Search results for: algebra-volume-2

Algebra

Author : Falko Lorenz
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This is Volume II of a two-volume introductory text in classical algebra. The text moves methodically with numerous examples and details so that readers with some basic knowledge of algebra can read it without difficulty. It is recommended either as a textbook for some particular algebraic topic or as a reference book for consultations in a selected fundamental branch of algebra. The book contains a wealth of material. Amongst the topics covered in Volume are the theory of ordered fields and Nullstellen Theorems. Known researcher Lorenz also includes the fundamentals of the theory of quadratic forms, of valuations, local fields and modules. What’s more, the book contains some lesser known or nontraditional results – for instance, Tsen's results on the solubility of systems of polynomial equations with a sufficiently large number of indeterminates.

Algebra

Author : B.L. van der Waerden
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This beautiful text transformed the graduate teaching of algebra in Europe and the United States. It clearly and succinctly formulated the conceptual and structural insights which Noether had expressed so forcefully and combined it with the elegance and understanding with which Artin had lectured. This second volume of the English translation of B.L. van der Waerden’s text Algebra is the first softcover printing of the original translation.

Linear Algebra Volume 2

Author : A. G. Hamilton
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Emphasis is placed on applications in preference to more theoretical aspects throughout this readable introduction to linear algebra for specialists as well as non-specialists. An expanded version of A First Course in Linear Algebra.

Grassmann Algebra

Author : John Browne
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This book is an abridged draft edition. It is being published now in this form due to circumstances beyond the author's control. There will not be another edition. You will miss some things you might have expected: page numbers in the table of contents, a comprehensive bibliography and references, an index, a well-reviewed text .. . This book (Volume 2) follows on from Volume 1 so you may also need Volume 1 for reference. The book shows how the hypercomplex and associative algebras are hidden in Grassmann algebra. It shows how the quaternions and octonions and their split variants, and the geometric and Clifford algebras, are simply Grassmann algebra. It does this by extending its two familiar product operations, the exterior and interior products to define a suite of products together called the generalized Grassmann product. It shows how hypercomplex, geometric and Clifford products may then be defined as linear combinations of generalized Grassmann products in which the scalar coefficients are restricted to unity or negative unity only. This binary variability is sufficient to endow properties to a product operation, for example associativity. The book concludes by finding four associative product operations, two of which being the geometric and Clifford products. But these work on Grassmann entities only, so they are operations of the Grassmann algebra. In sum: this book shows how some important linear algebras such as the hypercomplex, geometric and Clifford algebras can be constructed entirely within Grassmann algebra by defining specialized product operations using only the exterior and interior products.

Commutative Algebra

Author : Oscar Zariski
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This second volume of our treatise on commutative algebra deals largely with three basic topics, which go beyond the more or less classical material of volume I and are on the whole of a more advanced nature and a more recent vintage. These topics are: (a) valuation theory; (b) theory of polynomial and power series rings (including generalizations to graded rings and modules); (c) local algebra. Because most of these topics have either their source or their best motivation in algebraic geom etry, the algebro-geometric connections and applications of the purely algebraic material are constantly stressed and abundantly scattered through out the exposition. Thus, this volume can be used in part as an introduc tion to some basic concepts and the arithmetic foundations of algebraic geometry. The reader who is not immediately concerned with geometric applications may omit the algebro-geometric material in a first reading (see" Instructions to the reader," page vii), but it is only fair to say that many a reader will find it more instructive to find out immediately what is the geometric motivation behind the purely algebraic material of this volume. The first 8 sections of Chapter VI (including § 5bis) deal directly with properties of places, rather than with those of the valuation associated with a place. These, therefore, are properties of valuations in which the value group of the valuation is not involved.

Handbook of Categorical Algebra Volume 2 Categories and Structures

Author : Francis Borceux
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The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The second, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibred categories. There is ample material here for a graduate course in category theory, and the book should also serve as a reference for users.

Commutative Algebra Volume II

Author : Oscar Zariski
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The second text in this two-book series extends the classical material of Volume I, which focuses on field theory and the ideal theory of Noetherian rings and Dedekind domains. The connection of Volume II's material to algebraic geometry is stressed throughout the presentation, making this book a practical introduction to some basic concepts and the arithmetical foundations of algebraic geometry. The opening chapter deals with properties of places and is followed by a chapter that explores the classical properties of polynomial and power series rings and their applications to algebraic geometry. The final chapter examines the theory of local rings, which provides the algebraic basis for the local study of algebraic and analytical varieties. Several helpful Appendixes conclude the text.

An Approach to Algebra Volume 2

Author : Claudia Patricia Chapa Tamez
File Size : 62.1 MB
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Since mathematical principles have remained the same all throughout the world for centuries, Mathematics has been considered by many the “universal language of numbers”. For some, Mathematics causes anxiety or fear because it seems difficult to understand. One of the objectives of this eBook is to make the material more visually, technologically and multiculturally attrac- tive, with the aid of videos, pictures, games, animations and interactive exercises so that Mathemat-ics can become more interesting and accessible for today’s worldwide students since “evidence is mounting to support technology advocates’ claims that 21st-century information and communication tools, as well as more traditional computer-assisted instructional applications, can positively influence student learning processes and outcomes (Cradler, 2002)”. The role of mathematics in our modern world is crucial for today’s global communication and for a multitude of scientific and technological applications and advances.

Polynomials and the mod 2 Steenrod Algebra Volume 2 Representations of GL n F2

Author : Grant Walker
File Size : 76.49 MB
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This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's `hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n, F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.

Algebra Volume 2

Author : JRL Enterprises, Incorporated
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Foundations of Mathematics

Author : Angela G. Shirley
File Size : 81.41 MB
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This volume, Introductory Linear Algebra & Analytical Geometry, introduces students to basic concepts in linear algebra and coordinate geometry - vectors, lines, planes in 3-dimensions, matrices, determinants and systems of linear equations. The emphasis on equipping the student with powerful tools of linear algebra while building a solid foundation on which to pursue further studies in Mathematics or Mathematics-related fields. Students will appreciate the detailed notes on each topic, the many worked examples, as well as the model solutions to exam questions.

Comprehensive Algebra Vol 2

Author : KUMAR
File Size : 88.19 MB
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?Comprehensive Algebra , Vol.2 is the final volume of the two-part series on Algebra.Together with Vol.1, this book will provide a complete and comprehensive coverage of the topic.In the process, it sharpens the problem solving skill of aspirants of the key topic in mathematics.

Selected Exercises in Algebra

Author : Rocco Chirivì
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This book, the first of two volumes, contains over 250 selected exercises in Algebra which have featured as exam questions for the Arithmetic course taught by the authors at the University of Pisa. Each exercise is presented together with one or more solutions, carefully written with consistent language and notation. A distinguishing feature of this book is the fact that each exercise is unique and requires some creative thinking in order to be solved. The themes covered in this volume are: mathematical induction, combinatorics, modular arithmetic, Abelian groups, commutative rings, polynomials, field extensions, finite fields. The book includes a detailed section recalling relevant theory which can be used as a reference for study and revision. A list of preliminary exercises introduces the main techniques to be applied in solving the proposed exam questions. This volume is aimed at first year students in Mathematics and Computer Science.

Elements of Algebra

Author : Leonhard Euler
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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Year 9 Maths Max Series

Author : Matrix Education
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Year 9 Maths Max Series, Number and Algebra Volume 2 covers the topics 'Equations & Linear Relationships' from the NSW Mathematics Stage 5.2 and 5.3 Syllabus.

Studies in Modern Algebra Volume 2

Author : A. Adrian Albert
File Size : 74.43 MB
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A Graduate Course in Algebra

Author : Ioannis Farmakis
File Size : 50.75 MB
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This comprehensive two-volume book deals with algebra, broadly conceived. Volume 1 (Chapters 1–6) comprises material for a first year graduate course in algebra, offering the instructor a number of options in designing such a course. Volume 1, provides as well all essential material that students need to prepare for the qualifying exam in algebra at most American and European universities. Volume 2 (Chapters 7–13) forms the basis for a second year graduate course in topics in algebra. As the table of contents shows, that volume provides ample material accommodating a variety of topics that may be included in a second year course. To facilitate matters for the reader, there is a chart showing the interdependence of the chapters.

UCSMP Algebra Volume 2 Chapters 7 13

Author : Susan Brown
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Polynomials and the mod 2 Steenrod Algebra

Author : Grant Walker
File Size : 69.45 MB
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The second of two volumes covering the Steenrod algebra and its various applications. Ideal for researchers in pure mathematics.

Algebras Rings and Modules

Author : Michiel Hazewinkel
File Size : 83.35 MB
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This second volume of this text covers the classical aspects of the theory of groups and their representations. It also offers a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras. It reviews key recent developments in the theory of special ring classes including Frobenius, quasi-Frobenius, and others.