Mathematical Lie groups are smooth differentiable manifolds and as such can be studied using differential calculus, in contrast with the case of more general topological groups. Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. Lie groups provide a natural framework for analyzing the continuous symmetries of differential equations in much the same way as permutation groups are used in Galois theory for analyzing the discrete symmetries of algebraic equations. An extension of Galois theory to the case of continuous symmetry groups was one of Lie's principal motivations.
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Book Description Paul Kisak, 2015. Paperback. Book Condition: Like New. First Edition. A nearly new copy, square and tight with no creases or splits. Contents fresh and clean, not showing any pen-marks. Not from a library so no such stamps or labels. Thus a tidy book in very presentable condition. Bookseller Inventory # 082553