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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...

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...

Bones and Cartilage provides the most in-depth review and synthesis assembled on the topic, across all vertebrates. It examines the function, development and evolution of bone and cartilage as tissues, organs and skeletal systems. It describes how bone and cartilage develop in embryos and are maintained in adults, how bone is repaired when we break a leg, or regenerates when a newt grows a new limb, or a lizard a new tail.

The second edition of Bones and Cartilage includes the most recent knowledge of molecular, cellular, developmental and evolutionary processes,...

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 Schrodinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone-von Neumann Theorem; the...

A presentation of all aspects of neural crest cell origins (embryological and evolutionary) development and evolution; neural crest cell behavior (migration) and anomalies (neurocristopathies and birth defects) that arise from defective neural crest development. The treatment of development will include discussions of cellular, molecular and genetic aspects of the differentiation and morphogenesis of neural crest cells and structures derived from neural crest cells. The origins of the neural crest in embryology will be discussed using the recent information on the molecular basis of the...

The new field of evolutionary developmental biology is one of the most exciting areas of contemporary biology. The fundamental principle of evolutionary developmental biology ("evo-devo") is that evolution acts through inherited changes in the development of the organism. "Evo-devo" is not merely a fusion of the fields of developmental and evolutionary biology, the grafting of a developmental perspective onto evolutionary biology, or the incorporation of an evolutionary perspective into developmental biology. Evo-devo strives for a unification of genomic, developmental, organismal,...