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Mathematical structures = from linear algebra over rings to geometry with sheaves /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Mathematical structures/ by Joachim Hilgert.
其他題名:	from linear algebra over rings to geometry with sheaves /
作者:	Hilgert, Joachim.
出版者:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2024.,
面頁冊數:	x, 333 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Geometry, Algebraic. -
電子資源:	https://doi.org/10.1007/978-3-662-69412-1
ISBN:	9783662694121

Mathematical structures = from linear algebra over rings to geometry with sheaves /
Hilgert, Joachim.

Mathematical structuresfrom linear algebra over rings to geometry with sheaves /[electronic resource] :by Joachim Hilgert. - Berlin, Heidelberg :Springer Berlin Heidelberg :2024. - x, 333 p. :ill., digital ;24 cm. - Mathematics study resources,v. 132731-3832 ;. - Mathematics study resources ;4..

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.

ISBN: 9783662694121

Standard No.: 10.1007/978-3-662-69412-1doiSubjects--Topical Terms:

580393
Geometry, Algebraic.

LC Class. No.: QA564 / .H5513 2024

Dewey Class. No.: 516.35

Mathematical structures = from linear algebra over rings to geometry with sheaves /
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520 $a 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.
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