Introduction to abstract algebra, an: sets, groups, rings, and fields, Weintraub, Steven Howard (lehigh Univ, Usa)

Автор: Ryota Matsuura
Название: A Friendly Introduction to Abstract Algebra
ISBN: 1470468816 ISBN-13(EAN): 9781470468811
Издательство: Mare Nostrum (Eurospan)
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Цена: 57690.00 T
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Описание: 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.

Автор: Thomas Q. Sibley
Название: Thinking Algebraically: An Introduction to Abstract Algebra
ISBN: 1470460300 ISBN-13(EAN): 9781470460303
Издательство: Mare Nostrum (Eurospan)
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Цена: 71060.00 T
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Описание: Thinking Algebraically presents the insights of abstract algebra in a welcoming and accessible way. It succeeds in combining the advantages of rings-first and groups-first approaches while avoiding the disadvantages. After an historical overview, the first chapter studies familiar examples and elementary properties of groups and rings simultaneously to motivate the modern understanding of algebra. The text builds intuition for abstract algebra starting from high school algebra. In addition to the standard number systems, polynomials, vectors, and matrices, the first chapter introduces modular arithmetic and dihedral groups. The second chapter builds on these basic examples and properties, enabling students to learn structural ideas common to rings and groups: isomorphism, homomorphism, and direct product. The third chapter investigates introductory group theory. Later chapters delve more deeply into groups, rings, and fields, including Galois theory, and they also introduce other topics, such as lattices. The exposition is clear and conversational throughout. The book has numerous exercises in each section as well as supplemental exercises and projects for each chapter. Many examples and well over 100 figures provide support for learning. Short biographies introduce the mathematicians who proved many of the results. The book presents a pathway to algebraic thinking in a semester- or year-long algebra course.

Автор: Hungerford
Название: Abstract Algebra Introduction Softcover
ISBN: 0357670876 ISBN-13(EAN): 9780357670873
Издательство: Cengage Learning
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Цена: 85530.00 T
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Описание: Abstract Algebra: An Introduction is set apart by its thematic development and organization. The chapters are organized around two themes: arithmetic and congruence. Each theme is developed first for the integers, then for polynomials, and finally for rings and groups. This enables students to see where many abstract concepts come from, why they are important, and how they relate to one another. New to this edition is a groups first option that enables those who prefer to cover groups before rings to do so easily.

Автор: Smith
Название: Introduction to Abstract Algebra, Second Edition
ISBN: 1498731619 ISBN-13(EAN): 9781498731614
Издательство: Taylor&Francis
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Цена: 107190.00 T
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Описание:

Introduction to Abstract Algebra, Second Edition presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It avoids the usual groups first/rings first dilemma by introducing semigroups and monoids, the multiplicative structures of rings, along with groups.
This new edition of a widely adopted textbook covers applications from biology, science, and engineering. It offers numerous updates based on feedback from first edition adopters, as well as improved and simplified proofs of a number of important theorems. Many new exercises have been added, while new study projects examine skewfields, quaternions, and octonions.
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. These three chapters provide a quick introduction to algebra, sufficient to exhibit irrational numbers or to gain a taste of cryptography.
Chapters four through seven cover abstract groups and monoids, orthogonal groups, stochastic matrices, Lagrange's theorem, groups of units of monoids, homomorphisms, rings, and integral domains. The first seven chapters provide basic coverage of abstract algebra, suitable for a one-semester or two-quarter course.
Each chapter includes exercises of varying levels of difficulty, chapter notes that point out variations in notation and approach, and study projects that cover an array of applications and developments of the theory.
The final chapters deal with slightly more advanced topics, suitable for a second-semester or third-quarter course. These chapters delve deeper into the theory of rings, fields, and groups. They discuss modules, including vector spaces and abelian groups, group theory, and quasigroups.
This textbook is suitable for use in an undergraduate course on abstract algebra for mathematics, computer science, and education majors, along with students from other STEM fields.

Автор: Strang, Gilbert
Название: Introduction to linear algebra
ISBN: 1733146652 ISBN-13(EAN): 9781733146654
Издательство: Cambridge Academ
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Цена: 79190.00 T
Наличие на складе: Невозможна поставка.
Описание: Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains the quality of earlier editions while at the same time seeing numerous minor improvements and major additions. The latter include: a new chapter on singular values and singular vectors, including ways to analyze a matrix of data; a revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages; a new section on linear algebra and cryptography; and a new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (e.g. practice problems, exams, development of textbook examples), plus codes in MATLAB, Julia, and Python.

Автор: Strang
Название: Introduction to Linear Algebra 5 ed.
ISBN: 0980232775 ISBN-13(EAN): 9780980232776
Издательство: Cambridge Academ
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Цена: 0.00 T
Наличие на складе: Невозможна поставка.
Описание: Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains all the qualities of earlier editions, while at the same time seeing numerous minor improvements and major additions. The latter include: • A new chapter on singular values and singular vectors, including ways to analyze a matrix of data • A revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages • A new section on linear algebra and cryptography • A new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (including practice problems, exams, and development of textbook examples), plus codes in MATLAB®, Julia, and Python.

Автор: Armand Borel
Название: Introduction to Arithmetic Groups
ISBN: 1470452316 ISBN-13(EAN): 9781470452315
Издательство: Mare Nostrum (Eurospan)
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Цена: 51750.00 T
Наличие на складе: Невозможна поставка.
Описание: Fifty years after it was first published, Armand Borel`s Introduction aux groupes arithmetiques continues to be very important for the theory of arithmetic groups. In particular, Chapter III of the book remains the standard reference for fundamental results on reduction theory.

Автор: Kolenkow, Robert
Название: Introduction to groups and their matrices for science students
ISBN: 1108831087 ISBN-13(EAN): 9781108831086
Издательство: Cambridge Academ
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Цена: 47510.00 T
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Описание: Group theory, originating from algebraic structures in mathematics, has long been an important computational tool in many areas of physics, chemistry and other applied sciences. This comprehensive primer to group theory is ideal at advanced undergraduate and graduate level for topics courses, reading groups, or self-study.

Автор: Kirillov, Alexander, Jr.
Название: Introduction to lie groups and lie algebras
ISBN: 1316614107 ISBN-13(EAN): 9781316614105
Издательство: Cambridge Academ
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Цена: 40130.00 T
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Описание: This graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. Written in an informal style, this is a contemporary introduction to the subject. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras.

Автор: Nachtergaele Bruno Et Al
Название: Linear Algebra As An Introduction To Abstract Mathematics
ISBN: 9814730351 ISBN-13(EAN): 9789814730358
Издательство: World Scientific Publishing
Цена: 61250.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:

This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.

Автор: Nachtergaele Bruno Et Al
Название: Linear Algebra As An Introduction To Abstract Mathematics
ISBN: 9814723770 ISBN-13(EAN): 9789814723770
Издательство: World Scientific Publishing
Цена: 31680.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:

This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.

Автор: Steven Howard Weintraub
Название: Introduction To Abstract Algebra, An: Sets, Groups, Rings, And Fields
ISBN: 9811246661 ISBN-13(EAN): 9789811246661
Издательство: World Scientific Publishing
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Цена: 142560.00 T
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Описание: This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level.It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers.In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory.As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Written with an eye toward number theory, it contains numerous applications to number theory (including proofs of Fermat's theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular.Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further.