Exploring Abstract Algebra With Mathematica

Author : Allen C. Hibbard,Kenneth M. Levasseur
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461215301

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Exploring Abstract Algebra With Mathematica® by Allen C. Hibbard,Kenneth M. Levasseur Pdf

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.

Author : William Paulsen
Publisher : CRC Press
Page : 0 pages
File Size : 52,5 Mb
Release : 2009-07-29
Category : Political Science
ISBN : 1420094521

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Abstract Algebra by William Paulsen Pdf

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.

Author : Crista Arangala
Publisher : CRC Press
Page : 155 pages
File Size : 52,5 Mb
Release : 2014-11-13
Category : Mathematics
ISBN : 9781482241495

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Exploring Linear Algebra by Crista Arangala Pdf

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.

Author : William Paulsen
Publisher : CRC Press
Page : 650 pages
File Size : 43,9 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9781315362410

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Abstract Algebra by William Paulsen Pdf

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.

Author : Allen C. Hibbard,Ellen J. Maycock
Publisher : Mathematical Association of America (MAA)
Page : 174 pages
File Size : 49,8 Mb
Release : 2002
Category : Mathematics
ISBN : UOM:39076002450661

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Innovations in Teaching Abstract Algebra by Allen C. Hibbard,Ellen J. Maycock Pdf

Author : John K. Osoinach, Jr.
Publisher : American Mathematical Soc.
Page : 199 pages
File Size : 51,8 Mb
Release : 2021-10-04
Category : Education
ISBN : 9781470464424

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Discovering Abstract Algebra by John K. Osoinach, Jr. Pdf

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.

Author : Ryota Matsuura
Publisher : American Mathematical Society
Page : 404 pages
File Size : 46,9 Mb
Release : 2022-07-06
Category : Mathematics
ISBN : 9781470468811

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A Friendly Introduction to Abstract Algebra by Ryota Matsuura Pdf

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.

Author : Jeremy Gray
Publisher : Springer
Page : 415 pages
File Size : 53,5 Mb
Release : 2018-08-07
Category : Mathematics
ISBN : 9783319947730

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A History of Abstract Algebra by Jeremy Gray Pdf

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.

Author : Israel Kleiner
Publisher : Springer Science & Business Media
Page : 175 pages
File Size : 55,5 Mb
Release : 2007-10-02
Category : Mathematics
ISBN : 9780817646844

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A History of Abstract Algebra by Israel Kleiner Pdf

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.

Author : Stephen Lovett
Publisher : CRC Press
Page : 1032 pages
File Size : 53,8 Mb
Release : 2022-07-05
Category : Mathematics
ISBN : 9781000605525

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Abstract Algebra by Stephen Lovett Pdf

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.

Author : Derek J.S. Robinson
Publisher : Walter de Gruyter GmbH & Co KG
Page : 347 pages
File Size : 46,6 Mb
Release : 2015-05-19
Category : Mathematics
ISBN : 9783110340877

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Abstract Algebra by Derek J.S. Robinson Pdf

This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems and error correcting codes are described. Another feature of the book is that group theory and ring theory are carried further than is often done at this level. There is ample material here for a two semester course in abstract algebra. The importance of proof is stressed and rigorous proofs of almost all results are given. But care has been taken to lead the reader through the proofs by gentle stages. There are nearly 400 problems, of varying degrees of difficulty, to test the reader's skill and progress. The book should be suitable for students in the third or fourth year of study at a North American university or in the second or third year at a university in Europe, and should ease the transition to (post)graduate studies.

Author : Crista Arangala,Karen A. Yokley
Publisher : CRC Press
Page : 123 pages
File Size : 50,5 Mb
Release : 2016-08-19
Category : Mathematics
ISBN : 9781498771061

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Exploring Calculus by Crista Arangala,Karen A. Yokley Pdf

This text is meant to be a hands-on lab manual that can be used in class every day to guide the exploration of the theory and applications of differential and integral calculus. For the most part, labs can be used individually or in a sequence. Each lab consists of an explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections. The exercise sections integrate problems, technology, Mathematica R visualization, and Mathematica CDFs that allow students to discover the theory and applications of differential and integral calculus in a meaningful and memorable way. Employs Mathematica to calculate and explore concepts and theories of calculus Uses engaging labs to inspire learning Includes many applications to a variety of fields that can promote research projects User-friendly approach that can be used for classroom work or independent exploratory learning

Author : Gary L. Mullen,James A. Sellers
Publisher : CRC Press
Page : 204 pages
File Size : 49,7 Mb
Release : 2016-12-19
Category : Mathematics
ISBN : 9781482250077

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Abstract Algebra by Gary L. Mullen,James A. Sellers Pdf

Abstract 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

Author : John W. Lawrence,Frank A. Zorzitto
Publisher : Cambridge University Press
Page : 639 pages
File Size : 54,6 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9781108836654

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An Introduction to Abstract Algebra by John W. Lawrence,Frank A. Zorzitto Pdf

A lucid guide to abstract algebra, this comprehensive textbook provides in depth coverage for upper undergraduate students.

Author : James R. Kirkwood,Bessie H. Kirkwood
Publisher : CRC Press
Page : 304 pages
File Size : 47,8 Mb
Release : 2017-12-15
Category : Mathematics
ISBN : 9781351253116

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Elementary Linear Algebra by James R. Kirkwood,Bessie H. Kirkwood Pdf

Elementary Linear Algebra is written for the first undergraduate course. The book focuses on the importance of linear algebra in many disciplines such as engineering, economics, statistics, and computer science. The text reinforces critical ideas and lessons of traditional topics. More importantly, the book is written in a manner that deeply ingrains computational methods.