# A Course in Metric Geometry (Graduate Studies in Mathematics) by Dmitri Burago

# A Course in Metric Geometry (Graduate Studies in Mathematics) by Dmitri Burago

"Synopsis 'Metric geometry' is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Caratheodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces).The authors tend to work with 'easy-to-touch' mathematical objects using 'easy-to-visualize' methods. The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities.The book contains many exercises, which form a vital part of exposition."

Must have math tools for graduate study in economics. Sturm on the geometry of metric measure spaces. A course in metric geometry american mathematical society. Newest metric geometry questions mathematics stack. Textbook remendation metric geometry mathoverflow. Course descriptions wake forest university. Manifolds and differential geometry graduate studies in. Download a course in metric geometry softarchive. Graduate program course offerings university of pittsburgh. A course in metric geometry ebook 2001 worldcat. Category metric geometry. Metric system conversions amp geometry study. Courses in mathematics math mississippi state university. Linear measurements in metric amp english units study. Course descriptions university of texas at austin.

Metric system conversions amp geometry chapter summary feel confident in your understanding of the metric system conversions and geometry by taking advantage of the study resources in this. Graduate studies in mathematics gsm is a series of graduate level textbooks in mathematics published by the american mathematical society ams these books elaborate on several theories from notable personas such as martin schechter and terence tao in the mathematical industry the books in this series are published only in hardcover. Math 2990 independent study 1 15 credits this course is for all graduate students not under the direct supervision of a specific faculty member in addition to a student s formal course load this study is for preparation for the preliminary prehensive and overview examinations math 3000 research and dissertation for the phd degree.

A course in metric geometry dmitri burago yuri burago sergei v ivanov metric geometry is an approach to geometry based on the notion of length on a topological space this approach experienced a very fast development in the last few decades and penetrated into many. This book is a graduate level introduction to the tools and structures of modern differential geometry included are the topics usually found in a course on differentiable manifolds such as vector bundles tensors differential forms de rham cohomology the frobenius theorem and basic lie group theory. The department offers the following wide range of graduate courses in most of the main areas of mathematics courses numbered 6000 6999 are taken by senior undergraduates as well as by beginning masters degree students these courses generally carry three hours of credit per semester courses numbered 8000 8999 are taken by masters and ph d students they generally carry three hours of credit.

Metric geometry is an approach to geometry based on the notion of length on a topological space this approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines such as group theory dynamical systems and partial differential equations. Unless specifically exempted by the director of graduate studies all first year graduate students are required to take the core courses mat 530 mat 531 mat 534 mat 535 mat 536 mat 532 and mat 533 during their first year this requirement is automatically waived for students who have passed the prehensive examination.