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The classification of the finite simple groups is one of the major intellectual achievements of this century but it remains almost completely unknown outside of the mathematics community This introduction to group theory is also an attempt to make this important work better known Emphasizing classification themes throughout the book gives a clear and comprehensive introduction to groups and covers all topics likely to be encountered in an undergraduate course Introductory chapters explain the concepts of group subgroup and normal subgroup and quotient group The homomorphism and isomorphism theorems are explained along with an introduction to Gsets Subsequent chapters deal with finite abelian groups the JordanHolder theorem soluble groups pgroups and group extensions The numerous worked examples and exercises in this excellent and selfcontained introduction will also encourage undergraduates and first year graduates to further study
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The classification of the finite simple groups is one of the major intellectual achievements of this century but it remains almost completely unknown outside of the mathematics community This introduction to group theory is also an attempt to make this important work better known Emphasizing classification themes throughout the book gives a clear and comprehensive introduction to groups and covers all topics likely to be encountered in an undergraduate course Introductory chapters explain the concepts of group subgroup and normal subgroup and quotient group The homomorphism and isomorphism theorems are explained along with an introduction to Gsets Subsequent chapters deal with finite abelian groups the JordanHolder theorem soluble groups pgroups and group extensions The numerous worked examples and exercises in this excellent and selfcontained introduction will also encourage undergraduates and first year graduates to further study
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Here is a muchneeded basic text that covers a vital area in physics for beginning graduate students The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quartercentury This was achieved through the use of scaling and field theoretic techniques which have since become standard equipment in many areas of physics especially quantum field theory This book provides a thorough introduction to these techniques one that assumes only a sound undergraduate background in physics and mathematics Continuous phase transitions are introduced then the necessary statistical mechanics is summarized followed by standard models some exact solutions and techniques for numerical simulations The real space renormalization group and mean field theory are next explained and illustrated The last eight chapters cover the LandauGinzburg model from physical motivation through diagrammatic perturbation theory and renormalization to the renormalization group and the calculation of critical exponents above and below the critical temperature
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