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Author: Alexei Davydov
Publisher: American Mathematical Soc.
ISBN: 0821839705
Category : Mathematics
Languages : en
Pages : 482
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Book Description
Category theory has become the universal language of modern mathematics. This book is a collection of articles applying methods of category theory to the areas of algebra, geometry, and mathematical physics. Among others, this book contains articles on higher categories and their applications and on homotopy theoretic methods. The reader can learn about the exciting new interactions of category theory with very traditional mathematical disciplines.
Author: Alexei Davydov
Publisher: American Mathematical Soc.
ISBN: 0821839705
Category : Mathematics
Languages : en
Pages : 482
Get Book Here
Book Description
Category theory has become the universal language of modern mathematics. This book is a collection of articles applying methods of category theory to the areas of algebra, geometry, and mathematical physics. Among others, this book contains articles on higher categories and their applications and on homotopy theoretic methods. The reader can learn about the exciting new interactions of category theory with very traditional mathematical disciplines.
Author: Peter Szekeres
Publisher: Cambridge University Press
ISBN: 9780521829601
Category : Mathematics
Languages : en
Pages : 620
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Book Description
This textbook, first published in 2004, provides an introduction to the major mathematical structures used in physics today.
Author: Tom Leinster
Publisher: Cambridge University Press
ISBN: 0521532159
Category : Mathematics
Languages : en
Pages : 451
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Book Description
Foundations of higher dimensional category theory for graduate students and researchers in mathematics and mathematical physics.
Author: Venzo de Sabbata
Publisher: CRC Press
ISBN: 1584887737
Category : Mathematics
Languages : en
Pages : 186
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Book Description
Bringing geometric algebra to the mainstream of physics pedagogy, Geometric Algebra and Applications to Physics not only presents geometric algebra as a discipline within mathematical physics, but the book also shows how geometric algebra can be applied to numerous fundamental problems in physics, especially in experimental situations. This
Author: Bernard F. Schutz
Publisher: Cambridge University Press
ISBN: 1107268141
Category : Science
Languages : en
Pages : 272
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Book Description
In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.
Author: Tom Leinster
Publisher: Cambridge University Press
ISBN: 1107044243
Category : Mathematics
Languages : en
Pages : 193
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Book Description
A short introduction ideal for students learning category theory for the first time.
Author: Francis Borceux
Publisher: Springer Science & Business Media
ISBN: 9781402019616
Category : Mathematics
Languages : en
Pages : 504
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Book Description
The purpose of the book is to take stock of the situation concerning Algebra via Category Theory in the last fifteen years, where the new and synthetic notions of Mal'cev, protomodular, homological and semi-abelian categories emerged. These notions force attention on the fibration of points and allow a unified treatment of the main algebraic: homological lemmas, Noether isomorphisms, commutator theory. The book gives full importance to examples and makes strong connections with Universal Algebra. One of its aims is to allow appreciating how productive the essential categorical constraint is: knowing an object, not from inside via its elements, but from outside via its relations with its environment. The book is intended to be a powerful tool in the hands of researchers in category theory, homology theory and universal algebra, as well as a textbook for graduate courses on these topics.
Author: Gerd Rudolph
Publisher: Springer Science & Business Media
ISBN: 9400753454
Category : Science
Languages : en
Pages : 766
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Book Description
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.
Author: Robin Hartshorne
Publisher: Springer Science & Business Media
ISBN: 1475738498
Category : Mathematics
Languages : en
Pages : 511
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Book Description
An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Author: Tony Pantev
Publisher: American Mathematical Soc.
ISBN: 1470415577
Category : Mathematics
Languages : en
Pages : 334
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Book Description
This volume contains the proceedings of the CATS4 Conference on Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, held from July 2-7, 2012, at CIRM in Luminy, France. Over the past several years, the CATS conference series has brought together top level researchers from around the world interested in relative and higher category theory and its applications to classical mathematical domains. Included in this volume is a collection of articles covering the applications of categories and stacks to geometry, topology and algebra. Techniques such as localization, model categories, simplicial objects, sheaves of categories, mapping stacks, dg structures, hereditary categories, and derived stacks, are applied to give new insight on cluster algebra, Lagrangians, trace theories, loop spaces, structured surfaces, stability, ind-coherent complexes and 1-affineness showing up in geometric Langlands, branching out to many related topics along the way.
