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An Elementary Approach To Homological Algebra
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Book Synopsis An Elementary Approach to Homological Algebra by : L.R. Vermani
Download or read book An Elementary Approach to Homological Algebra written by L.R. Vermani and published by CRC Press. This book was released on 2003-05-28 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homological algebra was developed as an area of study almost 50 years ago, and many books on the subject exist. However, few, if any, of these books are written at a level appropriate for students approaching the subject for the first time. An Elementary Approach to Homological Algebra fills that void. Designed to meet the needs of beginning
Book Synopsis (Mostly) Commutative Algebra by : Antoine Chambert-Loir
Download or read book (Mostly) Commutative Algebra written by Antoine Chambert-Loir and published by Springer Nature. This book was released on 2021-04-08 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book stems from lectures on commutative algebra for 4th-year university students at two French universities (Paris and Rennes). At that level, students have already followed a basic course in linear algebra and are essentially fluent with the language of vector spaces over fields. The topics introduced include arithmetic of rings, modules, especially principal ideal rings and the classification of modules over such rings, Galois theory, as well as an introduction to more advanced topics such as homological algebra, tensor products, and algebraic concepts involved in algebraic geometry. More than 300 exercises will allow the reader to deepen his understanding of the subject. The book also includes 11 historical vignettes about mathematicians who contributed to commutative algebra.
Book Synopsis An Introduction to Homological Algebra by : Charles A. Weibel
Download or read book An Introduction to Homological Algebra written by Charles A. Weibel and published by Cambridge University Press. This book was released on 1995-10-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.
Book Synopsis An Elementary Approach To Design And Analysis Of Algorithms by : Lekh Rej Vermani
Download or read book An Elementary Approach To Design And Analysis Of Algorithms written by Lekh Rej Vermani and published by World Scientific. This book was released on 2019-05-29 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The book under review is an interesting elaboration that fills the gaps in libraries for concisely written and student-friendly books about essentials in computer science … I recommend this book for anyone who would like to study algorithms, learn a lot about computer science or simply would like to deepen their knowledge … The book is written in very simple English and can be understood even by those with limited knowledge of the English language. It should be emphasized that, despite the fact that the book consists of many examples, mathematical formulas and theorems, it is very hard to find any mistakes, errors or typos.'zbMATHIn computer science, an algorithm is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing and automated reasoning tasks.As an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing 'output' and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.This book introduces a set of concepts in solving problems computationally such as Growth of Functions; Backtracking; Divide and Conquer; Greedy Algorithms; Dynamic Programming; Elementary Graph Algorithms; Minimal Spanning Tree; Single-Source Shortest Paths; All Pairs Shortest Paths; Flow Networks; Polynomial Multiplication, to ways of solving NP-Complete Problems, supported with comprehensive, and detailed problems and solutions, making it an ideal resource to those studying computer science, computer engineering and information technology.
Book Synopsis Elementary Concepts of Topology by : Paul Alexandroff
Download or read book Elementary Concepts of Topology written by Paul Alexandroff and published by Courier Corporation. This book was released on 2012-08-13 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.
Book Synopsis Commutative Algebra by : David Eisenbud
Download or read book Commutative Algebra written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
Book Synopsis Methods of Homological Algebra by : Sergei I. Gelfand
Download or read book Methods of Homological Algebra written by Sergei I. Gelfand and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. 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. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn about a modern approach to homological algebra and to use it in their work.
Book Synopsis Representation Theory by : Alexander Zimmermann
Download or read book Representation Theory written by Alexander Zimmermann and published by Springer. This book was released on 2014-08-15 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.
Book Synopsis Homological Theory of Representations by : Henning Krause
Download or read book Homological Theory of Representations written by Henning Krause and published by Cambridge University Press. This book was released on 2021-11-18 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern developments in representation theory rely heavily on homological methods. This book for advanced graduate students and researchers introduces these methods from their foundations up and discusses several landmark results that illustrate their power and beauty. Categorical foundations include abelian and derived categories, with an emphasis on localisation, spectra, and purity. The representation theoretic focus is on module categories of Artin algebras, with discussions of the representation theory of finite groups and finite quivers. Also covered are Gorenstein and quasi-hereditary algebras, including Schur algebras, which model polynomial representations of general linear groups, and the Morita theory of derived categories via tilting objects. The final part is devoted to a systematic introduction to the theory of purity for locally finitely presented categories, covering pure-injectives, definable subcategories, and Ziegler spectra. With its clear, detailed exposition of important topics in modern representation theory, many of which were unavailable in one volume until now, it deserves a place in every representation theorist's library.
Book Synopsis Categorical Homotopy Theory by : Emily Riehl
Download or read book Categorical Homotopy Theory written by Emily Riehl and published by Cambridge University Press. This book was released on 2014-05-26 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.
Book Synopsis Algebraic Operads by : Jean-Louis Loday
Download or read book Algebraic Operads written by Jean-Louis Loday and published by Springer Science & Business Media. This book was released on 2012-08-08 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many areas of mathematics some “higher operations” are arising. These havebecome so important that several research projects refer to such expressions. Higher operationsform new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the Homotopy Transfer Theorem. Although the necessary notions of algebra are recalled, readers are expected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included. After a low-level chapter on Algebra, accessible to (advanced) undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers.
Book Synopsis Automorphisms of Finite Groups by : Inder Bir Singh Passi
Download or read book Automorphisms of Finite Groups written by Inder Bir Singh Passi and published by Springer. This book was released on 2019-01-12 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups. It is broadly divided into three parts: the first part offers an exposition of the fundamental exact sequence of Wells that relates automorphisms, derivations and cohomology of groups, along with some interesting applications of the sequence. The second part offers an account of important developments on a conjecture that a finite group has at least a prescribed number of automorphisms if the order of the group is sufficiently large. A non-abelian group of prime-power order is said to have divisibility property if its order divides that of its automorphism group. The final part of the book discusses the literature on divisibility property of groups culminating in the existence of groups without this property. Unifying various ideas developed over the years, this largely self-contained book includes results that are either proved or with complete references provided. It is aimed at researchers working in group theory, in particular, graduate students in algebra.
Book Synopsis Algebraic Geometry by : Robin Hartshorne
Download or read book Algebraic Geometry written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Book Synopsis Symbolic Computation with Infinite Sequences of P-groups with Fixed Coclass by : Dörte Feichtenschlager
Download or read book Symbolic Computation with Infinite Sequences of P-groups with Fixed Coclass written by Dörte Feichtenschlager and published by Logos Verlag Berlin GmbH. This book was released on 2010 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classification of finite emph {p-groups is a much investigated problem, though in general it seems impossible. Leedham-Green & Newman defined a new invariant for finite emph {p-groups, the coclass. They suggested to try to classify finite emph {p-groups by coclass. One step towards such a classification was the introduction of so-called infinite coclass sequences by du Sautoy and Eick & Leedham-Green. The groups in such a sequence can be described by a parametrised presentation. For prime 2 and a fixed coclass r it holds that almost all 2-groups of coclass r fall into finitely many infinite coclass sequences. So describing the infinite sequences yields an almost classification in these cases. In this work it is shown that using the parametrised presentations one can compute certain invariants for almost all groups in an infinite coclass sequence, especially the Schur multiplicator. This is done by introducing a way to work with almost all groups at a time by a symbolic computation.
Book Synopsis Difference Algebra by : Alexander Levin
Download or read book Difference Algebra written by Alexander Levin and published by Springer Science & Business Media. This book was released on 2008-04-19 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Difference algebra grew out of the study of algebraic difference equations with coefficients from functional fields. The first stage of this development of the theory is associated with its founder, J.F. Ritt (1893-1951), and R. Cohn, whose book Difference Algebra (1965) remained the only fundamental monograph on the subject for many years. Nowadays, difference algebra has overgrown the frame of the theory of ordinary algebraic difference equations and appears as a rich theory with applications to the study of equations in finite differences, functional equations, differential equations with delay, algebraic structures with operators, group and semigroup rings. The monograph is intended for graduate students and researchers in difference and differential algebra, commutative algebra, ring theory, and algebraic geometry. The book is self-contained; it requires no prerequisites other than the knowledge of basic algebraic concepts and a mathematical maturity of an advanced undergraduate.
Book Synopsis Lecture Notes in Algebraic Topology by : James F. Davis
Download or read book Lecture Notes in Algebraic Topology written by James F. Davis and published by American Mathematical Society. This book was released on 2023-05-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Book Synopsis Advanced Algebra by : Anthony W. Knapp
Download or read book Advanced Algebra written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2007-10-11 with total page 757 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole.
