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This text offers a clear, efficient exposition of Galois Theory with exercises and complete proofs. Topics include: Cardano's formulas, the Fundamental Theorem, Galois' Great Theorem (solvability for radicals of a polynomial is equivalent to solvability of its Galois Group), and computation of Galois group of cubics and quartics. There are appendices on group theory and on ruler-compass constructions. Developed on the basis of a second-semeste...

This new edition, now in two parts, has been significantly reorganised and many sections have been rewritten. The first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. The second part presents many topics mentioned in the first part in greater depth and in more detail.

This is the second part of the new edition of Advanced Modern Algebra. The material has been significantly reorganised and sections have been rewritten. The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra.

This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. This first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory.

Anyone who has studied abstract algebra and linear algebra as an undergraduate can understand this book. The first six chapters provide material for a first course, while the rest of the book covers more advanced topics. This revised edition retains the clarity of presentation that was the hallmark of the previous editions. From the reviews: "Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas alo...

A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.

A clear, efficient exposition of this topic with complete proofs and exercises, covering cubic and quartic formulas, fundamental theory of Galois theory, insolvability of the quintic, Galoiss Great Theorem, and computation of Galois groups of cubics and quartics. Suitable for first-year graduate students, either as a text for a course or for study outside the classroom, this new edition has been completely rewritten in an attempt to make proof...

A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.

Anyone who has studied abstract algebra and linear algebra as an undergraduate can understand this book. The first six chapters provide material for a first course, while the rest of the book covers more advanced topics. This revised edition retains the clarity of presentation that was the hallmark of the previous editions. From the reviews: "Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas alo...

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

With a wealth of examples as well as abundant applications to Algebra, this is a must-read work: a clearly written, easy-to-follow guide to Homological Algebra.  The author provides a treatment of Homological Algebra which approaches the subject in terms of its origins in algebraic topology.  In this brand new edition the text has been fully updated and revised throughout and new material on sheaves and abelian categories has been added.   App...

This 3-part treatment begins with the mechanics of writing proofs, proceeds to considerations of the area and circumference of circles, and concludes with examinations of complex numbers and their application, via De Moivre's theorem, to real numbers. "I recommend this as a textbook or supplemental textbook." -- "Brian Rogers, The Mathematical Association of America." 1998 edition.