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Lie Groups, Lie Algebras, and Representations
This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for th...
Quantum Theory for Mathematicians
Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.
Lie Groups, Lie Algebras, and Representations
This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way that minimizes the amount of manifold theory needed. Thus, I neither assume a prior course on differentiable manifolds nor provide a con densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the...
Lie Groups, Lie Algebras, and Representations
Lie groups, Lie algebras, and representation theory are the main focus of this text. In order to keep the prerequisites to a minimum, the author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader to get to the heart of the subject quickly, and covers all of the most interesting examples. The book also introduces the often-intimidating machinery of roots and the Weyl group in a gradual way, using examples and representation theory as motivation. The text is divided into two parts. The first covers Lie groups and Lie algebras and the relationship between them, along with basic representation theory. The second part covers t...
Cutaneous Lymphoma
Drs. John C. Hall and Brian J. Hall have assembled world leaders on this ever-changing topic of Cutaneous Lymphoma, to explore advances in research. The text first discusses the new classifications of cutaneous lymphoma. Epidemiology is then reviewed. A general approach to the patient suspected of having a cutaneous lymphoma is outlined. Diagnosis, histopathology, molecular genetics, and treatment of each subgroup is discussed. Precursors and mimics, which make this such a fascinating group of diseases, are reviewed. Systemic considerations of this primarily cutaneous disease are also covered. Molecular genetics of cutaneous lymphomas that have helped advance all of medicine are discussed, and finally, the future of this dynamic area of medicine is detailed.
Anesthesia
A unique review reference featuring nearly 1,000 multiple choice questions. Each question focuses on a key concept or anesthesia problem encountered in daily practice. Answers, explanations, case analyses and references follow, making the information relevant to patient care and standard procedures.
Communications and British Operations on the Western Front, 1914-1918
This book reveals the impact of communications on the military operations of the British Expeditionary Force during the First World War.
Representations of Finite and Compact Groups
This text is a comprehensive pedagogical presentation of the theory of representation of finite and compact Lie groups. It considers both the general theory and representation of specific groups. Representation theory is discussed on the following types of groups: finite groups of rotations, permutation groups, and classical compact semisimple Lie groups. Along the way, the structure theory of the compact semisimple Lie groups is exposed. This is aimed at research mathematicians and graduate students studying group theory.
The R Student Companion
This student-oriented manual describes how to use R in college science and mathematics courses. The manual features fully developed exercises based around the main precalculus analysis skills needed in the standard college general education courses in science and math. The exercises illustrate a wide variety of applications and subjects. The author presents applications drawn from all sciences and social sciences and includes the most often used features of R on a reference card in the back of the book. In addition, each chapter provides a set of computational challenges: exercises in R calculations that are designed to be performed alone or in groups.
