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Abstract algebraan introductory course /

Lee, Gregory T.

Abstract algebraan introductory course /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Abstract algebraby Gregory T. Lee.
其他題名:	an introductory course /
作者:	Lee, Gregory T.
出版者:	Cham :Springer International Publishing :2018.
面頁冊數:	xi, 302 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Algebra, Abstract.
電子資源:	http://dx.doi.org/10.1007/978-3-319-77649-1
ISBN:	9783319776491$q(electronic bk.)

Abstract algebraan introductory course /
Lee, Gregory T.

Abstract algebraan introductory course /[electronic resource] :by Gregory T. Lee. - Cham :Springer International Publishing :2018. - xi, 302 p. :ill., digital ;24 cm. - Springer undergraduate mathematics series,1615-2085. - Springer undergraduate mathematics series..

Part I Preliminaries -- 1 Relations and Functions -- 2 The Integers and Modular Arithmetic -- Part II Groups -- 3 Introduction to Groups -- 4 Factor Groups and Homomorphisms -- 5 Direct Products and the Classification of Finite Abelian Groups -- 6 Symmetric and Alternating Groups -- 7 The Sylow Theorems -- Part III Rings -- 8 Introduction to Rings -- 9 Ideals, Factor Rings and Homomorphisms -- 10 Special Types of Domains -- Part IV Fields and Polynomials -- 11 Irreducible Polynomials -- 12 Vector Spaces and Field Extensions -- Part V Applications -- 13 Public Key Cryptography -- 14 Straightedge and Compass Constructions -- A The Complex Numbers -- B Matrix Algebra -- Solutions -- Index.

This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite abelian groups. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. The final part contains applications to public key cryptography as well as classical straightedge and compass constructions. Explaining key topics at a gentle pace, this book is aimed at undergraduate students. It assumes no prior knowledge of the subject and contains over 500 exercises, half of which have detailed solutions provided.

ISBN: 9783319776491$q(electronic bk.)

Standard No.: 10.1007/978-3-319-77649-1doiSubjects--Topical Terms:

185961
Algebra, Abstract.

LC Class. No.: QA162

Dewey Class. No.: 512.02

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505 0 $a Part I Preliminaries -- 1 Relations and Functions -- 2 The Integers and Modular Arithmetic -- Part II Groups -- 3 Introduction to Groups -- 4 Factor Groups and Homomorphisms -- 5 Direct Products and the Classification of Finite Abelian Groups -- 6 Symmetric and Alternating Groups -- 7 The Sylow Theorems -- Part III Rings -- 8 Introduction to Rings -- 9 Ideals, Factor Rings and Homomorphisms -- 10 Special Types of Domains -- Part IV Fields and Polynomials -- 11 Irreducible Polynomials -- 12 Vector Spaces and Field Extensions -- Part V Applications -- 13 Public Key Cryptography -- 14 Straightedge and Compass Constructions -- A The Complex Numbers -- B Matrix Algebra -- Solutions -- Index.
520 $a This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite abelian groups. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. The final part contains applications to public key cryptography as well as classical straightedge and compass constructions. Explaining key topics at a gentle pace, this book is aimed at undergraduate students. It assumes no prior knowledge of the subject and contains over 500 exercises, half of which have detailed solutions provided.
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