A Field Guide to Algebra (Undergraduate Texts in Mathematics) - Softcover

Chambert-Loir, Antoine

Softcover

ISBN 10: 1441919473 ISBN 13: 9781441919472

Verlag: Springer, 2010

Inhaltsangabe

This unique textbook focuses on the structure of fields and is intended for a second course in abstract algebra. Besides providing proofs of the transcendance of pi and e, the book includes material on differential Galois groups and a proof of Hilbert's irreducibility theorem. The reader will hear about equations, both polynomial and differential, and about the algebraic structure of their solutions. In explaining these concepts, the author also provides comments on their historical development and leads the reader along many interesting paths.

In addition, there are theorems from analysis: as stated before, the transcendence of the numbers pi and e, the fact that the complex numbers form an algebraically closed field, and also Puiseux's theorem that shows how one can parametrize the roots of polynomial equations, the coefficients of which are allowed to vary. There are exercises at the end of each chapter, varying in degree from easy to difficult. To make the book more lively, the author has incorporated pictures from the history of mathematics, including scans of mathematical stamps and pictures of mathematicians.

Antoine Chambert-Loir taught this book when he was Professor at École polytechnique, Palaiseau, France. He is now Professor at Université de Rennes 1.

Über diesen Titel

Über die Autorin bzw. den Autor

Antoine Chambert-Loir is Professor at Université de Rennes 1.

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This unique textbook focuses on the structure of fields and is intended for a second course in abstract algebra. Besides providing proofs of the transcendance of pi and e, the book includes material on differential Galois groups and a proof of Hilbert's irreducibility theorem. The reader will hear about equations, both polynomial and differential, and about the algebraic structure of their solutions. In explaining these concepts, the author also provides comments on their historical development and leads the reader along many interesting paths.

In addition, there are theorems from analysis: as stated before, the transcendence of the numbers pi and e, the fact that the complex numbers form an algebraically closed field, and also Puiseux's theorem that shows how one can parametrize the roots of polynomial equations, the coefficients of which are allowed to vary. There are exercises at the end of each chapter, varying in degree from easy to difficult. To make the book more lively, the author has incorporated pictures from the history of mathematics, including scans of mathematical stamps and pictures of mathematicians.

Antoine Chambert-Loir taught this book when he was Professor at École polytechnique, Palaiseau, France. He is now Professor at Université de Rennes 1.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2010
• Sprache: Englisch
• ISBN 10: 1441919473
• ISBN 13: 9781441919472
• Einband: Taschenbuch
• Anzahl der Seiten: 208
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Tiergartenstr. 17; Heidelberg; 69121; Deutschland