Exploring Abstract Algebra With Mathematicar

Download Exploring Abstract Algebra With Mathematicar full books in PDF, epub, and Kindle. Read online Exploring Abstract Algebra With Mathematicar ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Exploring Abstract Algebra With Mathematica®

Author : Allen C. Hibbard
Publisher : Springer Science & Business Media
ISBN 13 : 1461215307
Total Pages : 476 pages
Book Rating : 4.4/5 (612 download)

DOWNLOAD NOW!

Book Synopsis Exploring Abstract Algebra With Mathematica® by : Allen C. Hibbard

Download or read book Exploring Abstract Algebra With Mathematica® written by Allen C. Hibbard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This upper-division laboratory supplement for courses in abstract algebra consists of several Mathematica packages programmed as a foundation for group and ring theory. Additionally, the "user's guide" illustrates the functionality of the underlying code, while the lab portion of the book reflects the contents of the Mathematica-based electronic notebooks. Students interact with both the printed and electronic versions of the material in the laboratory, and can look up details and reference information in the user's guide. Exercises occur in the stream of the text of the lab, which provides a context within which to answer, and the questions are designed to be either written into the electronic notebook, or on paper. The notebooks are available in both 2.2 and 3.0 versions of Mathematica, and run across all platforms for which Mathematica exits. A very timely and unique addition to the undergraduate abstract algebra curriculum, filling a tremendous void in the literature.

Abstract Algebra

Author : William Paulsen
Publisher : CRC Press
ISBN 13 : 9781420094527
Total Pages : 0 pages
Book Rating : 4.0/5 (945 download)

DOWNLOAD NOW!

Book Synopsis Abstract Algebra by : William Paulsen

Download or read book Abstract Algebra written by William Paulsen and published by CRC Press. This book was released on 2009-07-29 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: By integrating the use of GAP and Mathematica®, Abstract Algebra: An Interactive Approach presents a hands-on approach to learning about groups, rings, and fields. Each chapter includes both GAP and Mathematica commands, corresponding Mathematica notebooks, traditional exercises, and several interactive computer problems that utilize GAP and Mathematica to explore groups and rings. Although the book gives the option to use technology in the classroom, it does not sacrifice mathematical rigor. It covers classical proofs, such as Abel’s theorem, as well as many graduate-level 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. He also incorporates problem sequences that allow students to delve into interesting topics in depth, including Fermat’s two square theorem. 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.

Abstract Algebra

Author : William Paulsen
Publisher : CRC Press
ISBN 13 : 1498719791
Total Pages : 484 pages
Book Rating : 4.4/5 (987 download)

DOWNLOAD NOW!

Book Synopsis Abstract Algebra by : William Paulsen

Download or read book Abstract Algebra written by William Paulsen and published by CRC Press. This book was released on 2018-09-03 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. 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.

Discovering Abstract Algebra

Author : John K. Osoinach, Jr.
Publisher : American Mathematical Soc.
ISBN 13 : 147046442X
Total Pages : 199 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis Discovering Abstract Algebra by : John K. Osoinach, Jr.

Download or read book Discovering Abstract Algebra written by John K. Osoinach, Jr. and published by American Mathematical Soc.. This book was released on 2021-10-04 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discovering Abstract Algebra takes an Inquiry-Based Learning approach to the subject, leading students to discover for themselves its main themes and techniques. Concepts are introduced conversationally through extensive examples and student investigation before being formally defined. Students will develop skills in carefully making statements and writing proofs, while they simultaneously build a sense of ownership over the ideas and results. The book has been extensively tested and reinforced at points of common student misunderstanding or confusion, and includes a wealth of exercises at a variety of levels. The contents were deliberately organized to follow the recommendations of the MAA's 2015 Curriculum Guide. The book is ideal for a one- or two-semester course in abstract algebra, and will prepare students well for graduate-level study in algebra.

A History of Abstract Algebra

Author : Israel Kleiner
Publisher : Springer Science & Business Media
ISBN 13 : 0817646841
Total Pages : 175 pages
Book Rating : 4.8/5 (176 download)

DOWNLOAD NOW!

Book Synopsis A History of Abstract Algebra by : Israel Kleiner

Download or read book A History of Abstract Algebra written by Israel Kleiner and published by Springer Science & Business Media. This book was released on 2007-10-02 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Exploring Linear Algebra

Author : Crista Arangala
Publisher : CRC Press
ISBN 13 : 1482241498
Total Pages : 155 pages
Book Rating : 4.4/5 (822 download)

DOWNLOAD NOW!

Book Synopsis Exploring Linear Algebra by : Crista Arangala

Download or read book Exploring Linear Algebra written by Crista Arangala and published by CRC Press. This book was released on 2014-11-13 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring Linear Algebra: Labs and Projects with Mathematica® is a hands-on lab manual for daily use in the classroom. Each lab includes exercises, theorems, and problems that guide your students on an exploration of linear algebra. The exercises section integrates problems, technology, Mathematica® visualization, and Mathematica CDFs, enabling students to discover the theory and applications of linear algebra in a meaningful way. The theorems and problems section presents the theoretical aspects of linear algebra. Students are encouraged to discover the truth of each theorem and problem, to move toward proving (or disproving) each statement, and to present their results to their peers. Each chapter also contains a project set consisting of application-driven projects that emphasize the material in the chapter. Students can use these projects as the basis for further undergraduate research.

Abstract Algebra

Author : Gregory T. Lee
Publisher : Springer
ISBN 13 : 3319776495
Total Pages : 297 pages
Book Rating : 4.3/5 (197 download)

DOWNLOAD NOW!

Book Synopsis Abstract Algebra by : Gregory T. Lee

Download or read book Abstract Algebra written by Gregory T. Lee and published by Springer. This book was released on 2018-04-13 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. 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. 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

Author : Stephen Lovett
Publisher : CRC Press
ISBN 13 : 1000605442
Total Pages : 570 pages
Book Rating : 4.0/5 (6 download)

DOWNLOAD NOW!

Book Synopsis Abstract Algebra by : Stephen Lovett

Download or read book Abstract Algebra written by Stephen Lovett and published by CRC Press. This book was released on 2022-07-05 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: When a student of mathematics studies abstract algebra, he or she inevitably faces questions in the vein of, "What is abstract algebra" or "What makes it abstract?" Algebra, in its broadest sense, describes a way of thinking about classes of sets equipped with binary operations. In high school algebra, a student explores properties of operations (+, −, ×, and ÷) on real numbers. Abstract algebra studies properties of operations without specifying what types of number or object we work with. Any theorem established in the abstract context holds not only for real numbers but for every possible algebraic structure that has operations with the stated properties. This textbook intends to serve as a first course in abstract algebra. The selection of topics serves both of the common trends in such a course: a balanced introduction to groups, rings, and fields; or a course that primarily emphasizes group theory. The writing style is student-centered, conscientiously motivating definitions and offering many illustrative examples. Various sections or sometimes just examples or exercises introduce applications to geometry, number theory, cryptography and many other areas. This book offers a unique feature in the lists of projects at the end of each section. the author does not view projects as just something extra or cute, but rather an opportunity for a student to work on and demonstrate their potential for open-ended investigation. The projects ideas come in two flavors: investigative or expository. The investigative projects briefly present a topic and posed open-ended questions that invite the student to explore the topic, asking and to trying to answer their own questions. Expository projects invite the student to explore a topic with algebraic content or pertain to a particular mathematician’s work through responsible research. The exercises challenge the student to prove new results using the theorems presented in the text. The student then becomes an active participant in the development of the field.

A Friendly Introduction to Abstract Algebra

Author : Ryota Matsuura
Publisher : American Mathematical Society
ISBN 13 : 1470468816
Total Pages : 404 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis A Friendly Introduction to Abstract Algebra by : Ryota Matsuura

Download or read book A Friendly Introduction to Abstract Algebra written by Ryota Matsuura and published by American Mathematical Society. This book was released on 2022-07-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Friendly Introduction to Abstract Algebra offers a new approach to laying a foundation for abstract mathematics. Prior experience with proofs is not assumed, and the book takes time to build proof-writing skills in ways that will serve students through a lifetime of learning and creating mathematics. The author's pedagogical philosophy is that when students abstract from a wide range of examples, they are better equipped to conjecture, formalize, and prove new ideas in abstract algebra. Thus, students thoroughly explore all concepts through illuminating examples before formal definitions are introduced. The instruction in proof writing is similarly grounded in student exploration and experience. Throughout the book, the author carefully explains where the ideas in a given proof come from, along with hints and tips on how students can derive those proofs on their own. Readers of this text are not just consumers of mathematical knowledge. Rather, they are learning mathematics by creating mathematics. The author's gentle, helpful writing voice makes this text a particularly appealing choice for instructors and students alike. The book's website has companion materials that support the active-learning approaches in the book, including in-class modules designed to facilitate student exploration.

A History of Abstract Algebra

Author : Jeremy Gray
Publisher : Springer
ISBN 13 : 3319947737
Total Pages : 412 pages
Book Rating : 4.3/5 (199 download)

DOWNLOAD NOW!

Book Synopsis A History of Abstract Algebra by : Jeremy Gray

Download or read book A History of Abstract Algebra written by Jeremy Gray and published by Springer. This book was released on 2018-08-07 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationship between Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.

Exploring Analytic Geometry with Mathematica

Author : Donald L. Vossler
Publisher : Academic Press
ISBN 13 : 9780127282558
Total Pages : 865 pages
Book Rating : 4.2/5 (825 download)

DOWNLOAD NOW!

Book Synopsis Exploring Analytic Geometry with Mathematica by : Donald L. Vossler

Download or read book Exploring Analytic Geometry with Mathematica written by Donald L. Vossler and published by Academic Press. This book was released on 2000 with total page 865 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of two-dimensional analytic geometry has gone in and out of fashion several times over the past century, however this classic field of mathematics has once again become popular due to the growing power of personal computers and the availability of powerful mathematical software systems, such as Mathematica, that can provide an interactive environment for studying the field. By combining the power of Mathematica with an analytic geometry software system called Descarta2D, the author has succeeded in meshing an ancient field of study with modern computational tools, the result being a simple, yet powerful, approach to studying analytic geometry. Students, engineers and mathematicians alike who are interested in analytic geometry can use this book and software for the study, research or just plain enjoyment of analytic geometry. Mathematica provides an attractive environment for studying analytic geometry. Mathematica supports both numeric and symbolic computations meaning that geometry problems can be solved for special cases using numbers, as well as general cases producing formulas. Mathematica also has good facilities for producing graphical plots which are useful for visualizing the graphs of two-dimensional geometry. * A classic study in analytic geometry, complete with in-line Mathematica dialogs illustrating every concept as it is introduced * Excellent theoretical presentation *Fully explained examples of all key concepts * Interactive Mathematica notebooks for the entire book * Provides a complete computer-based environment for study of analytic geometry * All chapters and reference material are provided on CD-ROM in addition to being printedin the book * Complete software system: Descarta2D * A software system, including source code, for the underlying computer implementation, called Descarta2D is provided * Part VII of the book is a listing of the (30) Mathematica files supporting Descarta2D; the source code is also supplied on CD-ROM * Explorations * More than 120 challenging problems in analytic geometry are posed; Complete solutions are provided both as interactive Mathematica notebooks on CD-ROM and as printed material in the book * Mathematica and Descarta2D Hints expand the reader's knowledge and understanding of Descarta2D and Mathematica * Sortware developed with Mathematica 3.0 and is compatible with Mathematica 4.0 * Detailed reference manual * Complete documentation for Descarta2D * Fully integrated into the Mathematica Help Browser

Abstract Algebra

Author : Derek J.S. Robinson
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110691213
Total Pages : 506 pages
Book Rating : 4.1/5 (16 download)

DOWNLOAD NOW!

Book Synopsis Abstract Algebra by : Derek J.S. Robinson

Download or read book Abstract Algebra written by Derek J.S. Robinson and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-02-07 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and the information and physical sciences. In addition to introducing the main concepts of modern algebra – groups, rings, modules and fields – the book contains numerous applications, which are intended to illustrate the concepts and to show the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems, error correcting codes and economics are described. There is ample material here for a two semester course in abstract algebra. Proofs of almost all results are given. The reader led through the proofs in gentle stages. There are more than 500 problems, of varying degrees of diffi culty. The book should be suitable for advanced undergraduate students in their fi nal year of study and for fi rst or second year graduate students at a university in Europe or North America. In this third edition three new chapters have been added: an introduction to the representation theory of fi nite groups, free groups and presentations of groups, an introduction to category theory.

Abstract Algebra and Famous Impossibilities

Author : Sidney A. Morris
Publisher : Springer Nature
ISBN 13 : 3031056981
Total Pages : 233 pages
Book Rating : 4.0/5 (31 download)

DOWNLOAD NOW!

Book Synopsis Abstract Algebra and Famous Impossibilities by : Sidney A. Morris

Download or read book Abstract Algebra and Famous Impossibilities written by Sidney A. Morris and published by Springer Nature. This book was released on 2022-11-26 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook develops the abstract algebra necessary to prove the impossibility of four famous mathematical feats: squaring the circle, trisecting the angle, doubling the cube, and solving quintic equations. All the relevant concepts about fields are introduced concretely, with the geometrical questions providing motivation for the algebraic concepts. By focusing on problems that are as easy to approach as they were fiendishly difficult to resolve, the authors provide a uniquely accessible introduction to the power of abstraction. Beginning with a brief account of the history of these fabled problems, the book goes on to present the theory of fields, polynomials, field extensions, and irreducible polynomials. Straightedge and compass constructions establish the standards for constructability, and offer a glimpse into why squaring, doubling, and trisecting appeared so tractable to professional and amateur mathematicians alike. However, the connection between geometry and algebra allows the reader to bypass two millennia of failed geometric attempts, arriving at the elegant algebraic conclusion that such constructions are impossible. From here, focus turns to a challenging problem within algebra itself: finding a general formula for solving a quintic polynomial. The proof of the impossibility of this task is presented using Abel’s original approach. Abstract Algebra and Famous Impossibilities illustrates the enormous power of algebraic abstraction by exploring several notable historical triumphs. This new edition adds the fourth impossibility: solving general quintic equations. Students and instructors alike will appreciate the illuminating examples, conversational commentary, and engaging exercises that accompany each section. A first course in linear algebra is assumed, along with a basic familiarity with integral calculus.

Learning Abstract Algebra with ISETL

Author : Ed Dubinsky
Publisher : Springer-Verlag
ISBN 13 : 3662254549
Total Pages : 269 pages
Book Rating : 4.6/5 (622 download)

DOWNLOAD NOW!

Book Synopsis Learning Abstract Algebra with ISETL by : Ed Dubinsky

Download or read book Learning Abstract Algebra with ISETL written by Ed Dubinsky and published by Springer-Verlag. This book was released on 2019-06-12 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Innovations in Teaching Abstract Algebra

Author : Allen C. Hibbard
Publisher : Mathematical Association of America (MAA)
ISBN 13 :
Total Pages : 174 pages
Book Rating : 4.3/5 (97 download)

DOWNLOAD NOW!

Book Synopsis Innovations in Teaching Abstract Algebra by : Allen C. Hibbard

Download or read book Innovations in Teaching Abstract Algebra written by Allen C. Hibbard and published by Mathematical Association of America (MAA). This book was released on 2002 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebra and Number Theory

Author : Martyn R. Dixon
Publisher : John Wiley & Sons
ISBN 13 : 9780470640531
Total Pages : 544 pages
Book Rating : 4.6/5 (45 download)

DOWNLOAD NOW!

Book Synopsis Algebra and Number Theory by : Martyn R. Dixon

Download or read book Algebra and Number Theory written by Martyn R. Dixon and published by John Wiley & Sons. This book was released on 2011-07-15 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines—linear algebra, abstract algebra, and number theory—into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts. The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory. Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material. Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education.

Introduction to Abstract Algebra

Author : Jonathan D. H. Smith
Publisher : CRC Press
ISBN 13 : 1420063723
Total Pages : 330 pages
Book Rating : 4.4/5 (2 download)

DOWNLOAD NOW!

Book Synopsis Introduction to Abstract Algebra by : Jonathan D. H. Smith

Download or read book Introduction to Abstract Algebra written by Jonathan D. H. Smith and published by CRC Press. This book was released on 2016-04-19 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles. A Quick Introduction to Algebra The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. The author also uses equivalence relations to introduce rational numbers and modular arithmetic as well as to present the first isomorphism theorem at the set level. The Basics of Abstract Algebra for a First-Semester Course Subsequent chapters cover orthogonal groups, stochastic matrices, Lagrange’s theorem, and groups of units of monoids. The text also deals with homomorphisms, which lead to Cayley’s theorem of reducing abstract groups to concrete groups of permutations. It then explores rings, integral domains, and fields. Advanced Topics for a Second-Semester Course The final, mostly self-contained chapters delve deeper into the theory of rings, fields, and groups. They discuss modules (such as vector spaces and abelian groups), group theory, and quasigroups.