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Graduate Texts in Mathematics #286
Lectures on Convex Geometry
This book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book.
Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry.
Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.
Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry.
Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.
- GenresMathematics
305 pages, Kindle Edition
First published August 28, 2020
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September 16, 2021
Covers a good amount of convex geometry - most if not all of the topics I've heard about in research settings (and this being my first comprehensive course, it will pretty helpful to flesh out some of the details).
That being said, I feel like often the proofs and intuition sometimes pop out of nowhere -- some of the early proofs have diagrams which are helpful, but adding more diagrams later on would be helpful as well. Also some explicit examples (esp. for abstract hard to grasp things like mixed volumes) would be great too. That being said, at this level, I'm not surprised there's no explicit examples since most readers should be able to construct some for themselves.
Worth noting that I don't know if these criticisms apply to the published version of this material - I was working on the PDF version based on Hug/Weil's course given in Karlsruhe.
That being said, I feel like often the proofs and intuition sometimes pop out of nowhere -- some of the early proofs have diagrams which are helpful, but adding more diagrams later on would be helpful as well. Also some explicit examples (esp. for abstract hard to grasp things like mixed volumes) would be great too. That being said, at this level, I'm not surprised there's no explicit examples since most readers should be able to construct some for themselves.
Worth noting that I don't know if these criticisms apply to the published version of this material - I was working on the PDF version based on Hug/Weil's course given in Karlsruhe.
Displaying 1 of 1 review