Bijan Davvaz: A First Course in Group Theory

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Cover: 9789811663642 | A First Course in Group Theory | Bijan Davvaz | Buch | Englisch | 2021

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Sprache: Englisch

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Beschreibung

This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. Topics on important examples of groups (like cyclic groups, permutation groups, group of arithmetical functions, matrix groups and linear groups), Lagrange¿s theorem, normal subgroups, factor groups, derived subgroup, homomorphism, isomorphism and automorphism of groups have been discussed in depth. Covering all major topics, this book is targeted to undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the reader.

Über den Autor

Bijan Davvaz is Professor at the Department of Mathematics, Yazd University, Iran. Earlier, he served as the Head of the Department of Mathematics (1998-2002), Chairman of the Faculty of Science (2004-2006), and Vice-President for Research (2006-2008) at Yazd University, Iran. He earned his Ph.D. in Mathematics with a thesis on "Topics in Algebraic Hyperstructures" from Tarbiat Modarres University, Iran, and completed his M.Sc. in Mathematics from the University of Tehran, Iran. His areas of interest include algebra, algebraic hyperstructures, rough sets and fuzzy logic. On the editorial boards for 25 mathematical journals, Prof. Davvaz has authored 6 books and over 600 research papers, especially on algebra, fuzzy logic, algebraic hyperstructures and their applications.

Zusammenfassung

Discusses group theory from theoretical as well as geometrical point of view

Contains coloured images for better explanation

Includes solved examples and exercises at the end of each chapter

Inhaltsverzeichnis

Preliminaries Notions.- Symmetries of Shapes.- Binary Operations.- Cyclic Groups.- Inverse Functions and Permutations.- Group of Arithmetical Functions.- Matrix Groups.- Translation and Scaling Matrices.- Cosets of Subgroups and Lagrange's Theorem.- Normal Subgroups and Factor Groups.- Some Special Subgroups.- Commutators and Derived Subgroups.- Maximal Subgroups.- Group Homomorphisms.- Homomorphisms and Their Properties.- Cayley's Theorem.- Another View of Linear Groups.

Details

Erscheinungsjahr:	2021
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	308
Inhalt:	xv 291 S. 4 s/w Illustr. 79 farbige Illustr. 291 p. 83 illus. 79 illus. in color.
ISBN-13:	9789811663642
ISBN-10:	9811663645
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Davvaz, Bijan
Auflage:	1st ed. 2021
Hersteller:	Springer Singapore Springer Nature Singapore
Maße:	241 x 160 x 23 mm
Von/Mit:	Bijan Davvaz
Erscheinungsdatum:	11.11.2021
Gewicht:	0,629 kg

preigu-id: 120473487