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Groups - Modular Mathematics Series
This text provides an introduction to group theory with an emphasis on clear examples. The authors present groups as naturally occurring structures arising from symmetry in geometrical figures and other mathematical objects. Written in a 'user-friendly' style, where new ideas are always motivated before being fully introduced, the text will help readers to gain confidence and skill in handling group theory notation before progressing on to applying it in complex situations. An ideal companion to any first or second year course on the topic.
1.Squares and circles 2.Functions and permutations 3.Linear transformations and matrices 4.The group axiom 5.Subgroups 1 6.Group actions 7.Relations and modular arithmetic 8.Homomorphisms and isomorphisms 9.Subgroups 2 10.Co-sets and Lagrange's theorem 11.Orbit-stabilizer theorem and applications 12.Finding subgroups 13.Groups of small order 14.Conjugacy 15.Faithful actions 16.Factor groups 17.Conclusions Suggestions for further projects Further reading.