Basic Notions of Algebra by Igor R. Shafarevich (PDF)

Description

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.

User’s Reviews

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

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

⭐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.

⭐An off-hand account of algebra by one of the best authorities of the subject. Recommended as a “serious” pass-time.

⭐Il libro è il frutto della profondità dello sguardo Russo che si è posato sull’Algebra: con esempi tratti da Analisi e Teoria dei Numeri in particolare, il libro è un piccolo capolavoro sulla orme di H. Weyl …

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