Sentences with phrase «algebraic structures»

Universal Algebra: Here, the properties which are common to all algebraic structures are studied.

This thorough knowledge of terminology allows high school students to manipulate algebraic structures and solve systems of equations.

Whitehead called each of these algebraic structures an algebraic manifold, which in his definition is a set with a commutative and associative operation.

Not exact matches

Universal Algebra, in precisely this sense, is a poor framework for mathematics insofar as it unites spatial manifolds and symbolic logic by introducing the common notion of an algebraic manifold (Whitehead's terminology) or a semi-group (current standard terminology), an object with very little structure or intrinsic interest.9 In this case, generalization comes at the expense of abstract sterility.

Using algebraic topology in a way that it has never been used before in neuroscience, a team from the Blue Brain Project has uncovered a universe of multi-dimensional geometrical structures and spaces within the networks of the brain.

In this latest research, using algebraic topology, multiple tests were performed on the virtual brain tissue to show that the multi-dimensional brain structures discovered could never be produced by chance.

Their analysis of these cliques, using methods from algebraic topology, revealed an organized geometric structure.

It contains over 25 well - structures questions that cover various Quadratic Equation problems - including Algebraic Fraction quadratic equations.

This lesson looks at the structure of the algebraic rule of the function and how it can be seen in a table and graph.

The design project in this case study involved high school students designing structures and then using algebraic and physics ideas to analyze the amount of load that the structure can support.

A Paradigm Shift readers won't find the phrase «algebraic thinking» in the Math Panel's report, but researchers and others have used the term to describe «particular ways of thinking, including analyzing relationships between quantities, noticing structure, studying change, generalizing, problem solving, modeling, justifying, proving, and predicting» (cai & Knuth, 2005).

When Descartes» analytical geometry treated space and extension, the res extensa of nature and the world, so «that its relations, however complicated, must always be expressible in algebraic formulae,» mathematics succeeded in reducing and translating all that man is not into patterns which are identical with human, mental structures... Now the phenomena could be saved only in so far as they could be reduced to a mathematical order, and this mathematical operation does not serve to prepare man's mind for the revelation of true being... that appear in the sensually given data, but serves, on the contrary, to reduce these data to the measures of the human mind, which, given enough distance, being sufficiently remote and uninvolved, can look upon and handle the multitude and variety of the concrete in accordance with its own patterns and symbols....

When Descartes» analytical geometry treated speace and extension, the res extensa of nature and the world, so «that its relations, however complicated, must always be expressible in algebraic formulae,» mathematics succeeded in reducing and translating all that man is not into patterns which are identical with human, mental structures....