Sentence examples for mathematical structures are from inspiring English sources

They claim that mathematical structures are nothing more than patterns, and humans clearly have the ability to recognize patterns.

In particular, knowledge of abstract objects could be obtained via the following two-step method (which corresponds to the actual methodology of mathematicians): first, stipulate which mathematical structures are to be theorized about by formulating some axioms that characterize the structures of interest; and second, deduce facts about these structures by proving theorems from the given axioms.

He argues that intertransformable mathematical structures are taken in standard mathematical practice to be the same structure.

And the issue is precisely to explain this use, that is, to provide some understanding of the grounds in terms of which we come to know that the relevant mathematical structures are isomorphic to the physical ones.

Sometimes it is thought that the mere fact that two mathematical structures are intertransformable is all that is needed for the transformation to be a gauge transformation and for the differences between the two structures to correspond to nothing physical.

On the other hand, an entire class of mathematical structures are referred to as 'spaces' even though they have nothing in common with the space of everyday experience (except some abstract algebraic properties, which is why these structures earned the title 'spaces' in the first place).

Saunders Mac Lane, also of the United States, and Eilenberg extended this axiomatic approach until many types of mathematical structures were presented in families, called categories.

Compared to someone like Xenakis whose mathematical structures were so unique, complicated, and idiosyncratic that few people dared to follow in his footsteps, Cage's chance procedures, coupled with his openness to new ideas, were the source of many younger artists' visions, in performance art, dance, theater and literature, as well in as music.

Compared to someone like Xenakis who's mathematical structures were so unique, complicated, and idiosyncratic that few people dared to follow in his footsteps, Cage's chance procedures, coupled with his openness to new ideas, were the source of many younger artists' visions, in performance art, dance, theater and literature, as well in as music.

Indeed, what would the appropriate logical language for specific mathematical structures be, especially when such structures could be reconstructed in a variety of formal languages?

Several fuzzified versions of the exiting mathematical structures were introduced in the literatures, particularly the fuzzification of metric space followed through adoption of different approaches.