Sets Groups And Mappings An Introduction To Abstract Mathematics

Author : Andrew D. Hwang
Publisher : American Mathematical Soc.
Page : 304 pages
File Size : 53,5 Mb
Release : 2019-09-26
Category : Algebra
ISBN : 9781470449322

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Sets, Groups, and Mappings: An Introduction to Abstract Mathematics by Andrew D. Hwang Pdf

This book introduces students to the world of advanced mathematics using algebraic structures as a unifying theme. Having no prerequisites beyond precalculus and an interest in abstract reasoning, the book is suitable for students of math education, computer science or physics who are looking for an easy-going entry into discrete mathematics, induction and recursion, groups and symmetry, and plane geometry. In its presentation, the book takes special care to forge linguistic and conceptual links between formal precision and underlying intuition, tending toward the concrete, but continually aiming to extend students' comfort with abstraction, experimentation, and non-trivial computation. The main part of the book can be used as the basis for a transition-to-proofs course that balances theory with examples, logical care with intuitive plausibility, and has sufficient informality to be accessible to students with disparate backgrounds. For students and instructors who wish to go further, the book also explores the Sylow theorems, classification of finitely-generated Abelian groups, and discrete groups of Euclidean plane transformations.

Author : Steven Howard Weintraub
Publisher : World Scientific
Page : 438 pages
File Size : 46,8 Mb
Release : 2022-05-25
Category : Mathematics
ISBN : 9789811246685

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Introduction To Abstract Algebra, An: Sets, Groups, Rings, And Fields by Steven Howard Weintraub Pdf

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.

Author : F. M. Hall
Publisher : Cambridge University Press
Page : 324 pages
File Size : 41,6 Mb
Release : 1972-04-06
Category : Mathematics
ISBN : 0521084849

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An Introduction to Abstract Algebra by F. M. Hall Pdf

This two-volume course on abstract algebra provides a broad introduction to the subject for those with no previous knowledge of it but who are well grounded in ordinary algebraic techniques. It starts from the beginning, leading up to fresh ideas gradually and in a fairly elementary manner, and moving from discussion of particular (concrete) cases to abstract ideas and methods. It thus avoids the common practice of presenting the reader with a mass of ideas at the beginning, which he is only later able to relate to his previous mathematical experience. The work contains many concrete examples of algebraic structures. Each chapter contains a few worked examples for the student - these are divided into straightforward and more advanced categories. Answers are provided. From general sets, Volume 1 leads on to discuss special sets of the integers, other number sets, residues, polynomials and vectors. A chapter on mappings is followed by a detailed study of the fundamental laws of algebra, and an account of the theory of groups which takes the idea of subgroups as far as Langrange's theorem. Some improvements in exposition found desirable by users of the book have been incorporated into the second edition and the opportunity has also been taken to correct a number of errors.

Author : Clive Reis
Publisher : World Scientific Publishing Company
Page : 508 pages
File Size : 53,9 Mb
Release : 2011-05-05
Category : Mathematics
ISBN : 9789813100718

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Abstract Algebra by Clive Reis Pdf

This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya–Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems. Considerable emphasis is placed on the algebraic system consisting of congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced — via congruence classes — to the idea of cosets and factor groups. This enables the transition to cosets and factor objects in a more abstract setting to be relatively painless. The chapters dealing with applications help to reinforce the concepts and methods developed in the context of more down-to-earth problems. Most introductory texts in abstract algebra either avoid cosets, factor objects and homomorphisms completely or introduce them towards the end of the book. In this book, these topics are dealt with early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible, even if there are alternative methods of proof.

Author : James Alexander Green
Publisher : Routledge/Thoemms Press
Page : 104 pages
File Size : 40,6 Mb
Release : 1965
Category : Mathematics
ISBN : STANFORD:36105031213650

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Sets and Groups by James Alexander Green Pdf

Author : D. G. Northcott
Publisher : Cambridge University Press
Page : 297 pages
File Size : 44,5 Mb
Release : 1980-05-08
Category : Mathematics
ISBN : 9780521229098

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Affine Sets and Affine Groups by D. G. Northcott Pdf

In these notes, first published in 1980, Professor Northcott provides a self-contained introduction to the theory of affine algebraic groups for mathematicians with a basic knowledge of communicative algebra and field theory. The book divides into two parts. The first four chapters contain all the geometry needed for the second half of the book which deals with affine groups. Alternatively the first part provides a sure introduction to the foundations of algebraic geometry. Any affine group has an associated Lie algebra. In the last two chapters, the author studies these algebras and shows how, in certain important cases, their properties can be transferred back to the groups from which they arose. These notes provide a clear and carefully written introduction to algebraic geometry and algebraic groups.

Author : Joseph J. Rotman
Publisher : Springer Science & Business Media
Page : 533 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461241768

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An Introduction to the Theory of Groups by Joseph J. Rotman Pdf

Anyone who has studied abstract algebra and linear algebra as an undergraduate can understand this book. The first six chapters provide material for a first course, while the rest of the book covers more advanced topics. This revised edition retains the clarity of presentation that was the hallmark of the previous editions. From the reviews: "Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his chosen route." --MATHEMATICAL REVIEWS

Author : Paul Alexandroff
Publisher : Courier Corporation
Page : 128 pages
File Size : 50,8 Mb
Release : 2013-07-24
Category : Mathematics
ISBN : 9780486275970

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An Introduction to the Theory of Groups by Paul Alexandroff Pdf

This introductory exposition of group theory by an eminent Russian mathematician is particularly suited to undergraduates. Includes a wealth of simple examples, primarily geometrical, and end-of-chapter exercises. 1959 edition.

Author : Derek J.S. Robinson
Publisher : Springer Science & Business Media
Page : 518 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781441985941

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A Course in the Theory of Groups by Derek J.S. Robinson Pdf

"An excellent up-to-date introduction to the theory of groups. It is general yet comprehensive, covering various branches of group theory. The 15 chapters contain the following main topics: free groups and presentations, free products, decompositions, Abelian groups, finite permutation groups, representations of groups, finite and infinite soluble groups, group extensions, generalizations of nilpotent and soluble groups, finiteness properties." —-ACTA SCIENTIARUM MATHEMATICARUM

Author : R. B. J. T. Allenby
Publisher : Unknown
Page : 294 pages
File Size : 52,5 Mb
Release : 1983
Category : Algebra, Abstract
ISBN : OCLC:1151154881

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Rings, Fields and Groups by R. B. J. T. Allenby Pdf

Author : Oleg Vladimirovič Bogopolʹskij
Publisher : European Mathematical Society
Page : 196 pages
File Size : 51,7 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190418

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Introduction to Group Theory by Oleg Vladimirovič Bogopolʹskij Pdf

This book quickly introduces beginners to general group theory and then focuses on three main themes : finite group theory, including sporadic groups combinatorial and geometric group theory, including the Bass-Serre theory of groups acting on trees the theory of train tracks by Bestvina and Handel for automorphisms of free groups With its many examples, exercises, and full solutions to selected exercises, this text provides a gentle introduction that is ideal for self-study and an excellent preparation for applications. A distinguished feature of the presentation is that algebraic and geometric techniques are balanced. The beautiful theory of train tracks is illustrated by two nontrivial examples. Presupposing only a basic knowledge of algebra, the book is addressed to anyone interested in group theory: from advanced undergraduate and graduate students to specialists.

Author : Steven Roman
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 41,6 Mb
Release : 2011-10-26
Category : Mathematics
ISBN : 9780817683016

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Fundamentals of Group Theory by Steven Roman Pdf

Fundamentals of Group Theory provides a comprehensive account of the basic theory of groups. Both classic and unique topics in the field are covered, such as an historical look at how Galois viewed groups, a discussion of commutator and Sylow subgroups, and a presentation of Birkhoff’s theorem. Written in a clear and accessible style, the work presents a solid introduction for students wishing to learn more about this widely applicable subject area. This book will be suitable for graduate courses in group theory and abstract algebra, and will also have appeal to advanced undergraduates. In addition it will serve as a valuable resource for those pursuing independent study. Group Theory is a timely and fundamental addition to literature in the study of groups.

Author : Clive Reis
Publisher : Unknown
Page : 574 pages
File Size : 43,9 Mb
Release : 2016
Category : Electronic books
ISBN : 9814730556

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Abstract Algebra by Clive Reis Pdf

Author : W.C. Waterhouse
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461262176

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Introduction to Affine Group Schemes by W.C. Waterhouse Pdf

Ah Love! Could you and I with Him consl?ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpoints and demonstrate how they offer complementary intuitive insight into the subject. In Part I we begin with a functorial idea, discussing some familiar processes for constructing groups. These turn out to be equivalent to the ring-theoretic objects called Hopf algebras, with which we can then con struct new examples. Study of their representations shows that they are closely related to groups of matrices, and closed sets in matrix space give us a geometric picture of some of the objects involved. This interplay of methods continues as we turn to specific results. In Part II, a geometric idea (connectedness) and one from classical matrix theory (Jordan decomposition) blend with the study of separable algebras. In Part III, a notion of differential prompted by the theory of Lie groups is used to prove the absence of nilpotents in certain Hopf algebras. The ring-theoretic work on faithful flatness in Part IV turns out to give the true explanation for the behavior of quotient group functors. Finally, the material is connected with other parts of algebra in Part V, which shows how twisted forms of any algebraic structure are governed by its automorphism group scheme.

Author : John F. Lucas
Publisher : Rowman & Littlefield
Page : 400 pages
File Size : 44,8 Mb
Release : 1990
Category : Mathematics
ISBN : 091267573X

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Introduction to Abstract Mathematics by John F. Lucas Pdf

This is a book about mathematics and mathematical thinking. It is intended for the serious learner who is interested in studying some deductive strategies in the context of a variety of elementary mathematical situations. No background beyond single-variable calculus is presumed.