Mathematical Perspectives

Mathematical Perspectives

Mathematics and physics are different enterprises: physics is looking for laws of nature, mathematics is trying to invent the structures and prove the theorems of mathematics. Of course these structures are not invented out of thin air but are linked, among other things, to physics. In this lecture I shall discuss a number of instances where mathematicians have come to the aid of physics and st...

Mathematical Perspectives

Control Theory : History , Mathematical Achievements and Perspectives

These notes are devoted to present some of the mathematical milestones of Control Theory. To do that, we first overview its origins and some of the main mathematical achievements. Then, we discuss the main domains of Sciences and Technologies where Control Theory arises and applies. This forces us to address modelling issues and to distinguish between the two main control theoretical approaches...

Computational Neuroscience: Mathematical and Statistical Perspectives

Mathematical and statistical models have played important roles in neuroscience, especially by describing the electrical activity of neurons recorded individually, or collectively across large networks. As the field moves forward rapidly, new challenges are emerging. For maximal effectiveness, those working to advance computational neuroscience will need to appreciate and exploit the complement...

Perspectives on Mathematical Knowledge for Teaching

Citizens’ possibilities to develop intuition and mathematical ideas appear in modern society through instrumentation and instrumentalization: Technology does not only shape the actions of the users but also the mathematical objects to be investigated are shaped by the users. The constructivist viewpoint states that both making of mathematics and teaching of mathematics must relate to this instr...