This paper presents two studies of an intervention designed to help undergraduates comprehend mathematical proofs. The intervention used multimedia resources that presented proofs with audio ...

J. R. Brown, Philosophy of mathematics: an introduction to the world of proofs and pictures, Routledge (1999). 2. R. B. Nelsen, Proofs without words I: exercises in ...

You might know it as an equation that tells you the relationship between the sides of a right triangle. Take any right triangle, if you know 2 of the sides, then you can find the 3nd side. But we can ...

Abstract: The recent machine learning requires huge machine resources and is often hard for users with limited resources. Although there are DPT, these are unsuitable for a situation where a trained ...