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A Gentle Introduction to Group Theory
The book is intended to serve as an introductory course in group theory geared towards second-year university students. It aims to provide them with the background needed to pursue more advanced courses in algebra and to provide a rich source of examples and exercises. Studying group theory began in the late eighteenth century and is still gaining importance due to its applications in physics, chemistry, geometry, and many fields in mathematics. The text is broadly divided into three parts. The first part establishes the prerequisite knowledge required to study group theory. This includes topics in set theory, geometry, and number theory. Each of the chapters ends with solved and unsolved ex...
Topics in Group Theory
The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed for readers approaching the subject for the first time, this book reviews all the essentials. It recaps the basic definitions and results, including Lagranges Theorem, the isomorphism theorems and group actions. Later chapters include material on chain conditions and finiteness conditions, free groups and the theory of presentations. In addition, a novel chapter of "entertainments" demonstrates an assortment of results that can be achieved with the theoretical machinery.
A Course on Group Theory
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.
Group Theory and Its Application to Physical Problems
One of the best-written, most skillful expositions of group theory and its physical applications, directed primarily to advanced undergraduate and graduate students in physics, especially quantum physics. With problems.
Visual Group Theory
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The Theory of Groups
Perhaps the first truly famous book devoted primarily to finite groups was Burnside's book. From the time of its second edition in 1911 until the appearance of Hall's book, there were few books of similar stature. Hall's book is still considered to be a classic source for fundamental results on the representation theory for finite groups, the Burnside problem, extensions and cohomology of groups, p-groups and much more. For the student who has already had an introduction to group theory, there is much treasure to be found in Hall's Theory of Groups.
Group Theory
Here is a 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.
A Course in Group Theory
Each chapter ends with a summary of the material covered and notes on the history and development of group theory.
Applied Group Theory
This text introduces advanced undergraduates and graduate students to symmetry relations by means of group theory. Key relationships are derived in detail from first principles. Rather than matrix theory, the treatment employs algebraic theory in deriving the properties of characters and projection operators. This approach is customarily employed in quantum mechanics courses and makes the connection to group structure clearer. Cayley diagrams illustrate the structure of finite groups. Permutation groups are considered in some detail, and the special methods needed for continuous groups are developed. The treatment's broad range of applications offers students assistance in analyzing the modes of motion of symmetric classical systems; the constitutive relations in crystalline systems; the modes of vibration in molecules; the molecular orbitals of molecules; the electronic structures of atoms; the attendant spectra; and fundamental particle multiplets. Each chapter concludes with a concise review, discussion questions, problems, and references. 1992 edition.
Visual Group Theory
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.
