A First Course in Group Theory
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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.
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.
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
Autor*in
Bijan Davvaz
Themen in »A First Course in Group Theory«
Group Theory Symmetry Permutation Groups Representation Sylow Theorems Groups of Geometric Objects Wallpaper Symmetry Groups Set Theory Combinatorics Algebraic Structures Lagrange’s Theorem Normal Subgroups Factor Groups Homomorphisms
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“Advanced school students and well-motivated undergraduates can profitably read it, and it is a very useful general reference for the history of substantial parts of mathematics, placed in the context of contemporary social and political events. … as a readable … and refreshingly detailed account of the whole sweep of ‘infinitesimal methods’ from antiquity to the 1990s, this book is highly recommended.” (Peter Giblin, The Mathematical Gazette, Vol. 107 (570), November, 2023)
“Davvaz's book, on the other hand, features many excellent discussions of groups of matrices. Indeed, matrix groups are used not just as examples of groups, but to help clarify and add depth to Davvaz's discussion of other families of groups. … . It is also, in my opinion, the highlight of the book.” (Benjamin Linowitz, MAA Reviews, February 20, 2022)
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