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Stillwell is the author of many textbooks and other books on mathematics including: Classical Topology and Combinatorial Group Theory, 1980, ISBN 0-387-97970-0. 2012 pbk reprint of 1993 2nd edition ISBN 978-0-387-97970-0. Mathematics and Its History, 1989, pbk reprint of 2nd edition 2002; 3rd edition 2010, ISBN 0-387-95336-1 [7]
The foundation of Lie theory is the exponential map relating Lie algebras to Lie groups which is called the Lie group–Lie algebra correspondence. The subject is part of differential geometry since Lie groups are differentiable manifolds. Lie groups evolve out of the identity (1) and the tangent vectors to one-parameter subgroups generate the ...
The book begins with a historical overview of the long struggles with the parallel postulate in Euclidean geometry, [3] and of the foundational crisis of the late 19th and early 20th centuries, [6] Then, after reviewing background material in real analysis and computability theory, [1] the book concentrates on the reverse mathematics of theorems in real analysis, [3] including the Bolzano ...
Undergraduate Texts in Mathematics (UTM) (ISSN 0172-6056) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are small yellow books of a standard size. The books in this series tend to be written at a more elementary level than ...
Unlike the previous ones, it is a constructive proof: the integrating Lie group is built as the quotient of the (infinite-dimensional) Banach Lie group of paths on the Lie algebra by a suitable subgroup. This proof was influential for Lie theory [6] since it paved the way to the generalisation of Lie third theorem for Lie groupoids and Lie ...
A naive theory in the sense of "naive set theory" is a non-formalized theory, that is, a theory that uses natural language to describe sets and operations on sets. Such theory treats sets as platonic absolute objects. The words and, or, if ... then, not, for some, for every are treated as in ordinary mathematics.
In mathematics, Theory of Lie groups is a series of books on Lie groups by Claude Chevalley ( 1946, 1951, 1955 ). The first in the series was one of the earliest books on Lie groups to treat them from the global point of view, and for many years was the standard text on Lie groups. The second and third volumes, on algebraic groups and Lie ...
The affine group of one dimension is a two-dimensional matrix Lie group, consisting of. 2 × 2 {\displaystyle 2\times 2} real, upper-triangular matrices, with the first diagonal entry being positive and the second diagonal entry being 1. Thus, the group consists of matrices of the form.