Abstract Algebra: An Introductory Course (Springer Undergraduate Mathematics Series) by Gregory T. Lee (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “The book is very clearly written. The author successfully presents the material in an appealing way. A big number of examples enriches the text and enlightens the key topics. Exercises of different level are included at the end of each chapter and solutions to approximately half of the exercises are included at the very end of the book. In summary … the book can definitely be recommended as text book for a first introduction to abstract algebra.” (C. Fuchs, Internationale Mathematische Nachrichten IMN, Vol. 73 (240), April, 2019)“The book provides the reader with valuable technical information regarding the introductory notions and main results of abstract algebra. The author presents concepts, theorems and applications in a very clear and fluent way within the manuscript. Thus, ‘Abstract Algebra. An Introductory Course’ is obviously a well written document with respect to the field of abstract algebra.” (Diana Maimut, zbMATH 1401.00003, 2019) From the Back Cover 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. About the Author Gregory T. Lee is a professor at Lakehead University specializing in group rings, a branch of abstract algebra. He has published numerous papers on the subject, as well as a monograph with Springer. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is just a catalog of theorems, definitions, and proofs. No applications or worked examples. This in NOT a text book, I consider ir a reference book.

⭐Excellent text with clear proofs and a nice survey of key topics in abstract algebra. For those using the text for self-study (n.b., I was an undergraduate math major almost 20 years ago, and we used Artin then; I was just revisiting the subject for fun), I found most of the exercises doable — the hardest ones are usually the even-numbered ones, which don’t have solutions. A few had me really stumped, and I had to resort to e-mailing the author for hints, or scouring the internet for solutions. I think those exercises which require some measure of creativity or ingenuity ought to have some hints, or be demarcated with an asterisk.

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