000 03672nam a22005775i 4500
001 978-3-662-69412-1
003 DE-He213
005 20251030112841.0
007 cr nn 008mamaa
008 240807s2024 gw | s |||| 0|eng d
020 _a9783662694121
_9978-3-662-69412-1
024 7 _a10.1007/978-3-662-69412-1
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
100 1 _aHilgert, Joachim.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_982028
245 1 0 _aMathematical Structures
_h[electronic resource] :
_bFrom Linear Algebra over Rings to Geometry with Sheaves /
_cby Joachim Hilgert.
250 _a1st ed. 2024.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2024.
300 _aX, 333 p. 85 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMathematics Study Resources,
_x2731-3832 ;
_v13
505 0 _aI 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.
520 _aThis 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. .
650 0 _aAlgebraic geometry.
650 0 _aGlobal analysis (Mathematics).
_969682
650 0 _aManifolds (Mathematics).
_969683
650 0 _aCommutative algebra.
_970151
650 0 _aCommutative rings.
_970152
650 0 _aAlgebra, Homological.
_970150
650 1 4 _aAlgebraic Geometry.
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_969685
650 2 4 _aCommutative Rings and Algebras.
_970156
650 2 4 _aCategory Theory, Homological Algebra.
_970155
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783662694114
776 0 8 _iPrinted edition:
_z9783662694138
830 0 _aMathematics Study Resources,
_x2731-3832 ;
_v13
_981153
856 4 0 _uhttps://doi.org/10.1007/978-3-662-69412-1
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c62300
_d62300