Another remarkable aspect is that such a seemingly simple problem would require such sophisticated and highly specialized mathematics for its proof.

Producing an image from a diffraction pattern requires sophisticated mathematics.

For example, the sophisticated mathematics used in cosmology say could find wider application (particularly in engineering - but see later).

With large sets, it becomes necessary to use more sophisticated mathematics to find the number of combinations.

Starbird seeks to make sophisticated mathematics accessible to the public.

Using sophisticated mathematics, a researcher can determine the protein's structure from the diffraction pattern.

That is an excellent example of how to become an expert in technology without having to deal with sophisticated mathematics.

Using sophisticated mathematics and computers, the researchers piece together a picture of the protein from the reflected X-rays, which form a pattern of dots.

Both types of quantitative analysts demand a strong knowledge of sophisticated mathematics and computer programming proficiency.

Internet marketing and advertising is a social market made for the use of heavy-duty computing and sophisticated mathematics.