This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (CINFINITY) manifolds, without using differential calculus.
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.
Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis.
This book arose from a conference on "e;Singularities and Computer Algebra"e; which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel's 70th birthday.
Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra.
This textbook combines the history of synthetic geometry, centered on the years 1800-1855, with a theorem-proof exposition of the geometry developed in those years.
This volume is the proceedings of the Conference on Algebra and Algebraic Geometry with Applications which was held July 19 - 26, 2000, at Purdue University to honor Professor Shreeram S.
Over the course of the last century, the systematic exploration of the relationship between Fourier analysis and other branches of mathematics has lead to important advances in geometry, number theory, and analysis, stimulated in part by Hurwitz's proof of the isoperimetric inequality using Fourier series.
Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research.
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory.
This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Grobner bases) and geometry (via quiver theory).
The discoveries of the past decade have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology.
An illuminating biography of one of the greatest geometers of the twentieth centuryDriven by a profound love of shapes and symmetries, Donald Coxeter (19072003) preserved the tradition of classical geometry when it was under attack by influential mathematicians who promoted a more algebraic and austere approach.
Zu jeder affinen Inzidenzebene, in welcher der große Satz von Desargues gilt (kurz: (D)-Ebene), wird mit Hilfe von Translationen und Streckungen ein zweidimensionaler Vektorraum über einem Schiefkörper hergeleitet.
This book provides advanced undergraduate physics and mathematics students with an accessible yet detailed understanding of the fundamentals of differential geometry and symmetries in classical physics.
The general theory of relativity, as formulated by Albert Einstein in 1915, provided an astoundingly original perspective on the physical nature of gr- itation, showing that it could be understood as a feature of a curvature in the four-dimensional continuum of space-time.
