Undergraduate Algebra

Undergraduate Algebra
Author: Serge Lang
Publisher: Springer Science & Business Media
Total Pages: 380
Release: 2013-06-29
Genre: Mathematics
ISBN: 1475768982

The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group

Undergraduate Algebra

Undergraduate Algebra
Author: Matej Brešar
Publisher: Springer
Total Pages: 316
Release: 2019-05-20
Genre: Mathematics
ISBN: 9783030140526

This textbook offers an innovative approach to abstract algebra, based on a unified treatment of similar concepts across different algebraic structures. This makes it possible to express the main ideas of algebra more clearly and to avoid unnecessary repetition. The book consists of two parts: The Language of Algebra and Algebra in Action. The unified approach to different algebraic structures is a primary feature of the first part, which discusses the basic notions of algebra at an elementary level. The second part is mathematically more complex, covering topics such as the Sylow theorems, modules over principal ideal domains, and Galois theory. Intended for an undergraduate course or for self-study, the book is written in a readable, conversational style, is rich in examples, and contains over 700 carefully selected exercises.

Undergraduate Commutative Algebra

Undergraduate Commutative Algebra
Author: Miles Reid
Publisher: Cambridge University Press
Total Pages: 172
Release: 1995-11-30
Genre: Mathematics
ISBN: 9780521458894

Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position of abstract algebra in today's world.

A Course in Algebra

A Course in Algebra
Author: Ėrnest Borisovich Vinberg
Publisher: American Mathematical Soc.
Total Pages: 532
Release: 2003-04-10
Genre: Mathematics
ISBN: 9780821834138

Presents modern algebra. This book includes such topics as affine and projective spaces, tensor algebra, Galois theory, Lie groups, and associative algebras and their representations. It is suitable for independent study for advanced undergraduates and graduate students.

Applied Abstract Algebra

Applied Abstract Algebra
Author: Rudolf Lidl
Publisher: Springer Science & Business Media
Total Pages: 500
Release: 2013-03-14
Genre: Mathematics
ISBN: 1475729413

Accessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract algebra of use in many other areas of discrete mathematics. Although this is a mathematics book, the authors have made great efforts to address the needs of users employing the techniques discussed. Fully worked out computational examples are backed by more than 500 exercises throughout the 40 sections. This new edition includes a new chapter on cryptology, and an enlarged chapter on applications of groups, while an extensive chapter has been added to survey other applications not included in the first edition. The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields.

A Concrete Introduction to Higher Algebra

A Concrete Introduction to Higher Algebra
Author: Lindsay N. Childs
Publisher: Springer Science & Business Media
Total Pages: 540
Release: 2012-12-04
Genre: Mathematics
ISBN: 1441987029

An informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials, with much emphasis placed on congruence classes leading the way to finite groups and finite fields. New examples and theory are integrated in a well-motivated fashion and made relevant by many applications -- to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises, ranging from routine examples to extensions of theory, are scattered throughout the book, with hints and answers for many of them included in an appendix.

Linear Algebra Done Right

Linear Algebra Done Right
Author: Sheldon Axler
Publisher: Springer Science & Business Media
Total Pages: 276
Release: 1997-07-18
Genre: Mathematics
ISBN: 9780387982595

This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.

A Book of Abstract Algebra

A Book of Abstract Algebra
Author: Charles C Pinter
Publisher: Courier Corporation
Total Pages: 402
Release: 2010-01-14
Genre: Mathematics
ISBN: 0486474178

Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

A Field Guide to Algebra

A Field Guide to Algebra
Author: Antoine Chambert-Loir
Publisher: Springer Science & Business Media
Total Pages: 199
Release: 2004-10-01
Genre: Mathematics
ISBN: 0387214283

This book has a nonstandard choice of topics, including material on differential galois groups and proofs of the transcendence of e and pi. The author uses a conversational tone and has included a selection of stamps to accompany the text.

Algebra

Algebra
Author: Thomas W. Hungerford
Publisher: Springer Science & Business Media
Total Pages: 523
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461261015

Finally a self-contained, one volume, graduate-level algebra text that is readable by the average graduate student and flexible enough to accommodate a wide variety of instructors and course contents. The guiding principle throughout is that the material should be presented as general as possible, consistent with good pedagogy. Therefore it stresses clarity rather than brevity and contains an extraordinarily large number of illustrative exercises.