**Author**: John Oprea

**Publisher:** MAA

**ISBN:** 9780883857489

**Category : **Mathematics

**Languages : **en

**Pages : **508

**Book Description**
Differential geometry has a long, wonderful history it has found relevance in areas ranging from machinery design of the classification of four-manifolds to the creation of theories of nature's fundamental forces to the study of DNA. This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole, it mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Differential geometry is not just for mathematics majors, it is also for students in engineering and the sciences. Into the mix of these ideas comes the opportunity to visualize concepts through the use of computer algebra systems such as Maple. The book emphasizes that this visualization goes hand-in-hand with the understanding of the mathematics behind the computer construction. Students will not only “see” geodesics on surfaces, but they will also see the effect that an abstract result such as the Clairaut relation can have on geodesics. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics. Students will also see how particles move under constraints. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.

**Author**: Yoshiaki Maeda

**Publisher:** Springer Science & Business Media

**ISBN:** 9401007047

**Category : **Science

**Languages : **en

**Pages : **308

**Book Description**
Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments. However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation problems, Poisson groupoids, operad theory, quantization problems, and D-branes. The meeting was attended by both mathematicians and physicists, which resulted in interesting discussions. This volume contains the refereed proceedings of this symposium. Providing a state of the art overview of research in these topics, this book is suitable as a source book for a seminar in noncommutative geometry and physics.

**Author**: Old?ich Kowalski

**Publisher:** World Scientific

**ISBN:** 9812790608

**Category : **Mathematics

**Languages : **en

**Pages : **732

**Book Description**
This volume contains invited lectures and selected research papers in the fields of classical and modern differential geometry, global analysis, and geometric methods in physics, presented at the 10th International Conference on Differential Geometry and its Applications (DGA2007), held in Olomouc, Czech Republic.The book covers recent developments and the latest results in the following fields: Riemannian geometry, connections, jets, differential invariants, the calculus of variations on manifolds, differential equations, Finsler structures, and geometric methods in physics. It is also a celebration of the 300th anniversary of the birth of one of the greatest mathematicians, Leonhard Euler, and includes the Euler lecture ?Leonhard Euler ? 300 years on? by R Wilson. Notable contributors include J F Cari¤ena, M Castrill¢n L¢pez, J Erichhorn, J-H Eschenburg, I Kol ?, A P Kopylov, J Korba?, O Kowalski, B Kruglikov, D Krupka, O Krupkov , R Landre, Haizhong Li, S Maeda, M A Malakhaltsev, O I Mokhov, J Mu¤oz Masqu, S Preston, V Rovenski, D J Saunders, M Sekizawa, J Slov k, J Szilasi, L Tam ssy, P Walczak, and others.

**Author**: J Janyska

**Publisher:** World Scientific

**ISBN:** 9814611700

**Category : **
**Languages : **en

**Pages : **480

**Book Description**
The proceedings consists of lectures and selected original research papers presented at the conference. The contents is divided into 3 parts: I. Geometric structures, II. the calculus of variations on manifolds, III. Geometric methods in physics. The volume also covers interdisciplinary areas between differential geometry and mathematical physics like field theory, relativity, classical and quantum mechanics. Contents:On the Chern-Griffiths Formulas for an Upper Bound for the Rank of a Web (V V Goldberg)Natural and Gauge-Natural Operators on the Space of Linear Connections on a Vector Bundle (J Janyska)General Natural Bundles and Operators (I Kolár)Classes Caracteristiques Residuelles (D Lehmann)Remarks on Globalization of the Langrangian Formalism (A Borowiec)A Fresh Approach to the Poincaré-Cartan Form for a Linear PDE and a Map Between Cohomologies (T Harding & F J Bloore)Variational Sequences on Finite Order Jet Spaces (D Krupka)Equivalence of Degenerate Lagrangians of Higher Order (M de León & P R Rodrigues)Quantum SU(2) Group of Woronowicz and Poisson Structures (J Grabowski)Nonholonomic Intermediate Integrals of Partial Differential Equations (V V Lychagin & Yu R Romanovsky)The Metric in the Superspace of Riemannian Metrics and Its Relation to Gravity (H J Schmidt)Spherically Symmetric Vacuum Spacetimes: Global Approach (R Siegl)and others Readership: Mathematicians and mathematical physicists.

**Author**: Shun-ichi Amari

**Publisher:** Springer

**ISBN:** 4431559787

**Category : **Mathematics

**Languages : **en

**Pages : **374

**Book Description**
This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.

**Author**: J. Madore

**Publisher:** Cambridge University Press

**ISBN:** 0521659914

**Category : **Mathematics

**Languages : **en

**Pages : **381

**Book Description**
A thoroughly revised introduction to non-commutative geometry.

**Author**: Quddus Khan

**Publisher:** Misha Books

**ISBN:** 9389055326

**Category : **Mathematics

**Languages : **en

**Pages : **578

**Book Description**
This book is intended to serve as a Textbook for Undergraduate and Post - graduate students of Mathematics. It will be useful to the researchers working in the field of Differential geometry and its applications to general theory of relativity and other applied areas. It will also be helpful in preparing for the competitive examinations like IAS, IES, NET, PCS, and UP Higher Education exams. The text starts with a chapter on Preliminaries discussing basic concepts and results which would be taken for general later in the subsequent chapters of this book. This is followed by the Study of the Tensors Algebra and its operations and types, Christoffel's symbols and its properties, the concept of covariant differentiation and its properties, Riemann's symbols and its properties, and application of tensor in different areas in part – I and the study of the Theory of Curves in Space, Concepts of a Surface and Fundamental forms, Envelopes and Developables, Curvature of Surface and Lines of Curvature, Fundamental Equations of Surface Theory, Theory of Geodesics, Differentiable Manifolds and Riemannian Manifold and Application of Differential Geometry in Part –II. KEY FEATURES: Provides basic Concepts in an easy to understand style; Presentation of the subject in a natural way; Includes a large number of solved examples and illuminating illustrations; Exercise questions at the end of the topic and at the end of each chapter; Proof of the theorems are given in an easy to understand style; Neat and clean figures are given at appropriate places; Notes and remarks are given at appropriate places.