In mathematics classes at all levels of schooling in all countries of the world, students can be observed solving problems .. The quality and authenticity of these mathematics problems has been the subject of many discussions and debates in recent years. Much of this attention has resulted in a rich, more diverse collection of problems being incorporated into school mathematics curricula. Altho...

This paper deals with the problem of estimating an appropriate hand posture to grasp an object, from 2D object’s visual cues in a many-to-many (objects,grasp) configuration. A statistical learning protocol implementing vector-valued regression is adopted for both classifying the most likely grasp type and estimating the hand posture. An extensive experimental evaluation on a publicly available ...

This article raises the question of what K-12 teachers need to know to teach mathematics and science well. It begins by examining reform proposals for K-12 science and mathematics teaching with an eye toward defining what good teaching practice consists of. It then examines a wide range of literature to delineate the varieties of knowledge that have been associated with this kind of teaching. W...

Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the co...

Next time you see some jugglers practising in a park, ask them whether they like mathematics. Chances are, they do. In fact, a lot of mathematically wired people would agree that juggling is “cool” and most younger mathematicians, physicists, computer scientists, engineers, etc. will at least have given juggling three balls a go at some point in their lives. I myself also belong to this categor...

These 20 lectures tell the story of an intellectual trip that starts in areas of mathematics, geometry and topology, that are known for their pure nature, but the trip ends with central concerns in discrete applied mathematics and mathematical economics. The ultimate goal is to revisit some beautiful problems in game theory, and optimization. Indeed, geometric and topological theorems have been...

Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the co...