Undergraduate algebra
著者
書誌事項
Undergraduate algebra
（Undergraduate texts in mathematics）
Springer-Verlag, c1990
2nd ed
- : us
- : gw
- : [pbk.]
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注記
Includes index
内容説明・目次
- 巻冊次
-
: us ISBN 9780387972794
内容説明
Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance each other. Illustrative examples accompany the general theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text.For the third edition, the author has included new material on product structure for matrices (e.g. the Iwasawa and polar decompositions), as well as a description of the conjugation representation of the diagonal group. He has also added material on polynomials, culminating in Noah Snyder's proof of the Mason-Stothers polynomial abc theorem.About the First Edition:"The exposition is down-to-earth and at the same time very smooth. The book can be covered easily in a one-year course and can be also used in a one-term course...the flavor of modern mathematics is sprinkled here and there.
"Hideyuki Matsumura, Zentralblatt
目次
Foreword * The Integers * Groups * Rings * Polynomials * Vector Spaces and Modules * Some Linear Groups * Field Theory * Finite Fields * The Real and Complex Numbers * Sets * Appendix * Index.
- 巻冊次
-
: [pbk.] ISBN 9783540780588
内容説明
Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance each other. Illustrative examples accompany the general theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text. For the third edition, the author has included new material on product structure for matrices (e.g. the Iwasawa and polar decompositions), as well as a description of the conjugation representation of the diagonal group. He has also added material on polynomials, culminating in Noah Snyderbs proof of the Mason-Stothers polynomial abc theorem. About the First Edition: The exposition is down-to-earth and at the same time very smooth. The book can be covered easily in a one-year course and can be also used in a one-term course...the flavor of modern mathematics is sprinkled here and there. - Hideyuki Matsumura, Zentralblatt
- 巻冊次
-
: gw ISBN 9783540972792
内容説明
"Undergraduate Algebra" is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, finite fields, Galois theory, and other topics. The author has also included a chapter on groups of matrices. Throughout the book, the author has attempted to strike a balance between abstraction and concrete results, providing illustrative examples to reinforce the general theory. Numerous exercises, ranging from the computational to the theoretical, have been added. In this second edition, some new topics have been included, such as Sylow groups, Mason's theorem on polynomials and the analogous ABC conjecture over the integers, while other topics, including symmetric polynomials and field theory, have been expanded. Additionally, there are many new exercises of varying difficulty, and concrete examples of major unsolved problems in algebra, written in a language accessible to undergraduates, have been included to illuminate the vitality of mathematics.
目次
Contents: The Integers.- Groups.- Rings.- Polynomials.- Vector Spaces and Modules.- Some Linear Groups.- Field Theory.- Finite Fields.- The Real and Complex Numbers.- Sets.- Appendix.- Index.
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