From Linear Algebra over Rings to Geometry with Sheaves
344 pages
13 hours of reading
Designed for second-year undergraduate mathematics students, this textbook emphasizes the connections between various mathematical fields. It encourages appreciation for specialized courses by focusing on the concept of mathematical structures, which are crucial across different areas of mathematics. The text aims to highlight similarities among disciplines, fostering a deeper understanding of the subject as a whole.
Focusing on Lie groups and their actions on manifolds, this book offers a thorough exploration of fundamental principles with practical applications. It is designed to be accessible for mathematicians and graduate students, making complex concepts easier to grasp. Additionally, the text includes appendices that cover essential theories and multilinear algebra, enriching the reader's understanding of the subject matter.
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, BrasilWalter D. Neumann, Columbia University, New York, USAMarkus J. Pflaum, University of Colorado, Boulder, USADierk Schleicher, Jacobs University, Bremen, GermanyKatrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019)Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019)Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019)Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021)Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
