Algebra Chapter 0

  algebra chapter 0: Algebra: Chapter 0 Paolo Aluffi, 2021-11-09 Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
  algebra chapter 0: Algebra: Chapter 0 Paolo Aluffi, 2009 Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
  algebra chapter 0: Algebra Paolo Aluffi, 2009 Offers an introduction to the main topics of algebra. This book also offers introduction of categories used as a unifying theme in the presentation of the main topics. It includes approximately 1,000 exercises that provide practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics.
  algebra chapter 0: Algebra Paolo Aluffi, 2021-06-03 A conversational introduction to abstract algebra from a modern, rings-first perspective, including a treatment of modules.
  algebra chapter 0: Categories and Sheaves Masaki Kashiwara, Pierre Schapira, 2005-12-19 Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.
  algebra chapter 0: Algebra I. Martin Isaacs, 2009 as a student. --Book Jacket.
  algebra chapter 0: An Invitation to General Algebra and Universal Constructions George M. Bergman, 2015-02-05 Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.
  algebra chapter 0: Introduction to Abstract Algebra W. Keith Nicholson, 2012-03-20 Praise for the Third Edition . . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . .—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetric polynomials The proof of Wedderburn's theorem on finite division rings The proof of the Wedderburn-Artin theorem Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.
  algebra chapter 0: Graduate Algebra Louis Halle Rowen, 2006 This book is an expanded text for a graduate course in commutative algebra, focusing on the algebraic underpinnings of algebraic geometry and of number theory. Accordingly, the theory of affine algebras is featured, treated both directly and via the theory of Noetherian and Artinian modules, and the theory of graded algebras is included to provide the foundation for projective varieties. Major topics include the theory of modules over a principal ideal domain, and its applicationsto matrix theory (including the Jordan decomposition), the Galois theory of field extensions, transcendence degree, the prime spectrum of an algebra, localization, and the classical theory of Noetherian and Artinian rings. Later chapters include some algebraic theory of elliptic curves (featuring theMordell-Weil theorem) and valuation theory, including local fields. One feature of the book is an extension of the text through a series of appendices. This permits the inclusion of more advanced material, such as transcendental field extensions, the discriminant and resultant, the theory of Dedekind domains, and basic theorems of rings of algebraic integers. An extended appendix on derivations includes the Jacobian conjecture and Makar-Limanov's theory of locally nilpotent derivations. Grobnerbases can be found in another appendix. Exercises provide a further extension of the text. The book can be used both as a textbook and as a reference source.
  algebra chapter 0: Abstract Algebra Paul B. Garrett, 2007-09-25 Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal mapping properties, rather than by constructions whose technical details are irrelevant. Addresses Common Curricular Weaknesses In addition to standard introductory material on the subject, such as Lagrange's and Sylow's theorems in group theory, the text provides important specific illustrations of general theory, discussing in detail finite fields, cyclotomic polynomials, and cyclotomic fields. The book also focuses on broader background, including brief but representative discussions of naive set theory and equivalents of the axiom of choice, quadratic reciprocity, Dirichlet's theorem on primes in arithmetic progressions, and some basic complex analysis. Numerous worked examples and exercises throughout facilitate a thorough understanding of the material.
  algebra chapter 0: Undergraduate Algebra Serge Lang, 2013-06-29 The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group
  algebra chapter 0: A Book of Abstract Algebra Charles C Pinter, 2010-01-14 Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
  algebra chapter 0: Advanced Linear Algebra Steven Roman, 2007-12-31 Covers a notably broad range of topics, including some topics not generally found in linear algebra books Contains a discussion of the basics of linear algebra
  algebra chapter 0: College Algebra Jay Abramson, 2018-01-07 College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned. Coverage and Scope In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction. Chapters 1 and 2 provide both a review and foundation for study of Functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that need the prerequisite skills built into the course. Chapter 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic Geometry Chapter 9: Sequences, Probability and Counting Theory
  algebra chapter 0: Applied Algebra and Functional Analysis Anthony N. Michel, Charles J. Herget, 1993-01-01 A valuable reference. — American Scientist. Excellent graduate-level treatment of set theory, algebra and analysis for applications in engineering and science. Fundamentals, algebraic structures, vector spaces and linear transformations, metric spaces, normed spaces and inner product spaces, linear operators, more. A generous number of exercises have been integrated into the text. 1981 edition.
  algebra chapter 0: Topics in Algebra I. N. Herstein, 1991-01-16 New edition includes extensive revisions of the material on finite groups and Galois Theory. New problems added throughout.
  algebra chapter 0: Algebra Serge Lang, 1967
  algebra chapter 0: Advanced Modern Algebra Joseph J. Rotman, 2023-02-22 This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165). Compared to the previous edition, the material has been significantly reorganized and many 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, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.
  algebra chapter 0: Elementary Algebraic Geometry Klaus Hulek, 2003 This book is a true introduction to the basic concepts and techniques of algebraic geometry. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory. The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary.
  algebra chapter 0: A History of Abstract Algebra Israel Kleiner, 2007-10-02 This book explores the history of abstract algebra. It shows how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved.
  algebra chapter 0: Introduction to Applied Linear Algebra Stephen Boyd, Lieven Vandenberghe, 2018-06-07 A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
  algebra chapter 0: A Course in Algebra Ėrnest Borisovich Vinberg, 2003-04-10 Presents modern algebra. This book includes such topics as affine and projective spaces, tensor algebra, Galois theory, Lie groups, and associative algebras and their representations. It is suitable for independent study for advanced undergraduates and graduate students.
  algebra chapter 0: Second Year Calculus David M. Bressoud, 2012-12-06 Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.
  algebra chapter 0: Basic Algebra Anthony W. Knapp, 2007-07-28 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. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.
  algebra chapter 0: Categorical Homotopy Theory Emily Riehl, 2014-05-26 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.
  algebra chapter 0: Algebra Saunders Mac Lane, Garrett Birkhoff, 2023-10-10 This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance. This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for groups, rings, fields, lattices, and vector spaces. This axiomatic approach—emphasized by Hilbert and developed in Germany by Noether, Artin, Van der Waerden, et al., in the 1920s—was popularized for the graduate level in the 1940s and 1950s to some degree by the authors' publication of A Survey of Modern Algebra. The present book presents the developments from that time to the first printing of this book. This third edition includes corrections made by the authors.
  algebra chapter 0: Introduction to Lie Algebras and Representation Theory J.E. Humphreys, 2012-12-06 This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with toral subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.
  algebra chapter 0: Algebra Thomas W. Hungerford, 2012-12-06 Finally a self-contained, one volume, graduate-level algebra text that is readable by the average graduate student and flexible enough to accommodate a wide variety of instructors and course contents. The guiding principle throughout is that the material should be presented as general as possible, consistent with good pedagogy. Therefore it stresses clarity rather than brevity and contains an extraordinarily large number of illustrative exercises.
  algebra chapter 0: Topology Tai-Danae Bradley, Tyler Bryson, John Terilla, 2020-08-18 A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.
  algebra chapter 0: $\textrm {C}^*$-Algebras and Finite-Dimensional Approximations Nathanial Patrick Brown, Narutaka Ozawa, 2008 $\textrm{C}*$-approximation theory has provided the foundation for many of the most important conceptual breakthroughs and applications of operator algebras. This book systematically studies (most of) the numerous types of approximation properties that have been important in recent years: nuclearity, exactness, quasidiagonality, local reflexivity, and others. Moreover, it contains user-friendly proofs, insofar as that is possible, of many fundamental results that were previously quite hard to extract from the literature. Indeed, perhaps the most important novelty of the first ten chapters is an earnest attempt to explain some fundamental, but difficult and technical, results as painlessly as possible. The latter half of the book presents related topics and applications--written with researchers and advanced, well-trained students in mind. The authors have tried to meet the needs both of students wishing to learn the basics of an important area of research as well as researchers who desire a fairly comprehensive reference for the theory and applications of $\textrm{C}*$-approximation theory.
  algebra chapter 0: Commutative Algebra David Eisenbud, 2013-12-01 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.
  algebra chapter 0: Geometric Algebra for Computer Science Leo Dorst, Daniel Fontijne, Stephen Mann, 2010-07-26 Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing * Written by leaders in the field providing essential information on this new technique for 3D graphics * This full colour book includes a website with GAViewer, a program to experiment with GA
  algebra chapter 0: Advanced Algebra Anthony W. Knapp, 2007-10-11 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.
  algebra chapter 0: Beginning and Intermediate Algebra Tyler Wallace, 2018-02-13 Get Better Results with high quality content, exercise sets, and step-by-step pedagogy! Tyler Wallace continues to offer an enlightened approach grounded in the fundamentals of classroom experience in Beginning and Intermediate Algebra. The text reflects the compassion and insight of its experienced author with features developed to address the specific needs of developmental level students. Throughout the text, the author communicates to students the very points their instructors are likely to make during lecture, and this helps to reinforce the concepts and provide instruction that leads students to mastery and success. The exercises, along with the number of practice problems and group activities available, permit instructors to choose from a wealth of problems, allowing ample opportunity for students to practice what they learn in lecture to hone their skills. In this way, the book perfectly complements any learning platform, whether traditional lecture or distance-learning; its instruction is so reflective of what comes from lecture, that students will feel as comfortable outside of class as they do inside class with their instructor.
  algebra chapter 0: Linear Algebra Done Right Sheldon Axler, 1997-07-18 This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
  algebra chapter 0: Applied Linear Algebra Lorenzo Adlai Sadun, 2007-12-20 Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle. Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrodinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings. Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform. The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises.
  algebra chapter 0: Introduction to Vertex Operator Algebras and Their Representations James Lepowsky, Haisheng Li, 2012-12-06 * Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.
  algebra chapter 0: Algebra Michael Artin, 2013-09-01 Algebra, Second Edition, by Michael Artin, is ideal for the honors undergraduate or introductory graduate course. The second edition of this classic text incorporates twenty years of feedback and the author's own teaching experience. The text discusses concrete topics of algebra in greater detail than most texts, preparing students for the more abstract concepts; linear algebra is tightly integrated throughout.
  algebra chapter 0: Quadratic Algebras Alexander Polishchuk, Leonid Positselski, 2005 This book introduces recent developments in the study of algebras defined by quadratic relations. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, non commutative geometry, $K$-theory, number theory, and non commutative linear algebra.The authors give a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincare-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes. The book can be used by graduate students and researchers working in algebra and any of the above-mentioned areas of mathematics.
  algebra chapter 0: A Concise Introduction to Linear Algebra Géza Schay, 2012-03-30 Building on the author's previous edition on the subject (Introduction to Linear Algebra, Jones & Bartlett, 1996), this book offers a refreshingly concise text suitable for a standard course in linear algebra, presenting a carefully selected array of essential topics that can be thoroughly covered in a single semester. Although the exposition generally falls in line with the material recommended by the Linear Algebra Curriculum Study Group, it notably deviates in providing an early emphasis on the geometric foundations of linear algebra. This gives students a more intuitive understanding of the subject and enables an easier grasp of more abstract concepts covered later in the course. The focus throughout is rooted in the mathematical fundamentals, but the text also investigates a number of interesting applications, including a section on computer graphics, a chapter on numerical methods, and many exercises and examples using MATLAB. Meanwhile, many visuals and problems (a complete solutions manual is available to instructors) are included to enhance and reinforce understanding throughout the book. Brief yet precise and rigorous, this work is an ideal choice for a one-semester course in linear algebra targeted primarily at math or physics majors. It is a valuable tool for any professor who teaches the subject.
知乎，让每一次点击都充满意义 —— 欢迎来到知乎，发现问题背 …
知乎，让每一次点击都充满意义 —— 欢迎来到知乎，发现问题背后的世界。

求推荐近世代数教材? - 知乎
Paolo Aluffi的《Algebra: Chapter 0》：范畴论就看这本。作者不喜欢像其他代数书一样“渗透”范畴论的思想，而是给读者更完整直观的印象。讲得通俗易懂，且不失严谨。目前只看了范畴论部分的内容，之后应该会把整理好的笔记发在知乎上～

如何评价algebra chapter 0和GTM211 algebra? - 知乎
题主对代数比较感兴趣，想了解这两本书的特点

准备学习抽象代数，各位大佬们推荐一下国外的教材？ - 知乎
27 Mar 2024 · 具体理由可以看 Algebra Chapter 0书评 以及某个没上过代数课的人关于代数的碎碎念 - Saturn.V的文章 - 知乎. Saturn.V：Algebra Chapter 0书评 以及某个没上过代数课的人关于代数的碎碎念 等. 反正pdf随便找，自己看看合不合适就行了

看了rudin的数分，觉得升华了不少…… 请问高代，抽代有没有类似 …
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业、友善的社区氛围、独特的产品机制以及结构化和易获得的优质内容，聚集了中文互联网科技、商业、 …

同济大学出版社的线性代数感觉不适合刚接触的同学，求推荐同类 …
如果你有时间与兴趣，接着看 Paolo Aluffi, ALGEBRA, Chapter 0（Chapter 0 是书名的一部分，不是第零章），学完之后你就基本可以宣称自己懂线性代数了。不过这个不强求了，你有极大的可能性看不下来，虽然我觉得这本书比起同类教材来异常清晰易懂，另外看下来也没 ...

物理学工作者怎么学范畴论（张量范畴）？ - 知乎
Paolo Aluffi的Algebra: Chapter 0第一章应该是非常适合入门的，可惜的是目前没有影印版，如果需要的话告诉我，我给你发电子版。 Tom Leinster的Basic Category Theory应该是个很不错的选择，在arxiv上有它的电子版。

有哪些比较好的抽象代数入门书籍？ - 知乎
27 Apr 2017 · Dummit foote的abstract algebra谁用谁知道. Motivation充足. 证明细节很多. 各种概念和定理例子很多. 习题很棒（还有答案2333） 而且涵盖范围很广，群环域模伽罗瓦理论乃至初步的交换代数和表示论都有. 现在我和同学讨论哪个书好都用这个句式 “Lee简直是几何界的dummit ...

数学中的 well-defined 是什么？ - 知乎
3 Dec 2013 · 图片来自Algebra Chapter 0. 最简单的例子，第一同构定理就告诉我们一个群同态 f 是如何划分等价关系的。 这个等价关系就是其核 Ker\,f 在 G 上划分出的陪集。 比如我们考虑全体可微函数构成的空间 C^1 以及其上的线性映射 \frac{d}{dx} (下文记作 D) D 的核 Ker\,D=\R,陪集 ...

自学数学分析读什么书？ - 知乎
这书一天十页两个月速通然后看done right，嗯，done right到了第七章左右没必要生啃了，到时候泛函分析的时候自然会清楚明白，缺乏动机的东西咱不看（或者某天突然有动机了再回来看，总之done right的对偶伴随这些写的真的不好）去学抽象代数，看Algebra Chapter 0 ...

知乎，让每一次点击都充满意义 —— 欢迎来到知乎，发现问题背 …
知乎，让每一次点击都充满意义 —— 欢迎来到知乎，发现问题背后的世界。

求推荐近世代数教材? - 知乎
Paolo Aluffi的《Algebra: Chapter 0》：范畴论就看这本。作者不喜欢像其他代数书一样“渗透”范畴论的思想，而是给读者更完整直观的印象。讲得通俗易懂，且不失严谨。目前只看了范畴论部 …

如何评价algebra chapter 0和GTM211 algebra? - 知乎
题主对代数比较感兴趣，想了解这两本书的特点

准备学习抽象代数，各位大佬们推荐一下国外的教材？ - 知乎
27 Mar 2024 · 具体理由可以看 Algebra Chapter 0书评 以及某个没上过代数课的人关于代数的碎碎念 - Saturn.V的文章 - 知乎. Saturn.V：Algebra Chapter 0书评 以及某个没上过代数课的人关 …

看了rudin的数分，觉得升华了不少…… 请问高代，抽代有没有类似 …
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业 …

同济大学出版社的线性代数感觉不适合刚接触的同学，求推荐同类 …
如果你有时间与兴趣，接着看 Paolo Aluffi, ALGEBRA, Chapter 0（Chapter 0 是书名的一部分，不是第零章），学完之后你就基本可以宣称自己懂线性代数了。不过这个不强求了，你有极大的 …

物理学工作者怎么学范畴论（张量范畴）？ - 知乎
Paolo Aluffi的Algebra: Chapter 0第一章应该是非常适合入门的，可惜的是目前没有影印版，如果需要的话告诉我，我给你发电子版。 Tom Leinster的Basic Category Theory应该是个很不错的 …

有哪些比较好的抽象代数入门书籍？ - 知乎
27 Apr 2017 · Dummit foote的abstract algebra谁用谁知道. Motivation充足. 证明细节很多. 各种概念和定理例子很多. 习题很棒（还有答案2333） 而且涵盖范围很广，群环域模伽罗瓦理论乃至 …

数学中的 well-defined 是什么？ - 知乎
3 Dec 2013 · 图片来自Algebra Chapter 0. 最简单的例子，第一同构定理就告诉我们一个群同态 f 是如何划分等价关系的。 这个等价关系就是其核 Ker\,f 在 G 上划分出的陪集。 比如我们考虑 …

自学数学分析读什么书？ - 知乎
这书一天十页两个月速通然后看done right，嗯，done right到了第七章左右没必要生啃了，到时候泛函分析的时候自然会清楚明白，缺乏动机的东西咱不看（或者某天突然有动机了再回来看， …