Homological Algebra

Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological a

We propose here a study of 'semiexact' and 'homological' categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, whe

In this book we want to explore aspects of coherence in homological algebra, that already appear in the classical situation of abelian groups or abelian categories.Lattices of subobjects are shown to

Accompanying the second edition of the first volume, originally published in 2000, this second volume concentrates on applying the principles to complexes of modules. Most of these results are already

Mathematicians Enochs (U. of Kentucky) and Jenda (Auburn U. Alabama) have revised and expanded their introduction for graduate students to a type of algebra that emerged in 1965, and now includes more

Categories, homological algebra, sheaves and their cohomology furnish useful methods for attacking problems in a variety of mathematical fields. This textbook provides an introduction to these methods, describing their elements and illustrating them by examples.

Homological algebra, because of its fundamental nature, is relevant to many branches of pure mathematics, including number theory, geometry, group theory and ring theory. Professor Northcott's aim is to introduce homological ideas and methods and to show some of the results which can be achieved. The early chapters provide the results needed to establish the theory of derived functors and to introduce torsion and extension functors. The new concepts are then applied to the theory of global dimensions, in an elucidation of the structure of commutative Noetherian rings of finite global dimension and in an account of the homology and cohomology theories of monoids and groups. A final section is devoted to comments on the various chapters, supplementary notes and suggestions for further reading. This book is designed with the needs and problems of the beginner in mind, providing a helpful and lucid account for those about to begin research, but will also be a useful work of reference for s

With a wealth of examples as well as abundant applications to algebra, this is a must-read work: an easy-to-follow, step-by-step guide to homological algebra. The author provides a treatment of homolo

This modern approach to homological algebra by two leading writers in the field is based on the systematic use of the language and ideas of derived categories and derived functors. It describes relati

This modern approach to homological algebra by two leading writers in the field is based on the systematic use of the language and ideas of derived categories and derived functors. It describes relati

From the reviews: "The book is well written. We find here many examples. Each chapter is followed by exercises, and at the end of the book there are outline solutions to some of them. [...] I especial

The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these to

Based on a series of lectures given at Sheffield during 1971–72, this text is designed to introduce the student to homological algebra avoiding the elaborate machinery usually associated with the subject. This book presents a number of important topics and develops the necessary tools to handle them on an ad hoc basis. The final chapter contains some previously unpublished material and will provide additional interest both for the keen student and his tutor. Some easily proven results and demonstrations are left as exercises for the reader and additional exercises are included to expand the main themes. Solutions are provided to all of these. A short bibliography provides references to other publications in which the reader may follow up the subjects treated in the book. Graduate students will find this an invaluable course text as will those undergraduates who come to this subject in their final year.

This precis, comprised of three volumes, of which this book is the first, exposes the mathematical elements which make up the foundations of a number of contemporary scientific methods: modern theory

This ultimate Algebra 1 workbook provides support for students at all levels as they navigate foundational concepts in algebra--featuring helpful recaps, hundreds of practice opportunities, a variety of question types, and a stepped-out solution process. Students love the direct, accessible approach of Everything You Need to Ace Pre-Algebra & Algebra 1 in One Big Fat Notebook. This hands-on workbook takes the same approach of easy-to-understand explanations of key concepts reinforced with examples solved step by step, fun doodles, helpful captions and call outs, and hundreds of exercises to provide additional practice of the Algebra 1 concepts students learn in class. Each question has a detailed answer explanation in the back of the book, allowing students to determine not only whether they got the answer right or wrong, but why.

Algebra I Essentials For Dummies (9781119590965) was previously published as Algebra I Essentials For Dummies (9780470618349). While this version features a new Dummies cover and design, the content i

Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis

The ultimate write-in Algebra 2 Workbook, with more than 130 exercises, plus step-by-step solutions, to give students all the extra practice they need to ace Algebra 2 class. Each chapter in this comprehensive workbook aligns with a chapter in the Algebra 2 study guide, providing students the opportunity to reinforce their Algebra 2 skills with extra in-depth practice. Each Workbook chapter begins with a brief recap of concepts and has 10-15 robust practice questions covering all the skills reviewed in each chapter. A variety of question types like solving equations, graphing functions, applying algebra skills to real world problems, and more, provide a broad assessment of student understanding. In the back of the book, an in-depth solutions section takes readers step-by-step through each problem, showing them how to get the right answer, and helping them check their work. More than a drill and kill workbook, it's a "how to" and "here's why" that can be used to supplement classroom ins

Pre-Algebra/Algebra 1 is the first real taste of high school math, and for most kids it''s like, uh-oh, we’re not in Kansas anymore! But help is here from the The Big Fat Notebooks, the series that ha

Physics is intended for a two-semester college course in introductory physics using algebra and trigonometry.

An essential undergraduate textbook on algebra, topology, and calculusAn Introduction to Analysis is an essential primer on basic results in algebra, topology, and calculus for undergraduate students

Travelling from zero to infinity and back again via algebra, polygons, probability and averages, friendly (but silly) robots guide the reader through the weirdness of mathematics. With up to 300 fascinating facts and 150 riotous gags, this engaging and hilarious book teaches readers why maths is so much weirder than they first thought

Margaret Hamilton loved numbers as a young girl. She knew how many miles it was to the moon (and how many back). She loved studying algebra and geometry and calculus and using math to solve problems i

IGCSE Mathematics Study Guide id designed for students taking the Ed-excel/ CIE IGCSE Mathematics examination. Following the latest IGCSE topic areas, including number properties, algebra, geometry, t

An amazing flap book that shows just how fascinating maths can be.Colourful double page topics introduce numbers, shapes and measuring, fractions, algebra, calculus and pi, and maths in everyday life.

An introduction to simple algebra concepts follows Paul, his sister, and his three cousins as they try and figure out how many tickets it takes to ride the exciting rides at the new amusement park, bu

Homological mirror symmetry has its origins in theoretical physics but is now of great interest in mathematics due to the deep connections it reveals between different areas of geometry and algebra. This book offers a self-contained and accessible introduction to the subject via the representation theory of algebras and quivers. It is suitable for graduate students and others without a great deal of background in homological algebra and modern geometry. Each part offers a different perspective on homological mirror symmetry. Part I introduces the A-infinity formalism and offers a glimpse of mirror symmetry using representations of quivers. Part II discusses various A- and B-models in mirror symmetry and their connections through toric and tropical geometry. Part III deals with mirror symmetry for Riemann surfaces. The main mathematical ideas are illustrated by means of simple examples coming mainly from the theory of surfaces, helping the reader connect theory with intuition.

Homological mirror symmetry has its origins in theoretical physics but is now of great interest in mathematics due to the deep connections it reveals between different areas of geometry and algebra. This book offers a self-contained and accessible introduction to the subject via the representation theory of algebras and quivers. It is suitable for graduate students and others without a great deal of background in homological algebra and modern geometry. Each part offers a different perspective on homological mirror symmetry. Part I introduces the A-infinity formalism and offers a glimpse of mirror symmetry using representations of quivers. Part II discusses various A- and B-models in mirror symmetry and their connections through toric and tropical geometry. Part III deals with mirror symmetry for Riemann surfaces. The main mathematical ideas are illustrated by means of simple examples coming mainly from the theory of surfaces, helping the reader connect theory with intuition.