There is no one best way for an undergraduate student to learn elementary algebra. Some kinds of presentations will please some learners and will disenchant others. This text presents elementary algebra organized accord ing to some principles of universal algebra. Many students find such a presentation of algebra appealing and easier to comprehend. The approach emphasizes the similarities and common concepts of the many algebraic structures. Such an approach to learning algebra must necessarily have its formal aspects, but we have tried in this presentation not to make abstraction a goal in itself. We have made great efforts to render the algebraic concepts intuitive and understandable. We have not hesitated to deviate from the form of the text when we feel it advisable for the learner. Often the presenta tions are concrete and may be regarded by some as out of fashion. How to present a particular topic is a subjective one dictated by the author's estima tion of what the student can best handle at this level. We do strive for consistent unifying terminology and notation. This means abandoning terms peculiar to one branch of algebra when there is available a more general term applicable to all of algebra. We hope that this text is readable by the student as well as the instructor. It is a goal of ours to free the instructor for more creative endeavors than reading the text to the students.
|Uitgever:||Springer-verlag Berlin And Heidelberg Gmbh & Co. Kg|
|Plaats van publicatie:||DE|
|Collectie:||Undergraduate Texts in Mathematics|
|Afmetingen:||235 x 155 x 0|
1 Set theory.- 2 Rings: Basic theory.- 3 Rings: Natural numbers and integers.- 4 Rings: Applications of the integers.- 5 Rings: Polynomials and factorization.- 6 Linear algebra: Modules.- 7 Linear algebra: The module of morphisms.- 8 Abstract systems.- 9 Monoids and groups.- 10 Linear algebra: Modules over principal domains and similarity.- Selected references.- Answers to questions.- Index of symbols.
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