03672nam a22005775i 4500 978-3-662-69412-1 DE-He213 20251030112841.0 cr nn 008mamaa 240807s2024 gw | s |||| 0|eng d 9783662694121 978-3-662-69412-1 10.1007/978-3-662-69412-1 doi QA564-609 PBMW bicssc MAT012010 bisacsh PBMW thema Hilgert, Joachim. author. aut http://id.loc.gov/vocabulary/relators/aut 82028 Mathematical Structures [electronic resource] : From Linear Algebra over Rings to Geometry with Sheaves / by Joachim Hilgert. 1st ed. 2024. Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2024. X, 333 p. 85 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Mathematics Study Resources, 2731-3832 ; 13 I Algebraic Structures -- 1 Rings -- 2 Modules -- 3 Multilinear Algebra -- 4 Pattern Recognition -- II Local Structures -- 5 Sheaves -- 6 Manifolds -- 7 Algebraic Varieties -- III Outlook -- 8 Transfer of Arguments and Structures -- 9 Specialization, Generalization and Unification of Structures. This textbook is intended to be accessible to any second-year undergraduate in mathematics who has attended courses on basic real analysis and linear algebra. It is meant to help students to appreciate the diverse specialized mathematics courses offered at their universities. Special emphasis is on similarities between mathematical fields and ways to compare them. The organizing principle is the concept of a mathematical structure which plays an important role in all areas of mathematics. The mathematical content used to explain the structural ideas covers in particular material that is typically taught in algebra and geometry courses. The discussion of ways to compare mathematical fields also provides introductions to categories and sheaves, whose ever-increasing role in modern mathematics suggests a more prominent role in teaching. The Author Joachim Hilgert is a retired professor of mathematics at the University of Paderborn. The book is the English translation of the second edition of “Mathematische Strukturen” (Springer, 2024) written in German. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content. . Algebraic geometry. Global analysis (Mathematics). 69682 Manifolds (Mathematics). 69683 Commutative algebra. 70151 Commutative rings. 70152 Algebra, Homological. 70150 Algebraic Geometry. Global Analysis and Analysis on Manifolds. 69685 Commutative Rings and Algebras. 70156 Category Theory, Homological Algebra. 70155 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783662694114 Printed edition: 9783662694138 Mathematics Study Resources, 2731-3832 ; 13 81153 https://doi.org/10.1007/978-3-662-69412-1 ZDB-2-SMA ZDB-2-SXMS 62300 62300