Overview

The book is an undergraduate textbook on abstract algebra, beginning with the theories of rings and groups. As this is the first really abstract material students meet, the pace here is gentle, and the basic concepts of subring, homomorphism, ideal, etc are developed in detail. Later, as students gain confidence with abstractions, they are led to further developments in group and ring theory (simple groups and extensions, Noetherian rings, an outline of universal algebra, lattices and categories) and to applications such as Galois theory and coding theory. There is also a chapter outlining the construction of the number systems from scratch and proving in three different ways that transcendental numbers exist.

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9780198501947

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Cameron goes somewhat against conventional wisdom by choosing rings over groups as the primary algebraic structure of study. This choice allows an introduction to the ideas of abstract algebra in a setting most students will find a bit more familiar and comfortable. After the obligatory chapter reviewing some of the basics of sets, functions, and logic, Cameron introduces the essentials of rings and fields and then the standard first topics in group theory. . . . Subsequent chapters provide ample opportunity to delve into less traditional and/or more advanced topics. . . . This book will support a very rigorous first course in abstract algebra and contains more than enough material to fill up a two-semester course. Upper-division undergraduate and graduate students. --Choice<br> This book contains more information than can be covered in a year-long algebra course, which allows for flexibility in its use. . . . Cameron's writing style is very enjoyable and reader-friendly. He uses entertaining verbs such as 'whittle' and 'blur' and gives many examples throughout the book. Modern and up-to-date analogies help students relate to concepts . . . Connections between concepts are emphasized. The use of certain terminology and notation is explained, and differences in notation are pointed out. . . . Even though the text is reader-friendly, a high level of rigor is maintained. Kernels are first defined as equivalence relations, polynomials are defined as infinite sequences, and three different proofs of the existence of transcendental numbers are given. . . . Cameron's book also includes some interesting mathematical folklore, which piques the interest of many students. --AmericanMathematical Monthly<br>

Cameron goes somewhat against conventional wisdom by choosing rings over groups as the primary algebraic structure of study. This choice allows an introduction to the ideas of abstract algebra in a setting most students will find a bit more familiar and comfortable. After the obligatory chapter reviewing some of the basics of sets, functions, and logic, Cameron introduces the essentials of rings and fields and then the standard first topics in group theory. . . . Subsequent chapters provide ample opportunity to delve into less traditional and/or more advanced topics. . . . This book will support a very rigorous first course in abstract algebra and contains more than enough material to fill up a two-semester course. Upper-division undergraduate and graduate students. --Choice This book contains more information than can be covered in a year-long algebra course, which allows for flexibility in its use. . . . Cameron's writing style is very enjoyable and reader-friendly. He uses entertaining verbs such as 'whittle' and 'blur' and gives many examples throughout the book. Modern and up-to-date analogies help students relate to concepts . . . Connections between concepts are emphasized. The use of certain terminology and notation is explained, and differences in notation are pointed out. . . . Even though the text is reader-friendly, a high level of rigor is maintained. Kernels are first defined as equivalence relations, polynomials are defined as infinite sequences, and three different proofs of the existence of transcendental numbers are given. . . . Cameron's book also includes some interesting mathematical folklore, which piques the interest of many students. --American Mathematical Monthly

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