Algebra and Number Theory (Paperback)
Benjamin Fine
ISBN 10: 3110789981 ISBN 13: 9783110789980
Editorial: De Gruyter, Berlin, 2023
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Descripción
Descripción:
Paperback. In the two-volume set A Selection of Highlights we present basics of mathematics in an exciting and pedagogically sound way. This volume examines fundamental results in Algebra and Number Theory along with their proofs and their history. In the second edition, we include additional material on perfect and triangular numbers. We also added new sections on elementary Group Theory, p-adic numbers, and Galois Theory. A true collection of mathematical gems in Algebra and Number Theory, including the integers, the reals, and the complex numbers, along with beautiful results from Galois Theory and associated geometric applications. Valuable for lecturers, teachers and students of mathematics as well as for all who are mathematically interested. 8410410511532117112100971161011003211510199111110100321011001051161051111104432112114101115101110116115321161041013298101971171161213297110100321189711410510111612132111102327797116104101109971161059911544321051103211297114116105991171089711432116 This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. N° de ref. del artículo 9783110789980
Sinopsis:
This second edition gives a thorough introduction to the vast field of Abstract Algebra with a focus on its rich applications. It is among the pioneers of a new approach to conveying abstract algebra starting with rings and fields, rather than with groups. Our teaching experience shows that examples of groups seem rather abstract and require a certain formal framework and mathematical maturity that would distract a course from its main objectives. Our philosophy is that the integers provide the most natural example of an algebraic structure that students know from school. A student who goes through ring theory first, will attain a solid background in Abstract Algebra and be able to move on to more advanced topics. The centerpiece of our book is the development of Galois Theory and its important applications, such as the solvability by radicals and the insolvability of the quintic, the fundamental theorem of algebra, the construction of regular n-gons and the famous impossibilities: squaring the circling, doubling the cube and trisecting an angle. However, our book is not limited to the foundations of abstract algebra but concludes with chapters on applications in Algebraic Geometry and Algebraic Cryptography.
Acerca del autor: B. Fine, USA; A. Moldenhauer and A. Schürenberg, Hamburg, Germany; G. Rosenberger, U Hamburg, Germany; L. Wienke, U Bremen, Germany.
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Detalles bibliográficos
Título: Algebra and Number Theory (Paperback)
Editorial: De Gruyter, Berlin
Año de publicación: 2023
Encuadernación: Paperback
Condición: new
Edición: 2ª Edición