Abstract Algebra: Suitable for Self-Study or Online Lectures: Mathematics Study Resources, cartea 7
Autor Marco Hienen Limba Engleză Paperback – 19 oct 2024
In addition to elementary algebraic structures such as groups, rings and solids, Galois theory in particular is developed together with its applications to the cyclotomic fields, finite fields or the question of the resolution of polynomial equations.
Special attention is paid to the natural development of the contents. Numerous intermediate explanations support this basic idea, show connections and help to better penetrate the underlying concepts.
The book is therefore particularly suitable for learning algebra in self-study or accompanying online lectures.
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Specificații
ISBN-13: 9783662679739
ISBN-10: 3662679736
Pagini: 307
Ilustrații: XI, 303 p. 140 illus., 2 illus. in color.
Dimensiuni: 155 x 235 x 21 mm
Greutate: 0.45 kg
Ediția:1st ed. 2024
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Mathematics Study Resources
Locul publicării:Berlin, Heidelberg, Germany
ISBN-10: 3662679736
Pagini: 307
Ilustrații: XI, 303 p. 140 illus., 2 illus. in color.
Dimensiuni: 155 x 235 x 21 mm
Greutate: 0.45 kg
Ediția:1st ed. 2024
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Mathematics Study Resources
Locul publicării:Berlin, Heidelberg, Germany
Cuprins
Motivation and prerequisites.- Field extensions and algebraic elements.- Groups.- Group quotients and normal divisors.- Rings and ideals.- Euclidean rings, principal ideal rings, Noetherian rings.- Factorial rings.- Quotient fields for integrality domains.- Irreducible polynomials in factorial rings.- Galois theory (I) - Theorem A and its variant A'.- Intermezzo - explicit example.- Normal fields extensions.- Separability.- Galois theory (II) - The main theorem.- Cyclotomic fields.- Finite fields.- More group theory - Group operations and Sylow.- Resolvability of polynomial equations.
Notă biografică
After a postdoctoral year at the University of Chicago, Prof. Dr. Marco Hien initially worked at the University of Regensburg. Since 2010, he has been Professor of Algebra and Number Theory at the University of Augsburg with the research areas of algebraic geometry and algebraic analysis. In 2020, he received the "Prize for Good Teaching" from the Bavarian Ministry of Science.
Textul de pe ultima copertă
This book contains the fundamental basics of algebra at university level.
In addition to elementary algebraic structures such as groups, rings and fields, the text in particular covers Galois theory together with its applications to cyclotomic fields, finite fields as well as solving polynomial equations.
Special emphasis is placed on the natural development of the contents. Various supplementary explanations support this basic idea, point out connections and help to better comprehend the underlying concepts.
The book is particularly suited as a textbook for learning algebra in self-study or to accompany online lectures.
The Author:
Prof. Dr. Marco Hien worked at the University of Regensburg after a postdoctoral year at the University of Chicago. Since 2010, he has been Professor of Algebra and Number Theory at the University of Augsburg with research interests in algebraic geometry and algebraic analysis. In 2020, he received the "Prize for Good Teaching" from the Bavarian Ministry of Science.
The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
In addition to elementary algebraic structures such as groups, rings and fields, the text in particular covers Galois theory together with its applications to cyclotomic fields, finite fields as well as solving polynomial equations.
Special emphasis is placed on the natural development of the contents. Various supplementary explanations support this basic idea, point out connections and help to better comprehend the underlying concepts.
The book is particularly suited as a textbook for learning algebra in self-study or to accompany online lectures.
The Author:
Prof. Dr. Marco Hien worked at the University of Regensburg after a postdoctoral year at the University of Chicago. Since 2010, he has been Professor of Algebra and Number Theory at the University of Augsburg with research interests in algebraic geometry and algebraic analysis. In 2020, he received the "Prize for Good Teaching" from the Bavarian Ministry of Science.
The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
Caracteristici
Develops the basic concepts and essential statements of abstract algebra up to the Galois theory step by step Contains a variety of motivational intermediate statements and encourages self-reflection Shows the effectiveness of the theory with many concrete examples