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Algebra: Concepts and Applications, Volume Two
by Carol Malloy Jack Price Jerry Cummins Kay Mcclain Yvonne MojicaAlgebra: Concepts & Applications, is a comprehensive Algebra 1 program that is available in full and two-volume editions. Algebra: Concepts & Applicationsuses a clean lesson design with many detailed examples and straightforward narration that make Algebra 1 topics inviting and Algebra 1 content understandable. Volume 1 contains Chapters 1-8 ofAlgebra: Concepts & Applicationsplus an initial section called Chapter A. Chapter A includes a pretest, lessonson prerequisite concepts, and a posttest. Designed for students who are challenged by high school mathematics, the 2007 edition has many new features and support components.
Algebra: Essentials and Applications
by Winston Holt RinehartAlgebra Essentials and Applications is focused, organized, and easy to follow. The program shows your students how to read, write, and understand the unique language of mathematics, so that they are prepared for every type of problem-solving and assessment situation.
Algebra: Form And Function
by Eric Connally Deborah Hughes-Hallett William G. MccallumThis book offers a fresh approach to algebra that focuses on teaching readers how to truly understand the principles, rather than viewing them merely as tools for other forms of mathematics. It relies on a storyline to form the backbone of the chapters and make the material more engaging. Conceptual exercise sets are included to show how the information is applied in the real world. Using symbolic notation as a framework, business professionals will come away with a vastly improved skill set.
Algebra: Form and Function (Second Edition)
by Eric Connally Elliot J. Marks Pat Shure Carl Swenson Deborah Hughes-Hallett Philip Cheifetz Ann Davidian Brigitte Lahme Patti Frazer Lock William G. Mccallum David Lovelock Ellen Schmierer Aysegul Sahin Adam H. Spiegler Selin KalaycýoðluAlgebra: Form and Function offers a fresh approach to algebra that focuses on teaching readers how to truly understand the principles, rather than viewing them merely as tools for other forms of mathematics. Meant for a College Algebra course, Algebra: Form and Function is an introduction to one of the fundamental aspects of modern society. Algebraic equations describe the laws of science, the principles of engineering, and the rules of business. The power of algebra lies in the efficient symbolic representation of complex ideas, which also presents the main difficulty in learning it. It is easy to forget the underlying structure of algebra and rely instead on a surface knowledge of algebraic manipulations. Most students rely on surface knowledge of algebraic manipulations without understanding the underlying structure of algebra that allows them to see patterns and apply it to multiple situations: McCallum focuses on the structure from the start.
Algebra: Groups, Rings, and Fields (Textbooks in Mathematics)
by Louis Halle Rowen Uzi VishneAlgebra is a subject we have become acquainted with during most of our mathematical education, often in connection with the solution of equations. Algebra: Groups, Rings, and Fields, Second Edition deals with developments related to their solutions.The principle at the heart of abstract algebra, a subject that enables one to deduce sweeping conclusions from elementary premises, is that the process of abstraction enables us to solve a variety of such problems with economy of effort. This leads to the glorious world of mathematical discovery.This second edition follows the original three-pronged approach: the theory of finite groups, number theory, and Galois’ amazing theory of field extensions tying solvability of equations to group theory.As algebra has branched out in many directions, the authors strive to keep the text manageable while at the same time introducing the student to exciting new paths. In order to support this approach, the authors broadened the first edition, giving monoids a greater role, and relying more on matrices. Hundreds of new exercises were added.A course in abstract algebra, properly presented, could treat mathematics as an art as well as a science. In this exposition, we try to present underlying ideas, as well as the results they yield.
Algebra: Groups, Rings, and Fields (Textbooks in Mathematics)
by Louis RowenThis text presents the concepts of higher algebra in a comprehensive and modern way for self-study and as a basis for a high-level undergraduate course. The author is one of the preeminent researchers in this field and brings the reader up to the recent frontiers of research including never-before-published material. From the table of contents: - Groups: Monoids and Groups - Cauchyís Theorem - Normal Subgroups - Classifying Groups - Finite Abelian Groups - Generators and Relations - When Is a Group a Group? (Cayley's Theorem) - Sylow Subgroups - Solvable Groups - Rings and Polynomials: An Introduction to Rings - The Structure Theory of Rings - The Field of Fractions - Polynomials and Euclidean Domains - Principal Ideal Domains - Famous Results from Number Theory - I Fields: Field Extensions - Finite Fields - The Galois Correspondence - Applications of the Galois Correspondence - Solving Equations by Radicals - Transcendental Numbers: e and p - Skew Field Theory - Each chapter includes a set of exercises
Algebra: Gruppen - Ringe - Körper
by Christian Karpfinger Kurt MeybergDieses vierfarbige Lehrbuch wendet sich an Studierende der Mathematik in Bachelor- und Lehramts-Studieng#65533;ngen. Es bietet in einem Band ein lebendiges Bild der mathematischen Inhalte, die #65533;blicherweise im ersten Studienjahr behandelt werden (und etliches mehr). Mathematik-Studierende finden wichtige Begriffe, S#65533;tze und Beweise ausf#65533;hrlich und mit vielen Beispielen erkl#65533;rt und werden an grundlegende Konzepte und Methoden herangef#65533;hrt. Im Mittelpunkt stehen das Verst#65533;ndnis der mathematischen Zusammenh#65533;nge und des Aufbaus der Theorie sowie die Strukturen und Ideen wichtiger S#65533;tze und Beweise. Es wird nicht nur ein in sich geschlossenes Theoriengeb#65533;ude dargestellt, sondern auch verdeutlicht, wie es entsteht und wozu die Inhalte sp#65533;ter ben#65533;tigt werden. Herausragende Merkmale sind: durchg#65533;ngig vierfarbiges Layout mit mehr als 600 Abbildungen pr#65533;gnant formulierte Kerngedanken bilden die Abschnitts#65533;berschriften Selbsttests in kurzen Abst#65533;nden erm#65533;glichen Lernkontrollen w#65533;hrend des Lesens farbige Merkk#65533;sten heben das Wichtigste hervor ,,Unter-der-Lupe"-Boxen zoomen in Beweise hinein, motivieren und erkl#65533;ren Details ,,Hintergrund-und-Ausblick"-Boxen stellen Zusammenh#65533;nge zu anderen Gebieten und weiterf#65533;hrenden Themen her Zusammenfassungen zu jedem Kapitel sowie #65533;bersichtsboxen mehr als 400 Verst#65533;ndnisfragen, Rechenaufgaben und Aufgaben zu Beweisen deutsch-englisches Symbol- und Begriffsglossar Der inhaltliche Schwerpunkt liegt auf den Themen der Vorlesungen Analysis 1 und 2 sowie Linearer Algebra 1 und 2. Behandelt werden dar#65533;ber hinaus Inhalte und Methodenkompetenzen, die vielerorts im ersten Studienjahr der Mathematikausbildung vermittelt werden. Auf der Website zum Buch www. matheweb. de finden Sie Hinweise, L#65533;sungswege und Ergebnisse zu allen Aufgaben Zusatzmaterialien wie Maple-Worksheets zu verschiedenen Themen des Buchs die M#65533;glichkeit, zu den Kapiteln Fragen zu stellen Das Buch wird allen Studierenden der Mathematik vom Beginn des Studiums bis in h#65533;here Semester hinein ein verl#65533;sslicher Begleiter sein.
Algebra: Gruppen - Ringe - Körper
by Christian Karpfinger Kurt MeybergDieses Lehrbuch zur Algebra bietet eine Einführung in die grundlegenden Begriffe und Methoden der modernen Algebra. Es werden die Themen eines Grundkurses zur Algebra ausführlich und motivierend behandelt. Die Algebra wird von vielen Studierenden als sehr abstrakt empfunden. Daher haben sich die Autoren bemüht, die Ergebnisse und Begriffe mit zahlreichen Beispielen zu unterlegen. Die Beweisführungen sind ausführlich, die Kapitel sind in kleine Lerneinheiten unterteilt. Diese Lerneinheiten führen Schritt für Schritt an die Ergebnisse heran und können durch diese Darstellung vom Leser besser nachvollzogen werden. Die zahlreichen Aufgaben unterschiedlicher Schwierigkeitsgrade zum Ende der Kapitel überprüfen das Gelernte und fördern das tiefere Verständnis der Theorie. Das Buch wurde für die 5. Auflage vollständig durchgesehen und um einen ausführlichen Abschnitt zum semidirekten Produkt von Gruppen erweitert. Zudem wurden Lösungsmethoden inklusive Beispiele für manche typischen Aufgabenstellungen übersichtlich zusammengestellt, z.B. zum Nachweis der Reduzibilität bzw. Irreduzibilität von Polynomen.
Algebra: Gruppen – Ringe – Körper
by Christian KarpfingerDieses Lehrbuch zur Algebra bietet eine Einführung in die grundlegenden Begriffe und Methoden der modernen Algebra. Es werden die Themen eines Grundkurses zur Algebra ausführlich und motivierend behandelt.Die Algebra wird von vielen Studierenden als sehr abstrakt empfunden. Daher hat sich der Autor bemüht, die Ergebnisse und Begriffe mit zahlreichen Beispielen zu unterlegen. Die Beweisführungen sind ausführlich, gelegentlich werden sogar verschiedene Beweise aufgezeigt. Die Kapitel sind in kleine Lerneinheiten unterteilt. Diese Lerneinheiten führen Schritt für Schritt an die Ergebnisse heran und können durch diese Darstellung vom Leser besser nachvollzogen werden. Der Autor hat stets darauf geachtet, dass erst dann neue Begriffe und Konzepte eingeführt werden, wenn ein gewisses Vertrauen im Umgang mit den bis dahin entwickelten Begriffen und Konzepten besteht. Das Vorgehen wird stets motiviert, schwierige Sachverhalte werden ausführlich erklärt und an Beispielen erprobt. DieLeser erhalten dadurch einen einfachen Zugang zu dem nicht ganz leichten Thema der Algebra.Die zahlreichen Aufgaben unterschiedlicher Schwierigkeitsgrade zum Ende der Kapitel überprüfen das Gelernte und fördern das tiefere Verständnis der Theorie. Das Buch wurde für die 6. Auflage vollständig durchgesehen und um zwei Beweise des quadratischen Reziprozitätsgesetzes ergänzt. Zudem erhalten Sie Zugang auf 300 Flashcards (Springer-Nature-Flashcards-App), mit denen Sie Ihr Verständnis der Theorie auf spielerische Weise testen und einüben können.
Algebra: Polynomials, Galois Theory and Applications
by Frédéric ButinSuitable for advanced undergraduates and graduate students in mathematics and computer science, this precise, self-contained treatment of Galois theory features detailed proofs and complete solutions to exercises. Originally published in French as Algèbre — Polynômes, théorie de Galois et applications informatiques, this 2017 Dover Aurora edition marks the volume's first English-language publication.The three-part treatment begins by providing the essential introduction to Galois theory. The second part is devoted to the algebraic, normal, and separable Galois extensions that constitute the center of the theory and examines abelian, cyclic, cyclotomic, and radical extensions. This section enables readers to acquire a comprehensive understanding of the Galois group of a polynomial. The third part deals with applications of Galois theory, including excellent discussions of several important real-world applications of these ideas, including cryptography and error-control coding theory. Symbolic computation via the Maple computer algebra system is incorporated throughout the text (though other software of symbolic computation could be used as well), along with a large number of very interesting exercises with full solutions.
Algebra: Structure and Method, Book 1
by Richard G. Brown Mary P. Dolciani Robert H. Sorgenfrey William L. ColeAn algebra book requires a different type of reading than a novel or a short story. Every sentence in a math book is full of information and logically linked to the surrounding sentences. You should read the sentences carefully and think about their meaning.
Algebra: Structure and Method, Book 1
by Richard G. Brown Mary P. Dolciani Robert H. Sorgenfrey William L. ColeAlgebra, Structure and Method textbook for ninth grade students.
Algebra: The Easy Way to Learn Algebra
by Hugh NeillAlgebra: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using Algebra.Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all the key areas of algebra including elementary operations, linear equations, formulae, simultaneous equations, quadratic equations, logarithms, variation, laws and sequences.Everything you will need is here in this one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions.Chapter 1: The meaning of algebraChapter 2: Elementary operations in algebraChapter 3: Brackets and operations with themChapter 4: Positive and negative numbersChapter 5: Equations and expressionsChapter 6: Linear equationsChapter 7: FormulaeChapter 8: Simultaneous equationsChapter 9: Linear inequalitiesChapter 10: Straight-line graphs; coordinatesChapter 11: Using inequalities to define regionsChapter 12: Multiplying algebraical expressions Chapter 13: FactorsChapter 14: FractionsChapter 15: Graphs of quadratic functionsChapter 16: Quadratic equationsChapter 17: IndicesChapter 18: LogarithmsChapter 19: Ratio and proportionChapter 20: VariationChapter 21: The determination of lawsChapter 22: Rational and irrational numbers and surdsChapter 23: Arithmetical and geometric sequences
Algebraic 3-D Modeling
by Andreas HartwigWritten for researchers and developers of three-dimensional modeling programs, this book examines the variety of existing systems while investigating the practical limitations of available software. From the table of contents: - Polyhedra - Boundary Models - A Small Language Modeler - The Algebraic Model - Computation of Algebraic Manifolds - Topol
Algebraic Analysis of Social Networks: Models, Methods and Applications Using R (Wiley Series in Computational and Quantitative Social Science)
by J. Antonio OstoicPresented in a comprehensive manner, this book provides a comprehensive foundation in algebraic approaches for the analysis of different types of social networks such as multiple, signed, and affiliation networks. The study of such configurations corresponds to the structural analysis within the social sciences, and the methods applied for the analysis are in the areas of abstract algebra, combinatorics, and graph theory. Current research in social networks has moved toward the examination of more realistic but also more complex social relations by which agents or actors are connected in multiple ways. Addressing this trend, this book offers hands-on training of the algebraic procedures presented along with the computer package multiplex, written by the book’s author specifically to perform analyses of multiple social networks. An introductory section on both complex networks and for R will feature, however the subjects themselves correspond to advanced courses on social network analysis with the specialization on algebraic models and methods.
Algebraic Approach to Data Processing: Techniques and Applications (Studies in Big Data #115)
by Vladik Kreinovich Julio C. UrendaThe book explores a new general approach to selecting—and designing—data processing techniques. Symmetry and invariance ideas behind this algebraic approach have been successful in physics, where many new theories are formulated in symmetry terms. The book explains this approach and expands it to new application areas ranging from engineering, medicine, education to social sciences. In many cases, this approach leads to optimal techniques and optimal solutions. That the same data processing techniques help us better analyze wooden structures, lung dysfunctions, and deep learning algorithms is a good indication that these techniques can be used in many other applications as well. The book is recommended to researchers and practitioners who need to select a data processing technique—or who want to design a new technique when the existing techniques do not work. It is also recommended to students who want to learn the state-of-the-art data processing.
Algebraic Approaches to Nuclear Structure
by A. CastenholzThis book is devoted to algebraic models and their applications. It presents a simple, but thorough, pedagogic approach, starting from the most elementary ideas and building up to the most recent results of advanced theories. The book is designed for a graduate level treatment.
Algebraic Approaches to Partial Differential Equations (Springer Monographs in Mathematics)
by Xiaoping XuThis book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation, the KP equation, the nonlinear Schrodinger equation, the Davey and Stewartson equations, the Boussinesq equations in geophysics, the Navier-Stokes equations and the boundary layer problems. In order to solve them, I have employed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions, symmetry transformations, linearization techniques and special functions. The book is self-contained and requires only a minimal understanding of calculus and linear algebra, making it accessible to a broad audience in the fields of mathematics, the sciences and engineering. Readers may find the exact solutions and mathematical skills needed in their own research.
Algebraic Circuits (Intelligent Systems Reference Library #66)
by Antonio Lloris Ruiz Encarnación Castillo Morales Luis Parrilla Roure Antonio García RíosThis book presents a complete and accurate study of algebraic circuits, digital circuits whose performance can be associated with any algebraic structure. The authors distinguish between basic algebraic circuits, such as Linear Feedback Shift Registers (LFSRs) and cellular automata and algebraic circuits, such as finite fields or Galois fields. The book includes a comprehensive review of representation systems, of arithmetic circuits implementing basic and more complex operations and of the residue number systems (RNS). It presents a study of basic algebraic circuits such as LFSRs and cellular automata as well as a study of circuits related to Galois fields, including two real cryptographic applications of Galois fields.
Algebraic Codes for Data Transmission
by Richard E. BlahutThe need to transmit and store massive amounts of data reliably and without error is a vital part of modern communications systems. Error-correcting codes play a fundamental role in minimising data corruption caused by defects such as noise, interference, crosstalk and packet loss. This book provides an accessible introduction to the basic elements of algebraic codes, and discusses their use in a variety of applications. The author describes a range of important coding techniques, including Reed-Solomon codes, BCH codes, trellis codes, and turbocodes. Throughout the book, mathematical theory is illustrated by reference to many practical examples. The book was first published in 2003 and is aimed at graduate students of electrical and computer engineering, and at practising engineers whose work involves communications or signal processing.
Algebraic Coding Theory Over Finite Commutative Rings (SpringerBriefs in Mathematics)
by Steven T. DoughertyThis book provides a self-contained introduction to algebraic coding theory over finite Frobenius rings. It is the first to offer a comprehensive account on the subject. Coding theory has its origins in the engineering problem of effective electronic communication where the alphabet is generally the binary field. Since its inception, it has grown as a branch of mathematics, and has since been expanded to consider any finite field, and later also Frobenius rings, as its alphabet. This book presents a broad view of the subject as a branch of pure mathematics and relates major results to other fields, including combinatorics, number theory and ring theory. Suitable for graduate students, the book will be of interest to anyone working in the field of coding theory, as well as algebraists and number theorists looking to apply coding theory to their own work.
Algebraic Combinatorics (Chapman Hall/crc Mathematics Ser. #6)
by Chris GodsilThis graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.
Algebraic Combinatorics and Coinvariant Spaces
by Francois BergeronWritten for graduate students in mathematics or non-specialist mathematicians who wish to learn the basics about some of the most important current research in the field, this book provides an intensive, yet accessible, introduction to the subject of algebraic combinatorics. After recalling basic notions of combinatorics, representation theory, and
Algebraic Combinatorics: Walks, Trees, Tableaux, and More (Undergraduate Texts in Mathematics #38)
by Richard P. StanleyWritten by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author's extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix-Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.
Algebraic Combinatorics: Walks, Trees, Tableaux, and More (Undergraduate Texts in Mathematics #38)
by Richard P. StanleyWritten by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound understanding to mathematical, engineering, and business models. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and rudiments of group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix-Tree Theorem, de Bruijn sequences, the Erdős–Moser conjecture, electrical networks, the Sperner property, shellability of simplicial complexes and face rings. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees.The new edition contains a bit more content than intended for a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Instructors may pick and choose chapters/sections for course inclusion and students can immerse themselves in exploring additional gems once the course has ended. A chapter on combinatorial commutative algebra (Chapter 12) is the heart of added material in this new edition. The author gives substantial application without requisites needed for algebraic topology and homological algebra. A sprinkling of additional exercises and a new section (13.8) involving commutative algebra, have been added.From reviews of the first edition:“This gentle book provides the perfect stepping-stone up. The various chapters treat diverse topics … . Stanley’s emphasis on ‘gems’ unites all this —he chooses his material to excite students and draw them into further study. … Summing Up: Highly recommended. Upper-division undergraduates and above.” —D. V. Feldman, Choice, Vol. 51(8), April, 2014