rings and Universal Groups (M van der Put)Cyclic Vectors (R C Churchill & J J Kovacic)Differential Algebraic Techniques in Hamiltonian Mechanics (R C Churchill)Moving Frames and Differential Algebra (E L Mansfield)Baxter Algebras and Differential Algebras (L Guo) Readership: Graduate students, pure mathematicians, logicians, algebraic geometers, applied mathematicians and physicists. Keywords:Differential Algebra;Mathematical Logic;Algebraic Geometry;Mathematical Physics
Author : Matthias Kreck
Publisher : American Mathematical Soc.
ISBN 13 : 0821848984
Total Pages : 234 pages
Book Rating : 4.82/5 ( download)
Download or read book Differential Algebraic Topology written by Matthias Kreck and published by American Mathematical Soc.. This book was released on 2010 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a geometric introduction to the homology of topological spaces and the cohomology of smooth manifolds. The author introduces a new class of stratified spaces, so-called stratifolds. He derives basic concepts from differential topology such as Sard's theorem, partitions of unity and transversality. Based on this, homology groups are constructed in the framework of stratifolds and the homology axioms are proved. This implies that for nice spaces these homology groups agree with ordinary singular homology. Besides the standard computations of homology groups using the axioms, straightforward constructions of important homology classes are given. The author also defines stratifold cohomology groups following an idea of Quillen. Again, certain important cohomology classes occur very naturally in this description, for example, the characteristic classes which are constructed in the book and applied later on. One of the most fundamental results, Poincare duality, is almost a triviality in this approach. Some fundamental invariants, such as the Euler characteristic and the signature, are derived from (co)homology groups. These invariants play a significant role in some of the most spectacular results in differential topology. In particular, the author proves a special case of Hirzebruch's signature theorem and presents as a highlight Milnor's exotic 7-spheres. This book is based on courses the author taught in Mainz and Heidelberg. Readers should be familiar with the basic notions of point-set topology and differential topology. The book can be used for a combined introduction to differential and algebraic topology, as well as for a quick presentation of (co)homology in a course about differential geometry.
Author : Marius van der Put
Publisher : Springer Science & Business Media
ISBN 13 : 3642557503
Total Pages : 446 pages
Book Rating : 4.07/5 ( download)
Download or read book Galois Theory of Linear Differential Equations written by Marius van der Put and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews
Author : Li Guo
Publisher : World Scientific
ISBN 13 : 9789810247034
Total Pages : 328 pages
Book Rating : 4.36/5 ( download)
Download or read book Differential Algebra and Related Topics written by Li Guo and published by World Scientific. This book was released on 2002 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential algebra explores properties of solutions of systems of (ordinary or partial, linear or non-linear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration and symmetry analysis of differential equations. These proceedings consist of tutorial and survey papers presented at the Second International Workshop on Differential Algebra and Related Topics at Rutgers University, Newark in April 2007. As a sequel to the proceedings of the First International Workshop, this volume covers more related subjects, and provides a modern and introductory treatment to many facets of differential algebra, including surveys of known results, open problems, and new, emerging, directions of research. It is therefore an excellent companion and reference text for graduate students and researchers.
