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...
Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory.
Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theor...
This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a definitive and self-contained manner, it features a natural progression of concepts from simple to difficult. Several innovative topics are featured, including differentiation of measures, elements of Functional Analysis, the Riesz Representation Theorem, Schwartz distributions, the area formula, Sobolev functions and applications to harmonic functions. Together, the selection of topics forms a sound foundation in real analysis that is...
This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a d...
It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet's Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet's ...
The fourth edition of this standard textbook of modern graph theory has been revised, updated, and substantially extended. Covering all major recent developments, it can be used both as a reliable textbook for an introductory course and as a graduate text.
The fourth edition of this standard textbook of modern graph theory has been revised, updated, and substantially extended. Covering all major recent d...
