Advanced Algebra PDF Download

Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
ISBN: 0817646132
Category : Mathematics
Languages : en
Pages : 757

View

Book Description
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.

Author: Kevin O'Meara
Publisher: OUP USA
ISBN: 0199793735
Category : Mathematics
Languages : en
Pages : 423

View

Book Description
This book develops the Weyr matrix canonical form, a largely unknown cousin of the Jordan form. It explores novel applications, including include matrix commutativity problems, approximate simultaneous diagonalization, and algebraic geometry. Module theory and algebraic geometry are employed but with self-contained accounts.

Author: Nathaniel Johnston
Publisher: Springer Nature
ISBN: 3030528111
Category : Mathematics
Languages : en
Pages : 482

View

Book Description
This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.

Author: Derek Portman
Publisher:
ISBN: 9781632386717
Category :
Languages : en
Pages : 219

View

Book Description
Algebra is an area of mathematics that studies mathematical symbols and their rules of manipulation. It is instrumental in equation solving and in the study of abstractions like rings, groups and fields. Algebraic structures can be modified using the operations of addition, multiplication, subtraction, etc. and characterized by associativity, commutativity and finite dimension, among others. Some common algebraic structures are groups, lattices, vector spaces, modules, etc. Hybrid structures are also under the scope of algebra such as lie group, topological group, Archimedean group, ordered groups, rings and fields, etc. The areas of study in algebra can be divided into linear and multilinear algebra, associative and nonassociative rings and algebras, general algebraic systems, group theory, field theory and polynomials, besides many others. This book presents the complex subject of algebra in the most comprehensible and easy to understand language. It covers in detail some existing theories and innovative concepts revolving around algebra. This book is a complete source of knowledge on the present status of this important field.

Author: Nicholas Loehr
Publisher: CRC Press
ISBN: 1466559012
Category : Mathematics
Languages : en
Pages : 634

View

Book Description
Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra covers theoretical aspects of the subject, along with examples, computations, and proofs. It explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra, analysis, combinatorics, numerical computation, and many other areas of mathematics. The book’s 20 chapters are grouped into six main areas: algebraic structures, matrices, structured matrices, geometric aspects of linear algebra, modules, and multilinear algebra. The level of abstraction gradually increases as students proceed through the text, moving from matrices to vector spaces to modules. Each chapter consists of a mathematical vignette devoted to the development of one specific topic. Some chapters look at introductory material from a sophisticated or abstract viewpoint while others provide elementary expositions of more theoretical concepts. Several chapters offer unusual perspectives or novel treatments of standard results. Unlike similar advanced mathematical texts, this one minimizes the dependence of each chapter on material found in previous chapters so that students may immediately turn to the relevant chapter without first wading through pages of earlier material to access the necessary algebraic background and theorems. Chapter summaries contain a structured list of the principal definitions and results. End-of-chapter exercises aid students in digesting the material. Students are encouraged to use a computer algebra system to help solve computationally intensive exercises.

Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
ISBN: 0817645292
Category : Mathematics
Languages : en
Pages : 762

View

Book Description
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.

Author: Bruce Elwyn Meserve
Publisher: Courier Corporation
ISBN: 9780486614700
Category : Mathematics
Languages : en
Pages : 324

View

Book Description
Uncommonly interesting introduction illuminates complexities of higher mathematics while offering a thorough understanding of elementary mathematics. Covers development of complex number system and elementary theories of numbers, polynomials and operations, determinants, matrices, constructions and graphical representations. Several exercises — without solutions.

Author: Bruce Cooperstein
Publisher: CRC Press
ISBN: 1439829691
Category : Mathematics
Languages : en
Pages : 361

View

Book Description
Advanced Linear Algebra focuses on vector spaces and the maps between them that preserve their structure (linear transformations). It starts with familiar concepts and then slowly builds to deeper results. Along with including many exercises and examples, each section reviews what students need to know before studying the material. The book first introduces vector spaces over fields as well as the fundamental concepts of linear combinations, span of vectors, linear independence, basis, and dimension. After covering linear transformations, it discusses the algebra of polynomials with coefficients in a field, concentrating on results that are consequences of the division algorithm. The author then develops the whole structure theory of a linear operator on a finite dimensional vector space from a collection of some simple results. He also explores the entire range of topics associated with inner product spaces, from the Gram–Schmidt process to the spectral theorems for normal and self-adjoint operators on an inner product space. The text goes on to rigorously describe the trace and determinant of linear operators and square matrices. The final two chapters focus on bilinear forms and tensor products and related material. Designed for advanced undergraduate and beginning graduate students, this textbook shows students the beauty of linear algebra. It also prepares them for further study in mathematics.

Author: Steven Roman
Publisher: Springer Science & Business Media
ISBN: 038727474X
Category : Mathematics
Languages : en
Pages : 488

View

Book Description
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

Author: Paolo Aluffi
Publisher: American Mathematical Soc.
ISBN: 147046571X
Category : Education
Languages : en
Pages : 713

View

Book Description
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.