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Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. It begins with an introduction to Gröbner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case with new application to coherent systems in reliability and two level factorial designs. The work paves the way, in the last two chapters, for the application of computer algebra to discrete probability and statistical modelling through the important concept of an algebraic statistical model.As the first book on the subject, Algebraic Statistics presents many opportunities for spin-off research and applications and should become a landmark work welcomed by both the statistical community and its relatives in mathematics and computer science. ... Read more

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Approximate Commutative Algebra is an emerging field of research which endeavours to bridge the gap between traditional exact Computational Commutative Algebra and approximate numerical computation. The last 50 years have seen enormous progress in the realm of exact Computational Commutative Algebra, and given the importance of polynomials in scientific modelling, it is very natural to want to extend these ideas to handle approximate, empirical data deriving from physical measurements of phenomena in the real world. In this volume nine contributions from established researchers describe various approaches to tackling a variety of problems arising in Approximate Commutative Algebra. ... Read more

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This second volume of this text covers the classical aspects of the theory of groups and their representations. It also offers a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras. It reviews key recent developments in the theory of special ring classes including Frobenius, quasi-Frobenius, and others.

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The authors provide a concise introduction to topics in commutative algebra, with an emphasis on worked examples and applications. Their treatment combines elegant algebraic theory with applications to number theory, problems in classical Greek geometry, and the theory of finite fields, which has important uses in other branches of science. Topics covered include rings and Euclidean rings, the four-squares theorem, fields and field extensions, finite cyclic groups and finite fields. The material can serve equally well as a textbook for an entire course or as preparation for the further study of abstract algebra. ... Read more

Customer Reviews (1)

Great Math Book
This is one of the best mathematics books I own. Chatters writting is clear and intuitive. ... Read more

Product Description
This is an English translation of the now classic "Algbre Locale - Multiplicits" originally published by Springer as LNM 11. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities. Many modifications to the original French text have been made for this English edition, making the text easier to read, without changing its intended informal character. ... Read more

Customer Reviews (1)

Serre as usual
This book is crystal clear and reads like a bedtime story.I wish I had it when I took commutative algebra. ... Read more

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This volume contains refereed papers on themes explored at the AMS-IMS-SIAM Summer Research Conference, Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra, held at Mount Holyoke College in 1992. The conference featured a series of one-hour invited lectures on recent advances in commutative algebra and interactions with such areas as algebraic geometry, representation theory, and combinatorics. The major themes of the conference were tight closure Hilbert functions, birational algebra, free resolutions and the homological conjectures, Rees algebras, and local cohomology. With contributions by several leading experts in the field, this volume provides an excellent survey of current research in commutative algebra. ... Read more

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The papers in this volume, some of which are expository, some strictly research, and some a combination, reflect the intent of the program. They give a cross-section of what is happening now in this area. Nearly all of the manuscripts were solicited from speakers at the conference, and in most instances the manuscript is based on the conference lecture. The editors hope that they will be of interest and of use both to experts and neophytes in the field. ... Read more

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From the reviews:

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This book is the first to be devoted entirely to fuzzy abstract algebra. It presents an up-to-date version of fuzzy commutative algebra, and focuses on the connection between L-subgroups of a group, and L-subfields of a field. In particular, an up-to-date treatment of nonlinear systems of fuzzy intersection equations is given. ... Read more

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This book gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. It gives a comprehensive treatment of Rees algebras and multiplicity theory while pointing to applications in many other problem areas. Its main goal is to provide complexity estimates by tracking numerically invariants of the structures that may occur.

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The present book is devoted to a study of relative Prüfer rings and Manis valuations, with an eye to application in real and p-adic geometry. If one wants to expand on the usual algebraic geometry over a non-algebraically closed base field, e.g. a real closed field or p-adically closed field, one typically meets lots of valuation domains. Usually they are not discrete and hence not noetherian. Thus, for a further develomemt of real algebraic and real analytic geometry in particular, and certainly also rigid analytic and p-adic geometry, new chapters of commutative algebra are needed, often of a non-noetherian nature. The present volume presents one such chapter. ... Read more

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This book provides a thorough and self-contained introduction to the theory of commutative Banach algebras, aimed at graduate students with a basic knowledge of functional analysis, topology, complex analysis, measure theory, and group theory. At the core of this text are the chapters on Gelfand's theory, regularity and spectral synthesis. Special emphasis is placed on applications in abstract harmonic analysis and on treating many special classes of commutative Banach algebras, such as uniform algebras, group algebras and Beurling algebras, and tensor products. Detailed proofs and a variety of exercises are given. The book is intended for graduate students taking a course on Banach algebras, with various possible specializations, or a Gelfand theory based course in harmonic analysis.

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In this introduction to commutative algebra, the author choses a route that leads the reader through the essential ideas, without getting embroiled in technicalities. He takes the reader quickly to the fundamentals of complex projective geometry, requiring only a basic knowledge of linear and multilinear algebra and some elementary group theory. The author divides the book into three parts. In the first, he develops the general theory of noetherian rings and modules. He includes a certain amount of homological algebra, and he emphasizes rings and modules of fractions as preparation for working with sheaves. In the second part, he discusses polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalization lemma and Hilbert's Nullstellensatz, the author introduces affine complex schemes and their morphisms; he then proves Zariski's main theorem and Chevalley's semi-continuity theorem. Finally, the author's detailed study of Weil and Cartier divisors provides a solid background for modern intersection theory. This is an excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra. ... Read more

Customer Reviews (1)

brief, but good
Peskine doesn't give a lot of explanations (he manages to cover on 30 pages what usually takes up half a book) and the exercises are tough, but the book is nevertheless well written, which makes it pretty easy to read and understand. Recommended for everyone willing to work their way through his one-line proofs ("Obvious.")! ... Read more

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This text introduces readers to the algebraic concepts of group and rings, providing a comprehensive discussion of theory as well as a significant number of applications for each.

Customer Reviews (8)

nothing abstract in this one
this book is the reason i changed my major from pure to applied mathematics. if you paid attention in your second grade arithmetic class, you won't learn anything new from this book. we used this in my so called "abstract algebra" course, but the author is too narrow minded to think of any algebra outside of arithmetic. i had perfect grades in the class, but i dropped it before the final because i was too disgusted with the presentation. you're better off going with a text on formal language theory like aho and ullman, or maybe algebra by birkhoff and mac lane. you could even write yourself something more informative on a 3 by 5 card.

Just okay.
Not a lot of details in this book.Mostly just theorems and their proofs.

Ugh
This textbook is the first math book I've had that doesn't have any homework answers in the back of the book. Instead, there are "helpful" hints for selected problems that aren't any help at all. This is very frustrating because I never know if I'm getting the right answer or not.

Excellent Introduction To Algebra
Rotman's book is a standard for first courses in Abstract Algebra.The book is easy to read and includes plenty of problems to work on.He even includes several standard syllabi in the preface, depending on the type of course that may be taught with it.It begins with some number theory, then goes into the traditional group and ring concepts.The only reason I would say to not buy this book is if you really don't like the theorem-proof, theorem-proof kind of writing, but if you don't, you're likely not interested in Abstract Algebra anyway.An excellent book for learning as well as reference.

no better than the first edition
It is always easy to add something to than to get rid of something from the book. I guess this is the case of the author when he prepares the second edition. However, I prefer the first edition because it is more readable, enjoyable, and most importantly, contains just enough information for the introduction to abstract algebra. There are huge number of textbooks on abstract algbra, and making another would not be the author's purpose of the revision, I hope, but it looks it is.
By adding more subjects in detail to the second edition, now it looks the same as any other, only to loose its expository and conversational style of writings, and became a reference-style textbook. ... Read more

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Designed for a one-semester course in mathematics, this textbook presents a concise and practical introduction to commutative algebra in terms of normal (normalized) structure. It shows how the nature of commutative algebra has been used by both number theory and algebraic geometry. Many worked examples and a number of problem (with hints) can be found in the volume. It is also a convenient reference for researchers who use basic commutative algebra. ... Read more