Algebra I
Textbook for Students of Mathematics
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Beschreibung
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.
This book is the first volume of an intensive “Russian-style” two-year graduate 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.
Challenging amount of material thoughtfully organized for deep and fast learning Large collection of exercises equipped with hints and a lot of problems for independent solution Simple modern explanation of subjects usually omitted in basic courses, such as representations of the symmetric group, geometry of algebraic varieties, meaty aspects of the category theory etc Includes supplementary material: sn.pub/extras
Autor*in
Alexey L. Gorodentsev
Themen in »Algebra I«
Fields Rings Modules Groups Linear Algebra Multilinear Algebra Representation Theory Commutative Algebra Algebraic Varieties Galois Theory
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“The book weaves together a great deal of classical material with a modern approach. … the book consists of the large number of exercises … which the author assigns for homework and the problems for independent study provided at the end of each chapter; a student who works through these will be well rewarded. … instructors would find it more suitable for a graduate course in which the students are already familiar with the more elementary parts of the material.” (John D. Dixon, zbMATH 1359.15001, 2017)
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