國立虎尾科技大學 |

Algebra I = Textbook for Students of Mathematics /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Algebra I/ by Alexey L. Gorodentsev.
其他題名:	Textbook for Students of Mathematics /
作者:	Gorodentsev, Alexey L.
面頁冊數:	XX, 564 p. 79 illus., 42 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Algebra. -
電子資源:	https://doi.org/10.1007/978-3-319-45285-2
ISBN:	9783319452852

Algebra I = Textbook for Students of Mathematics /
Gorodentsev, Alexey L.

Algebra ITextbook for Students of Mathematics /[electronic resource] :by Alexey L. Gorodentsev. - 1st ed. 2016. - XX, 564 p. 79 illus., 42 illus. in color.online resource.

Notations and Abbreviations -- 1 Set-Theoretic and Combinatorial Background -- 2 Integers and Residues -- 3 Polynomials and Simple Field Extensions -- 4 Elementary Functions and Power Series Expansions -- 5 Ideals, Quotient Rings, and Factorization -- 6 Vectors -- 7 Duality -- 8 Matrices -- 9 Determinants -- 10 Euclidean Spaces -- 11 Projective Spaces -- 12 Groups -- 13 Description of Groups -- 14 Modules over a Principal Ideal Domain -- 15 Linear Operators -- 16 Bilinear Forms -- 17 Quadratic Forms and Quadrics -- 18 Real Versus Complex -- 19 Hermitian Spaces -- 20 Quaternions and Spinors -- References -- Hints to Selected Exercises -- Index.

This book is the first volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them. The course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra, representation theory, category theory, commutative algebra, Galois theory, and algebraic geometry – topics that are often overlooked in standard undergraduate courses. This textbook is based on courses the author has conducted at the Independent University of Moscow and at the Faculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for independent study.

ISBN: 9783319452852

Standard No.: 10.1007/978-3-319-45285-2doiSubjects--Topical Terms:

579870
Algebra.

LC Class. No.: QA150-272

Dewey Class. No.: 512

Algebra I = Textbook for Students of Mathematics /
LDR:02930nam a22003975i 4500 001 979916
003 DE-He213
005 20200704082735.0
007 cr nn 008mamaa
008 201211s2016 gw | s |||| 0|eng d
020 $a 9783319452852 $9 978-3-319-45285-2
024 7 $a 10.1007/978-3-319-45285-2 $2 doi
035 $a 978-3-319-45285-2
050 4 $a QA150-272
072 7 $a PBF $2 bicssc
072 7 $a MAT002000 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512 $2 23
100 1 $a Gorodentsev, Alexey L. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1115820
245 1 0 $a Algebra I $h [electronic resource] : $b Textbook for Students of Mathematics / $c by Alexey L. Gorodentsev.
250 $a 1st ed. 2016.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a XX, 564 p. 79 illus., 42 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
505 0 $a Notations and Abbreviations -- 1 Set-Theoretic and Combinatorial Background -- 2 Integers and Residues -- 3 Polynomials and Simple Field Extensions -- 4 Elementary Functions and Power Series Expansions -- 5 Ideals, Quotient Rings, and Factorization -- 6 Vectors -- 7 Duality -- 8 Matrices -- 9 Determinants -- 10 Euclidean Spaces -- 11 Projective Spaces -- 12 Groups -- 13 Description of Groups -- 14 Modules over a Principal Ideal Domain -- 15 Linear Operators -- 16 Bilinear Forms -- 17 Quadratic Forms and Quadrics -- 18 Real Versus Complex -- 19 Hermitian Spaces -- 20 Quaternions and Spinors -- References -- Hints to Selected Exercises -- Index.
520 $a This book is the first volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them. The course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra, representation theory, category theory, commutative algebra, Galois theory, and algebraic geometry – topics that are often overlooked in standard undergraduate courses. This textbook is based on courses the author has conducted at the Independent University of Moscow and at the Faculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for independent study.
650 0 $a Algebra. $2 gtt $3 579870
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319452845
776 0 8 $i Printed edition: $z 9783319452869
776 0 8 $i Printed edition: $z 9783319832579
856 4 0 $u https://doi.org/10.1007/978-3-319-45285-2
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)