224,50 zł

Modern Differential Geometry For Physicists (2nd Edition) World Scientific Publishing Co Pte Ltd

Książki / Literatura obcojęzyczna

These lecture notes are the content of an introductory course on modern, co-ordinate-free differential geometry which is taken by first-year theoretical physics PhD students, or by students attending the one-year MSc course, "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen bearing in mind the way in which differential geometry is applied to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields, nonlinear sigma models and other types of nonlinear field systems that feature in modern quantum field theory. This edition of the text contains an additional chapter that introduces some of the basic ideas of general topology needed in differential geometry. A number of small corrections and additions have also been made. The volume is divided into four parts.The first provides an introduction to general topology, the second covers introductory co-ordinate-free differential geometry, the third examines geometrical aspects of the theory of Lie groups and Lie group actions on manifolds, and the fourth provides an introduction to the theory of fibre bundles. In the introduction to differential geometry the author lays considerable stress on the basic ideas of "tangent space structure", which he develops from several different points of view - some geometrical, others more algebraic.

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311,83 zł

Modern Mathematics And Applications In Computer Graphics And Vision World Scientific Publishing Co Pte Ltd

Książki / Literatura obcojęzyczna

The book presents a comprehensive overview of modern mathematical concepts, models, methods and tools with applications in computer graphics, computer vision and machine learning. Fifteen topics in modern mathematics are arranged in three parts: algebra, geometry and topology, with an emphasis on tensors and manifolds. and a separate part on applications. It can be used as a textbook for a selected topics course at the undergraduate or graduate level. It can also be used as fifteen short crash courses for self-study of any of the topics in any order, with minimal inter-chapter dependencies. This book is based on the lecture notes of two courses the author has taught in the US - "Gaming Mathematics" at the undergraduate level and "Mathematical Methods in Computer Graphics and Vision" at the graduate level, with considerable expansions.

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