This book gives a high level introduction to the main concepts of modern algebra. It contains numerous applications, such as: Polya colouring theory, latin squares, Steiner systems and error correcting codes are described, along with group and ring theory, which are all designed to show the relevance of algebra today. There are nearly 400 problems of varying degrees of difficulty, in order to test the reader's skill and progress.
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Book Description
Editorial Reviews
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"Altogether, this book represents a very gentle, user-friendly and skillful introduction to undergraduate abstract algebra for students in various fields of science. [...] a very experienced teacher has here presented a valuable introductory text on abstract algebra that can universally be used as a source for a one or two semester course on the subject for students in their second or third year of study: Without any doubt, this text is also very suitable for private study and exam preparation of undergraduates."Werner Kleinert in: Zentralblatt MATH 10/2003
About the Author
Derek J. S. Robinson is currently Professor of Mathematics at the University of Illinois in Urbana-Champaign.
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3 of 3 people found the following review helpful:
5.0 out of 5 stars
Compact introduction to algebra,
This review is from: An Introduction to Abstract Algebra (De Gruyter Textbook) (Paperback)
The first thing to not about this book is that it is dense. In my abstract algebra course we covered chapters 3-5 in an entire semester. However, it contained every proof we needed in class, and although it reads slowly, it was usually crystal-clear. Especially good is its treatment of group actions, which is sometimes lacking in introductory-level algebra books. There is a lot of additional material -- the author recommends covering chapters 1-7 in one semester, which may be feasible at institutions like MIT, but for the majority of students, the information contained in this book would be more than a year's worth. Chapter 8 contains almost a semester's worth of advanced linear algebra. Sometimes I wish there were a few more exercises in each chapter; especially in the beginning, because the proofs were relatively easy, it seemed like there wasn't a good enough selection of topics. The book is mercifully cheap, but even though it's paperback, it's very sturdy, and for such a low-cost choice, it has tons of content. Recommended.
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Inside This Book
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First Sentence:
The concepts introduced in this chapter are truly fundamental and underlie almost every branch of mathematics. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
finite solvable group, splitting field, defining relators, commutative ring with identity, ring axioms, permutation representation, finite group acting, transmitted codeword, check matrix, nilpotent class, orthogonal latin squares, cyclotomic polynomial, projective groups, triple system, irreducible polynomial, disjoint cycles, prime power order, finite simple groups, maximal subgroup, solvable groups, ascending chain condition Key Phrases - Capitalized Phrases (CAPs): (learn more)
Zorn's Lemma, Lagrange's Theorem, Euclid's Lemma, Gauss's Lemma, Sylow's Theorem, Well-Ordering Law, Correspondence Theorem, Fundamental Theorem of Galois Theory, First Isomorphism Theorem, Fundamental Theorem of Arithmetic, Second Isomorphism Theorem, Burnside's Lemma, Eisenstein's Criterion, Euclidean Algorithm, Axiom of Choice, Binomial Theorem, Cauchy's Theorem, Proof Let, Therefore Ker, Find the Galois, Modular Law New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The concepts introduced in this chapter are truly fundamental and underlie almost every branch of mathematics. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
finite solvable group, splitting field, defining relators, commutative ring with identity, ring axioms, permutation representation, finite group acting, transmitted codeword, check matrix, nilpotent class, orthogonal latin squares, cyclotomic polynomial, projective groups, triple system, irreducible polynomial, disjoint cycles, prime power order, finite simple groups, maximal subgroup, solvable groups, ascending chain condition Key Phrases - Capitalized Phrases (CAPs): (learn more)
Zorn's Lemma, Lagrange's Theorem, Euclid's Lemma, Gauss's Lemma, Sylow's Theorem, Well-Ordering Law, Correspondence Theorem, Fundamental Theorem of Galois Theory, First Isomorphism Theorem, Fundamental Theorem of Arithmetic, Second Isomorphism Theorem, Burnside's Lemma, Eisenstein's Criterion, Euclidean Algorithm, Axiom of Choice, Binomial Theorem, Cauchy's Theorem, Proof Let, Therefore Ker, Find the Galois, Modular Law New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 15
books:
See all 15 books this book cites
- Introduction to Field Theory by Iain T. Adamson in Back Matter
- Abstract Algebra, 3rd Edition by David S. Dummit in Back Matter
- A Course in Linear Algebra With Applications by Derek J. S. Robinson in Back Matter
- Galois Theory (Universitext) by Joseph Rotman in Back Matter
- First Course in Abstract Algebra, A (3rd Edition) by Joseph J. Rotman in Back Matter
See all 15 books this book cites
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