Group Theory

Author : Nathan Carter
Publisher : American Mathematical Soc.
ISBN 13 : 1470464330
Total Pages : 295 pages
Book Rating : 4.32/5 ( download)

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Download or read book Visual Group Theory written by Nathan Carter and published by American Mathematical Soc.. This book was released on 2021-06-08 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.

Author : W. R. Scott
Publisher : Courier Corporation
ISBN 13 : 0486140164
Total Pages : 512 pages
Book Rating : 4.62/5 ( download)

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Download or read book Group Theory written by W. R. Scott and published by Courier Corporation. This book was released on 2012-05-23 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is clear, well-organized coverage of the most standard theorems, including isomorphism theorems, transformations and subgroups, direct sums, abelian groups, and more. This undergraduate-level text features more than 500 exercises.

Author : Mildred S. Dresselhaus
Publisher : Springer Science & Business Media
ISBN 13 : 3540328998
Total Pages : 576 pages
Book Rating : 4.95/5 ( download)

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Download or read book Group Theory written by Mildred S. Dresselhaus and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.

Author : John S. Rose
Publisher : Courier Corporation
ISBN 13 : 0486170667
Total Pages : 320 pages
Book Rating : 4.64/5 ( download)

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Download or read book A Course on Group Theory written by John S. Rose and published by Courier Corporation. This book was released on 2013-05-27 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Text for advanced courses in group theory focuses on finite groups, with emphasis on group actions. Explores normal and arithmetical structures of groups as well as applications. 679 exercises. 1978 edition.

Author : I. Martin Isaacs
Publisher : American Mathematical Society
ISBN 13 : 1470471604
Total Pages : 368 pages
Book Rating : 4.06/5 ( download)

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Download or read book Finite Group Theory written by I. Martin Isaacs and published by American Mathematical Society. This book was released on 2023-01-24 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text begins with a review of group actions and Sylow theory. It includes semidirect products, the Schur–Zassenhaus theorem, the theory of commutators, coprime actions on groups, transfer theory, Frobenius groups, primitive and multiply transitive permutation groups, the simplicity of the PSL groups, the generalized Fitting subgroup and also Thompson's J-subgroup and his normal $p$-complement theorem. Topics that seldom (or never) appear in books are also covered. These include subnormality theory, a group-theoretic proof of Burnside's theorem about groups with order divisible by just two primes, the Wielandt automorphism tower theorem, Yoshida's transfer theorem, the “principal ideal theorem” of transfer theory and many smaller results that are not very well known. Proofs often contain original ideas, and they are given in complete detail. In many cases they are simpler than can be found elsewhere. The book is largely based on the author's lectures, and consequently, the style is friendly and somewhat informal. Finally, the book includes a large collection of problems at disparate levels of difficulty. These should enable students to practice group theory and not just read about it. Martin Isaacs is professor of mathematics at the University of Wisconsin, Madison. Over the years, he has received many teaching awards and is well known for his inspiring teaching and lecturing. He received the University of Wisconsin Distinguished Teaching Award in 1985, the Benjamin Smith Reynolds Teaching Award in 1989, and the Wisconsin Section MAA Teaching Award in 1993, to name only a few. He was also honored by being the selected MAA Pólya Lecturer in 2003–2005.

Author : John D. Dixon
Publisher : Courier Corporation
ISBN 13 : 0486459160
Total Pages : 194 pages
Book Rating : 4.65/5 ( download)

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Download or read book Problems in Group Theory written by John D. Dixon and published by Courier Corporation. This book was released on 2007-01-01 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 265 challenging problems in all phases of group theory, gathered for the most part from papers published since 1950, although some classics are included.

Author : A. Zee
Publisher : Princeton University Press
ISBN 13 : 1400881188
Total Pages : 632 pages
Book Rating : 4.85/5 ( download)

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Download or read book Group Theory in a Nutshell for Physicists written by A. Zee and published by Princeton University Press. This book was released on 2016-03-29 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise, modern textbook on group theory written especially for physicists Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-contained textbook on the subject written especially for physicists. Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study. Provides physicists with a modern and accessible introduction to group theory Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more Topics include finite group and character tables; real, pseudoreal, and complex representations; Weyl, Dirac, and Majorana equations; the expanding universe and group theory; grand unification; and much more The essential textbook for students and an invaluable resource for researchers Features a brief, self-contained treatment of linear algebra An online illustration package is available to professors Solutions manual (available only to professors)

Author : Predrag Cvitanović
Publisher : Princeton University Press
ISBN 13 : 0691202982
Total Pages : 278 pages
Book Rating : 4.83/5 ( download)

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Download or read book Group Theory written by Predrag Cvitanović and published by Princeton University Press. This book was released on 2020-05-26 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: If classical Lie groups preserve bilinear vector norms, what Lie groups preserve trilinear, quadrilinear, and higher order invariants? Answering this question from a fresh and original perspective, Predrag Cvitanovic takes the reader on the amazing, four-thousand-diagram journey through the theory of Lie groups. This book is the first to systematically develop, explain, and apply diagrammatic projection operators to construct all semi-simple Lie algebras, both classical and exceptional. The invariant tensors are presented in a somewhat unconventional, but in recent years widely used, "birdtracks" notation inspired by the Feynman diagrams of quantum field theory. Notably, invariant tensor diagrams replace algebraic reasoning in carrying out all group-theoretic computations. The diagrammatic approach is particularly effective in evaluating complicated coefficients and group weights, and revealing symmetries hidden by conventional algebraic or index notations. The book covers most topics needed in applications from this new perspective: permutations, Young projection operators, spinorial representations, Casimir operators, and Dynkin indices. Beyond this well-traveled territory, more exotic vistas open up, such as "negative dimensional" relations between various groups and their representations. The most intriguing result of classifying primitive invariants is the emergence of all exceptional Lie groups in a single family, and the attendant pattern of exceptional and classical Lie groups, the so-called Magic Triangle. Written in a lively and personable style, the book is aimed at researchers and graduate students in theoretical physics and mathematics.

Author : Michael Tinkham
Publisher : Courier Corporation
ISBN 13 : 0486131661
Total Pages : 354 pages
Book Rating : 4.65/5 ( download)

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Download or read book Group Theory and Quantum Mechanics written by Michael Tinkham and published by Courier Corporation. This book was released on 2012-04-20 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text develops the aspects of group theory most relevant to physics and chemistry (such as the theory of representations) and illustrates their applications to quantum mechanics. The first five chapters focus chiefly on the introduction of methods, illustrated by physical examples, and the final three chapters offer a systematic treatment of the quantum theory of atoms, molecules, and solids. The formal theory of finite groups and their representation is developed in Chapters 1 through 4 and illustrated by examples from the crystallographic point groups basic to solid-state and molecular theory. Chapter 5 is devoted to the theory of systems with full rotational symmetry, Chapter 6 to the systematic presentation of atomic structure, and Chapter 7 to molecular quantum mechanics. Chapter 8, which deals with solid-state physics, treats electronic energy band theory and magnetic crystal symmetry. A compact and worthwhile compilation of the scattered material on standard methods, this volume presumes a basic understanding of quantum theory.

Author : Cornelia Druţu
Publisher : American Mathematical Soc.
ISBN 13 : 1470411040
Total Pages : 819 pages
Book Rating : 4.46/5 ( download)

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Download or read book Geometric Group Theory written by Cornelia Druţu and published by American Mathematical Soc.. This book was released on 2018-03-28 with total page 819 pages. Available in PDF, EPUB and Kindle. Book excerpt: The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.