# Basic Algebra

## Along with a companion volume Advanced Algebra

Part of the Cornerstones book series (COR)

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Textbook

Part of the Cornerstones book series (COR)

*Basic Algebra* and *Advanced Algebra* systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole.

Key topics and features of *Basic Algebra:*

*Linear algebra and group theory build on each other continually

*Chapters on modern algebra treat groups, rings, fields, modules, and Galois groups, with emphasis on methods of computation throughout

*Three prominent themes recur and blend together at times: the analogy between integers and polynomials in one variable over a field, the interplay between linear algebra and group theory, and the relationship between number theory and geometry

*Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems

*The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; includes blocks of problems that introduce additional topics and applications for further study

*Applications to science and engineering (e.g., the fast Fourier transform, the theory of error-correcting codes, the use of the Jordan canonical form in solving linear systems of ordinary differential equations, and constructions of interest in mathematical physics) appear in sequences of problems

*Basic Algebra* presents the subject matter in a forward-looking way that takes into account its historical development. It is suitable as a text in a two-semester advanced undergraduate or first-year graduate sequence in algebra, possibly supplemented by some material from *Advanced Algebra *at the graduate level. It requires of the reader only familiarity with matrix algebra, an understanding of the geometry and reduction of linear equations, and an acquaintance with proofs.

Group theory Matrix Multilinear Algebra Vector space algebra linear algebra

- DOI https://doi.org/10.1007/978-0-8176-4529-8
- Copyright Information Birkhäuser Boston 2006
- Publisher Name Birkhäuser, Boston, MA
- eBook Packages Mathematics and Statistics
- Print ISBN 978-0-8176-3248-9
- Online ISBN 978-0-8176-4529-8
- Series Print ISSN 2197-182X
- Series Online ISSN 2197-1838
- Buy this book on publisher's site