This comprehensive presentation of modern algebra proceeds from the simplest structures involving only binary operation to the more complex. The authors believe that the student can develop the ability to construct and present proofs of theorems more easily when working with a system in which only one binary operation is under consideration. Features of this book include: the treatment of Z of convergence classes modulo n, discussed throughout most of the book; optional sections on some results of finite abelian groups; and real and complex numbers included for the benefit of students who would not otherwise cover this material. The second edition has new sections which place more emphasis on the composition of mappings, expanded treatment of mathematical introduction, additional material on rings and more thorough coverage of polynomials. Numerous examples, exercise sets and problems are included, key words and phrases are summarized at the end of each chapter and many figures and tables help the student to assimilate material more easily. References are listed at the end of the book, together with answers to about half of the computational exercises. The answers for the remaining computational exercises and some of the answers requiring proofs are available in the Instructors' Manual. This book should be of interest to degree and diploma students on introductory courses in algebra.
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Editorial Reviews
About the Author
Jimmie Gilbert is Professor of Mathematics at the University of South Carolina, Spartanburg.
Linda Gilbert is Professor of Mathematics at the University of South Carolina, Spartanburg. --This text refers to an out of print or unavailable edition of this title.
Linda Gilbert is Professor of Mathematics at the University of South Carolina, Spartanburg. --This text refers to an out of print or unavailable edition of this title.
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Most Helpful Customer Reviews
14 of 14 people found the following review helpful:
5.0 out of 5 stars
Great Book,
By Dillon (Houston, Texas, USA) - See all my reviews
This review is from: Elements of Modern Algebra (Hardcover)
I found the ideas in this book to be very accesible to the student with little mathematics experience (as I have). It is very straight foward, contains illuminating example problems, and even has an application section at the end of each chapter. Many abstract algebra books assume that you can prove anything. However, Gilbert's book focuses on the techniques of learning how to prove.
9 of 9 people found the following review helpful:
5.0 out of 5 stars
thats how math books should be written!!! (but plz, change that price there),
This review is from: Elements of Modern Algebra (Hardcover)
It is surely one of the books I most enjoyed!!
But its pricey, thats why a lot of colleges (or professors) try to avoid it. The book has eight chapters: 1) Fundamentals 2) The integers 3) Groups 4) More on Groups 5) Rings, Integral domains, and fields 6) More on rings 7) Real and Complex Numbers 8) Ploynomials. Definitions and Theorems stand out in Boxes, then later comes the examples!! (Plz Mathematicians who write books, just take a look here, see how nicely a book can be written, then go for the challenge). one of the good things in this book, is that it does not assume you took a class in number theory before, so it introduces in the first two chapters everything (from a typical number theory class) that you would need in modern algebra class. (that might be a drawback for a student who took number theory class, and his professor is determined to start from the first chapter in this book). other than the definitions and theorems stand out clearly, The author give examples on how that theorem can be used!! and The examples sometimes are really good!! What's best in this book, are the problems after each chapter, they rank from direct applications to theorems, to CHallenging problems! (at least challenging for me). But note that some of the problems depend on each other! so if ur stuck on one problem, that means you might need to use a result from an earlier problem in the same chapter. its a drawback that the author does not say "use problem ... to solve this one", I think they assume that anyone solving the problems, is solving all of them in sequence, which what students SHOULD do. There is no way you can get a good grasp on the material in this book, unless you are a genius, or you solve ALL the problems after each chapter (at least a very good amount of them). I found best thing to do is try solving them in sequence, if you dont have time to solve all of them, then skip the ones that you REALLY think you can solve, and this way you can use the result later on. I would recommend this book to anyone interested in modern (abstract) algebra! But I think a pre-requisite to self-study in this book is exposition to how to write proofs rigorously. (well sure thats the pre-requisite for any math course, but usually this subject is one of the first subjects studied in upper level math courses, and you better take another course that exposes you to how to write proofs, if your buying this book for self-study).
8 of 8 people found the following review helpful:
5.0 out of 5 stars
An excellent introduction to higher mathematics,
By Lee G. Gilman (Charlotte, NC, USA) - See all my reviews
This review is from: Elements of Modern Algebra (Hardcover)
I thoroughly enjoyed my modern algebra class, with an excellent professor and this excellent book. The book is very clearly written, and the concepts of sets, groups, rings, fields, and number systems are explained with detail. This is especially important since my summer research in number theory requires an understanding of these algebraic structures.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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integral domains, public key cryptosystem, unique factorization theorem, octic group, reverse order law, ordered integral domain, induction postulate, use complete induction, commutative ring with unity, translation cipher, affine cipher, distinct left cosets, distinct right cosets, abelian group with respect, parity check digit, identity element with respect, right distributive law, distinct nth roots, left distributive law, mapping composition, ring with respect, last nonzero remainder, distinct generators, finite permutation groups, rational zeros Key Phrases - Capitalized Phrases (CAPs): (learn more)
Cengage Learning, All Rights Reserved, False Label, Proof Let, Euclidean Algorithm, The Integers, Proof Assume, Division Algorithm, Proof Suppose, Prove Theorem, Well-Ordering Theorem, Lagrange's Theorem, Congruence of Integers, Eisenstein's Irreducibility Criterion, Finite Abelian Groups, Repeat Exercise, Direct Sums, Fundamentals Example, Cayley's Theorem, Ring Homomorphisms, Exercises In Exercises, Some Results, Work Exercise, Fundamental Theorem of Algebra, Properties of Composite Mappings Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
integral domains, public key cryptosystem, unique factorization theorem, octic group, reverse order law, ordered integral domain, induction postulate, use complete induction, commutative ring with unity, translation cipher, affine cipher, distinct left cosets, distinct right cosets, abelian group with respect, parity check digit, identity element with respect, right distributive law, distinct nth roots, left distributive law, mapping composition, ring with respect, last nonzero remainder, distinct generators, finite permutation groups, rational zeros Key Phrases - Capitalized Phrases (CAPs): (learn more)
Cengage Learning, All Rights Reserved, False Label, Proof Let, Euclidean Algorithm, The Integers, Proof Assume, Division Algorithm, Proof Suppose, Prove Theorem, Well-Ordering Theorem, Lagrange's Theorem, Congruence of Integers, Eisenstein's Irreducibility Criterion, Finite Abelian Groups, Repeat Exercise, Direct Sums, Fundamentals Example, Cayley's Theorem, Ring Homomorphisms, Exercises In Exercises, Some Results, Work Exercise, Fundamental Theorem of Algebra, Properties of Composite Mappings Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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