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...Pollicott (ed.) K. Schmidt (ed.) , ''Ergodic Theory of ${\bf Z} ^ { d }$-actions'' , ''Lecture Notes'' , '''228''' , London Math. Soc. (1996) pp. 1–61</

Let G be the group of 322,560 permutations of these 16 tiles generated by arbitrarily mixing r ...ns' interrelationships and symmetries can be explained fully only by using mathematics discovered just recently (relative to the patterns' age)-- in particular, t

...es of variables. Here, in general one does not consider the general linear group (that is, the entire set of non-degenerate linear changes of variables), bu ...al algebraic problems and their applications to geometry. The notions of a group, an invariant and the fundamental problems of the theory were formulated at

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al group meeting to study R. A. Fisher's newly published book, ''Design of

Accordingly, one defines the Euler formal group law $ F ( U,V ) \in K [ [ U,V ] ] $ As any [[Formal group|formal group]] law, $ F ( U,V ) $

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al Bucharest. He took a degree in mathematics in 1913, becoming then

The area of mathematics whose main object of study is the index of operators (cf. also [[Index of a ...heory is to study applications of the index theorems to geometry, physics, group representations, analysis, and other fields. There is a very long and fast

...ign="top"> D. Kazhdan, B. Kostant, S. Sternberg, "Hamiltonian group actions and dynamical systems of Calogero type" ''Comm. Pure Appl. Math.'' , '''31

The branch of numerical mathematics studying methods for finding approximate solutions to differential equation ...ng equations with variable, including discontinuous, coefficients. Another group of methods for constructing differences schemes which preserve the property

However, the most typical classification problems appear when there is a group $G$ acting on $\mathscr M$: then the natural equivalence relation arises, ...lectomorphisms form a finite-dimensional Lie group called the [[symplectic group]] and denoted by $\operatorname{Sp}(2n,\R)$ (fields other than $\R$ can als

...Consistency]], [[Proof theory]], and [[Unsolvability]]. For the history of mathematics associated with this problem, see [[Hilbert 2nd problem]] and [[Hilbert pro ...hout the assumption of the differentiability of the functions defining the group.