TAILIEUCHUNG - A Course in Metric Geometry

Often we mathematicians are inarticulate when challenged to explain why mathematics is such a critical aspect of K - 12 education today. We know it is, but are so involved in the subject that we have not looked at the broader perspective of the way in which mathematics actually interacts with today’s society. So what follows are some observations that may well be useful in this regard. It is strongly suggested that at a number of points in these courses for pre-service teachers, the instructor should take a few minutes to explain some of the (real) core applications of mathematics, so as to break the mind-set that mathematics. | A Course in Metric Geometry Dmitri Burago Yuri Burago Sergei Ivanov Department of Mathematics Pennsylvania State University E-mail address burago@ Steklov Institute for Mathematics at St. Petersburg E-mail address burago@ Steklov Institute for Mathematics at St. Petersburg E-mail address svivanov@ Contents Preface vii Chapter 1. Metric Spaces 1 . Definitions 1 . Examples 3 . Metrics and Topology 7 . Lipschitz Maps 9 . Complete Spaces 10 . Compact Spaces 13 . Hausdor Measure and Dimension 17 Chapter 2. Length Spaces 25 . Length Structures 25 . First Examples of Length Structures 30 . Length Structures Induced by Metrics 33 . Characterization of Intrinsic Metrics 38 . Shortest Paths 44 . Length and Hausdor Measure 53 . Length and Lipschitz Speed 55 Chapter 3. Constructions 59 . Locality Gluing and Maximal Metrics 59 . Polyhedral Spaces 67 . Isometries and Quotients 74 .

• Toán học
• measures suggest
• surprising given
• Asymptotic Expansion
• Homogenisation and Multiscale
• Topology Optimisation
• Composite Structures
• Functional analysis
• Tabular analysis
• Weighted mean
• Suggest suitable policy measures
• Marketing of pulses