Wholeheartedly recommended to every student and user of mathematics, this is an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields studied in every university maths course, through Lie groups to cohomology and category theory, the author shows how the origins of each concept can be related to attempts to model phenomena in physics or in other branches of mathematics. Required reading for mathematicians, from beginners to experts.
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Editorial Reviews
Review
From the reviews: "This is one of the few mathematical books, the reviewer has read from cover to cover ... The main merit is that nearly on every page you will find some unexpected insights..." (Zentralblatt für Mathematik und Ihre Grenzgebiete, 1991) "...which I read like a novel and undoubtedly will become a classic. ... A merit of the book under review is that it contains several important articles from journals which are not all so easily accessible. ... Furthermore, at the end of the book, there are some Notes by the author which are indispensible for the necessary historical background information. ... This valuable book should be on the shelf of every algebraist and algebraic geometer." (Nieuw Archief voor Wiskunde, 1992) "... There are few proofs in full, but there is an exhilarating combination of sureness of foot and lightness of touch in the exposition ... which transports the reader effortlessly across the whole spectrum of algebra.... The challenge to Ezekiel, "Can these bones live?" is, all too often, the reaction of students when introduced to the bare bones of the concepts and constructs of modern algebra. Shafarevich's book - which reads as comfortably as an extended essay - breathes life into the skeleton and will be of interest to many classes of readers..." (The Mathematical Gazette, 1991) "... According to the preface, the book is addressed to "students of mathematics in the first years of an undergraduate course, or theoretical physicists or mathematicians from outside algebra wanting to get an impression of the spirit of algebra and its place in mathematics." I think that this promise is fully justified. The beginner, the experts and also the interested scientist who had contact with algebraic notions - all will read this exceptional book with great pleasure and benefit." (Zeitschrift für Kristallographie, 1991) "This is a truly wonderful book, one that anyone teaching algebra should read and which should be pointed out to talented students, particularly those who want to know a little more about what and why abstract algebra is. This book is volume 1 in the Algebra section of the Springer Encyclopedia of Mathematical Sciences … . The examples are particularly well chosen, simple enough to understand… . one that will enrich your understanding of algebra and deepen your knowledge of mathematics as a whole." (Fernando Q. Gouvêa, MathDL, March, 2007)
From the Back Cover
From the reviews: "This is one of the few mathematical books, the reviewer has read from cover to cover ... The main merit is that nearly on every page you will find some unexpected insights..." Zentralblatt für Mathematik und Ihre Grenzgebiete, 1991 "...which I read like a novel and undoubtedly will become a classic. ... A merit of the book under review is that it contains several important articles from journals which are not all so easily accessible. ... Furthermore, at the end of the book, there are some Notes by the author which are indispensible for the necessary historical background information. ... This valuable book should be on the shelf of every algebraist and algebraic geometer." Nieuw Archief voor Wiskunde, 1992 "... There are few proofs in full, but there is an exhilarating combination of sureness of foot and lightness of touch in the exposition ... which transports the reader effortlessly across the whole spectrum of algebra.... The challenge to Ezekiel, "Can these bones live?" is, all too often, the reaction of students when introduced to the bare bones of the concepts and constructs of modern algebra. Shafarevich's book - which reads as comfortably as an extended essay - breathes life into the skeleton and will be of interest to many classes of readers..." The Mathematical Gazette, 1991 "... According to the preface, the book is addressed to "students of mathematics in the first years of an undergraduate course, or theoretical physicists or mathematicians from outside algebra wanting to get an impression of the spirit of algebra and its place in mathematics." I think that this promise is fully justified. The beginner, the experts and also the interested scientist who had contact with algebraic notions - all will read this exceptional book with great pleasure and benefit." Zeitschrift für Kristallographie, 1991
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Most Helpful Customer Reviews
21 of 24 people found the following review helpful:
5.0 out of 5 stars
Modern Mathematics from the viewpoint of Algebra.,
By quad@wisdom.weizmann.ac.il (Seoul,Korea) - See all my reviews
This review is from: Basic Notions of Algebra (Paperback)
The author explains not just the definitions but also the 'philosophy' of algebra with highly non- trivial examples from geometry,analysis & topology not to mention algebra itself. Examples motivate the concepts and show their usefulness. There is little number of formal proofs, but theorems are usually supported by natural 'explanations' which may be even more adequate. Frequently a single example in this book can replace a substantial theory of the corresponding subject. For example, about axioms of projective geometry. A reader with no knowledge of modern algebra can try reading it ,but it would be more interesting if familiar with subjects of undergraduate mathe matics. Then an undergraduate reader will get some ideas how modern math uses sophiscated tools from algebra to understand other subjects. Another merit of this book is that it can be smoothly followed by the author's famous 2-volume textbook on algebraic geometry.
6 of 13 people found the following review helpful:
5.0 out of 5 stars
Recreational but no-nonsense.,
By eltnjhon@jp.im.com (Tokyo) - See all my reviews
This review is from: Basic Notions of Algebra (Paperback)
An off-hand account of algebra by one of the best authorities of the subject. Recommended as a "serious" pass-time.
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Inside This Book
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First Sentence:
What is algebra? Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
stabiliser subgroup, central division algebras, purely imaginary quaternions, irreducible algebraic curve, semisimple module, semisimple ring, complex analytic manifold, crystallographic groups, universal mapping property, ring axioms, simple submodules, field axioms, semisimple algebras, torsion module, real number field, finite type, homomorphisms theorem, finite rank, algebraic groups Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Jordan's Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
What is algebra? Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
stabiliser subgroup, central division algebras, purely imaginary quaternions, irreducible algebraic curve, semisimple module, semisimple ring, complex analytic manifold, crystallographic groups, universal mapping property, ring axioms, simple submodules, field axioms, semisimple algebras, torsion module, real number field, finite type, homomorphisms theorem, finite rank, algebraic groups Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Jordan's Theorem 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)
23
books
cite this book:
See all 23 books citing this book
- Algebra IV: Infinite Groups. Linear Groups (Encyclopaedia of Mathematical Sciences) (v. 4) by A.I. Kostrikin in Back Matter (1), and Back Matter (2)
- Algebraic Geometry II: Cohomology of Algebraic Varieties. Algebraic Surfaces (Encyclopaedia of Mathematical Sciences) (v. 2) by I.R. Shafarevich on page 125, and Back Matter
- Moonshine beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics (Cambridge Monographs on Mathematical Physics) by Terry Gannon in Back Matter
- Ordinary Differential Equations and Smooth Dynamical Systems by S.Kh. Aranson in Back Matter
- Several Complex Variables II: Function Theory in Classical Domains. Complex Potential Theory (Encyclopaedia of Mathematical Sciences) (v. 2) by G.M. Khenkin in Back Matter
See all 23 books citing this book
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