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Abstract Algebra (Dover Books on Mathematics)
by W. E. DeskinsThis excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. These systems, which consist of sets of elements, operations, and relations among the elements, and prescriptive axioms, are abstractions and generalizations of various models which evolved from efforts to explain or discuss physical phenomena.In Chapter 1, the author discusses the essential ingredients of a mathematical system, and in the next four chapters covers the basic number systems, decompositions of integers, diophantine problems, and congruences. Chapters 6 through 9 examine groups, rings, domains, fields, polynomial rings, and quadratic domains.Chapters 10 through 13 cover modular systems, modules and vector spaces, linear transformations and matrices, and the elementary theory of matrices. The author, Professor of Mathematics at the University of Pittsburgh, includes many examples and, at the end of each chapter, a large number of problems of varying levels of difficulty.
Abstract Algebra: Structure and Application (Springer Undergraduate Texts in Mathematics and Technology)
by David R. Finston Patrick J. MorandiThis text seeks to generate interest in abstract algebra by introducing each new structure and topic via a real-world application. The down-to-earth presentation is accessible to a readership with no prior knowledge of abstract algebra. Students are led to algebraic concepts and questions in a natural way through their everyday experiences. Applications include: Identification numbers and modular arithmetic (linear) error-correcting codes, including cyclic codes ruler and compass constructions cryptography symmetry of patterns in the real plane Abstract Algebra: Structure and Application is suitable as a text for a first course on abstract algebra whose main purpose is to generate interest in the subject or as a supplementary text for more advanced courses. The material paves the way to subsequent courses that further develop the theory of abstract algebra and will appeal to students of mathematics, mathematics education, computer science, and engineering interested in applications of algebraic concepts.
Abstract Algebra: An Introductory Course (Springer Undergraduate Mathematics Series #First Edition)
by Gregory T. Lee<P>This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. <P> The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite abelian groups. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. The final part contains applications to public key cryptography as well as classical straightedge and compass constructions. <P> Explaining key topics at a gentle pace, this book is aimed at undergraduate students. It assumes no prior knowledge of the subject and contains over 500 exercises, half of which have detailed solutions provided.
Abstract Algebra: A Gentle Introduction
by Gary L. Mullen James A. SellersAbstract Algebra: A Gentle Introduction advantages a trend in mathematics textbook publishing towards smaller, less expensive and brief introductions to primary courses. The authors move away from the ‘everything for everyone’ approach so common in textbooks. Instead, they provide the reader with coverage of numerous algebraic topics to cover the most important areas of abstract algebra. Through a careful selection of topics, supported by interesting applications, the authors Intend the book to be used for a one-semester course in abstract algebra. It is suitable for an introductory course in for mathematics majors. The text is also very suitable for education majors who need to have an introduction to the topic. As textbooks go through various editions and authors employ the suggestions of numerous well-intentioned reviewers, these book become larger and larger and subsequently more expensive. This book is meant to counter that process. Here students are given a "gentle introduction," meant to provide enough for a course, yet also enough to encourage them toward future study of the topic. Features Groups before rings approach Interesting modern applications Appendix includes mathematical induction, the well-ordering principle, sets, functions, permutations, matrices, and complex nubers. Numerous exercises at the end of each section Chapter "Hint and Partial Solutions" offers built in solutions manual
Abstract Algebra: A Comprehensive Treatment (Pure and Applied Mathematics #267)
by Freddy Van Oystaeyen Claudia MeniniIn one exceptional volume, Abstract Algebra covers subject matter typically taught over the course of two or three years and offers a self-contained presentation, detailed definitions, and excellent chapter-matched exercises to smooth the trajectory of learning algebra from zero to one. Field-tested through advance use in the ERASMUS educational project in Europe, this ambitious, comprehensive book includes an original treatment of representation of finite groups that avoids the use of semisimple ring theory and explains sets, maps, posets, lattices, and other essentials of the algebraic language; Peano's axioms and cardinality; groupoids, semigroups, monoids, groups; and normal subgroups.
Abstract Algebra: An Interactive Approach (Second Edition) (Textbooks in Mathematics)
by William Paulsen<p>The new edition of Abstract Algebra: An Interactive Approach presents a hands-on and traditional approach to learning groups, rings, and fields. It then goes further to offer optional technology use to create opportunities for interactive learning and computer use. This new edition offers a more traditional approach offering additional topics to the primary syllabus placed after primary topics are covered. This creates a more natural flow to the order of the subjects presented. This edition is transformed by historical notes and better explanations of why topics are covered. <p>This innovative textbook shows how students can better grasp difficult algebraic concepts through the use of computer programs. It encourages students to experiment with various applications of abstract algebra, thereby obtaining a real-world perspective of this area. Each chapter includes, corresponding Sage notebooks, traditional exercises, and several interactive computer problems that utilize Sage and Mathematica® to explore groups, rings, fields and additional topics. This text does not sacrifice mathematical rigor. It covers classical proofs, such as Abel’s theorem, as well as many topics not found in most standard introductory texts. The author explores semi-direct products, polycyclic groups, Rubik’s Cube®-like puzzles, and Wedderburn’s theorem. The author also incorporates problem sequences that allow students to delve into interesting topics, including Fermat’s two square theorem.</p>
Abstract Algebra (Third Edition)
by John A. Beachy William D. BlairBeachy and Blair’s clear narrative presentation responds to the needs of inexperienced students who stumble over proof writing, who understand definitions and theorems but cannot do the problems, and who want more examples that tie into their previous experience. The authors introduce chapters by indicating why the material is important and, at the same time, relating the new material to things from the student’s background and linking the subject matter of the chapter to the broader picture.
Abstract Algebra with Applications: Volume 2: Rings and Fields (Pure and Applied Mathematics)
by Karlheinz SpindlerA comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.
Abstract Algebra with Applications: Volume 1: Vector Spaces and Groups (Pure and Applied Mathematics)
by Karlheinz SpindlerA comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.
Abstract Analytic Number Theory (Dover Books on Mathematics #Volume 12)
by John Knopfmacher"This book is well-written and the bibliography excellent," declared Mathematical Reviews of John Knopfmacher's innovative study. The three-part treatment applies classical analytic number theory to a wide variety of mathematical subjects not usually treated in an arithmetical way. The first part deals with arithmetical semigroups and algebraic enumeration problems; Part Two addresses arithmetical semigroups with analytical properties of classical type; and the final part explores analytical properties of other arithmetical systems.Because of its careful treatment of fundamental concepts and theorems, this text is accessible to readers with a moderate mathematical background, i.e., three years of university-level mathematics. An extensive bibliography is provided, and each chapter includes a selection of references to relevant research papers or books. The book concludes with an appendix that offers several unsolved questions, with interesting proposals for further development.
Abstract Lie Algebras
by David J WinterSolid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. Author David J. Winter, a Professor of Mathematics at the University of Michigan, also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields.Preliminary material covers modules and nonassociate algebras, followed by a compact, self-contained development of the theory of Lie algebras of characteristic 0. Topics include solvable and nilpotent Lie algebras, Cartan subalgebras, and Levi's radical splitting theorem and the complete reducibility of representations of semisimple Lie algebras. Additional subjects include the isomorphism theorem for semisimple Lie algebras and their irreducible modules, automorphism of Lie algebras, and the conjugacy of Cartan subalgebras and Borel subalgebras. An extensive theory of Cartan and related subalgebras of Lie algebras over arbitrary fields is developed in the final chapter, and an appendix offers background on the Zariski topology.
Abstract Methods in Partial Differential Equations
by Robert W. CarrollDetailed and self-contained, this treatment is directed to graduate students with some previous exposure to classical partial differential equations. The author examines a variety of modern abstract methods in partial differential equations, especially in the area of abstract evolution equations. Additional topics include the theory of nonlinear monotone operators applied to elliptic and variational problems. 1969 edition.
Abstract Sets and Finite Ordinals: An Introduction to the Study of Set Theory
by G. B. KeeneThis text unites the logical and philosophical aspects of set theory in a manner intelligible both to mathematicians without training in formal logic and to logicians without a mathematical background. It combines an elementary level of treatment with the highest possible degree of logical rigor and precision.Starting with an explanation of all the basic logical terms and related operations, the text progresses through a stage-by-stage elaboration that proves the fundamental theorems of finite sets. It focuses on the Bernays theory of finite classes and finite sets, exploring the system's basis and development, including Stage I and Stage II theorems, the theory of finite ordinals, and the theory of finite classes and finite sets. This volume represents an excellent text for undergraduates studying intermediate or advanced logic as well as a fine reference for professional mathematicians.
Abstract State Machines, Alloy, B, TLA, VDM, and Z: 5th International Conference, Abz 2016, Linz, Austria, May 23-27, 2016, Proceedings (Lecture Notes in Computer Science #9675)
by Michael Butler Atif Mashkoor Miklos Biro Laus-Dieter ScheweThis book constitutes the refereed proceedings of the 5th International Conference on Abstract State Machines, Alloy, B, TLA, VDM, and Z, ABZ 2016, held in Linz, Austria, in May 2016. <P><P> The 17 full and 15 short papers presented in this volume were carefully reviewed and selected from 61 submissions. They record the latest research developments in state-based formal methods Abstract State Machines, Alloy, B, Circus, Event-B, TLS+, VDM and Z.
Abstract State Machines, Alloy, B, TLA, VDM, and Z: 5th International Conference, ABZ 2016, Linz, Austria, May 23-27, 2016, Proceedings (Lecture Notes in Computer Science #9675)
by Michael Butler Klaus-Dieter Schewe Atif Mashkoor Miklos BiroThis bookconstitutes the refereed proceedings of the 5th International Conference on AbstractState Machines, Alloy, B, TLA, VDM, and Z, ABZ 2016, held in Linz, Austria, inMay 2016. The 17 full and 15 short papers presented in this volume were carefullyreviewed and selected from 61 submissions. They record the latest researchdevelopments in state-based formal methods Abstract State Machines, Alloy, B,Circus, Event-B, TLS+, VDM and Z.
Accelerated Lattice Boltzmann Model for Colloidal Suspensions: Rheology and Interface Morphology
by Hassan Farhat Joon Sang Lee Sasidhar KondarajuColloids are ubiquitous in the food, medical, cosmetics, polymers, water purification, and pharmaceutical industries. The thermal, mechanical, and storage properties of colloids are highly dependent on their interface morphology and their rheological behavior. Numerical methods provide a convenient and reliable tool for the study of colloids. Accelerated Lattice Boltzmann Model for Colloidal Suspensions introduce the main building-blocks for an improved lattice Boltzmann-based numerical tool designed for the study of colloidal rheology and interface morphology. This book also covers the migrating multi-block used to simulate single component, multi-component, multiphase, and single component multiphase flows and their validation by experimental, numerical, and analytical solutions. Among other topics discussed are the hybrid lattice Boltzmann method (LBM) for surfactant-covered droplets; biological suspensions such as blood; used in conjunction with the suppression of coalescence for investigating the rheology of colloids and microvasculature blood flow. The presented LBM model provides a flexible numerical platform consisting of various modules that could be used separately or in combination for the study of a variety of colloids and biological flow deformation problems.
Accentuate the Negative: Integers and Rational Numbers
by Glenda Lappan James T. Fey Susan N. Friel Elizabeth Difanis PhillipsIn this book; you will study integers and rational numbers, two specific sets of numbers that include positive and negative numbers. You will explore models that help you think about adding, subtracting, multiplying and dividing these numbers. You will also learn about the properties of operations on positive and negative numbers. Connected Mathematics® is a registered trademark of Pearson Education, Inc.
Accentuate the Negative, Integers and Rational Numbers
by Glenda Lappan James T. Fey William M. Fitzgerald Susan N. Friel Elizabeth Difanis PhillipsNIMAC-sourced textbook
Accentuate the Negative, Integers and Rational Numbers
by Glenda Lappan James T. Fey William M. Fitzgerald Susan N. Friel Elizabeth Difanis PhillipsNIMAC-sourced textbook
Accentuate the Negative, Integers and Rational Numbers (Texas)
by Glenda Lappan James T. Fey William M. Fitzgerald Susan N. Friel Elizabeth Difanis Phillips WestWordsNIMAC-sourced textbook
Acceptance Sampling in Quality Control
by Edward Schilling Dean NeubauerAcceptance Sampling in Quality Control, Third Edition presents the state of the art in the methodology of sampling while integrating both theory and best practices. It discusses various standards, including those from the ISO, MIL-STD and ASTM and explores how to set quality levels. The book also includes problems at the end of each chapter with solutions. This edition improves upon the previous editions especially in the areas of software applications and compliance sampling plans. New to the Third Edition: Numerous Microsoft Excel templates to address sampling plans are used. Commercial software applications are discussed at the end of many chapters. Discussion of quick switching systems has been expanded to account for the considerable recent activity in this area. Added discussion of zero acceptance number chained quick switching systems.
Accessible Mathematics: Ten Instructional Shifts That Raise Student Achievement
by Steven LeinwandRaising students' math achievement doesn't mean ripping up your planning book and starting over. InAccessible Mathematics Steven Leinwand (author of Sensible Mathematics) shows how small shifts in the good teaching you already do can make a big difference in student learning. <p><p> Accessible Mathematics is Leinwand's latest important book for math teachers. In it he focuses on the crucial issue of classroom instruction. He scours the research and visits highly effective classrooms for practical examples of small adjustments to your teaching that lead to deeper student learning in math. Some of his 10 classroom-tested teaching shifts may surprise you and others will validate your thinking. But all of them will improve your students' performance. <p> Thoroughly practical and ever-aware of the limits of teachers' time, Leinwand gives you everything you need to put his commonsense ideas to use immediately. His extensive planning advice will help you streamline your teaching to get more from everything you do. Classroom examples from every grade level model teaching language and instructional moves. And his suggestions for professional learning help increase your effectiveness through the power of collaboration. <p> Steven Leinwand shares your priority: raising the mathematical understanding and achievement of every one of your students. Read Accessible Mathematics, try his 10 suggestions in your practice, and discover how minor shifts in your teaching can put student learning into high gear.
An Accidental Statistician
by George E. BoxCelebrating the life of an admired pioneer in statisticsIn this captivating and inspiring memoir, world-renowned statistician George E. P. Box offers a firsthand account of his life and statistical work. Writing in an engaging, charming style, Dr. Box reveals the unlikely events that led him to a career in statistics, beginning with his job as a chemist conducting experiments for the British army during World War II. At this turning point in his life and career, Dr. Box taught himself the statistical methods necessary to analyze his own findings when there were no statisticians available to check his work.Throughout his autobiography, Dr. Box expertly weaves a personal and professional narrative to illustrate the effects his work had on his life and vice-versa. Interwoven between his research with time series analysis, experimental design, and the quality movement, Dr. Box recounts coming to the United States, his family life, and stories of the people who mean the most to him.This fascinating account balances the influence of both personal and professional relationships to demonstrate the extraordinary life of one of the greatest and most influential statisticians of our time. An Accidental Statistician also features:* Two forewords written by Dr. Box's former colleagues and closest confidants* Personal insights from more than a dozen statisticians on how Dr. Box has influenced and continues to touch their careers and lives* Numerous, previously unpublished photos from the author's personal collectionAn Accidental Statistician is a compelling read for statisticians in education or industry, mathematicians, engineers, and anyone interested in the life story of an influential intellectual who altered the world of modern statistics.
Accountability for After-School Care
by Alison Jacknowitz Angela Hawken Megan K. BeckettIncreasing numbers of children are participating in after-school programs, and with more federal and state funding the number of such programs is likely to grow. This growth has been occurring, however, with little guidance as to what program features or practices might be most helpful in nurturing the educational achievement, emotional development, and health of the children involved. This book helps fill that need for guidance by offering a set of 18 model practices against which after-school programs can be evaluated. The authors provide ways to score adherence to the criteria, from excellent to inadequate; survey forms for collecting the information to assign these grades; and an illustrative application of their approach to a set of real-world after-school programs.
Accountancy 12th Standard Tamil Medium Tamil Nadu Board
by Government Of Tamil NaduThis Accountancy textbook is the source of knowledge to provide you with the basic understanding of Accountancy and to make use of your analytical ability to make you an excellent person in applying the accounting principles to real business situations through various activities given in the textbook. The book contains 14 units, within which the subdivisions and various student activities are given in an organised way to make learning easy, systematic and a pleasure.