More old lectures

Excerpts from my old lectures on spinors

The development of ideas connected with spinors shows, once more, how important and beneficial is the interaction between mathematics and physics: spinors were discovered by mathematicians, but their importance comes from the role they were shown to play in physics. The initial misunderstandings and errors committed when trying to introduce spinors on manifolds, have shown how important it is t...

Lectures

Attention span during lectures: 8 seconds, 10 minutes, or more?

In the current climate of curriculum reform, the traditional lecture has come under fire for its perceived lack of effectiveness. Indeed, several institutions have reduced their lectures to 15 min in length based upon the "common knowledge" and "consensus" that there is a decline in students' attention 10-15 min into lectures. A review of the literature on this topic reveals many discussions re...

Using video lectures to make teaching more interactive

—Having worked for a long time with video-lectures, we devised a new teaching model that makes use of the recorded videos to free the teacher from part of his work and allowing him to concentrate his efforts on a more effective and involving teaching strategy. I. INTRODUCTION Video lectures are becoming more and more popular, especially since important educational institutions such as Princeton...

Lectures on Shimura Curves 3: More Fuchsian Groups

Proof: Writing Y (Γ) = Γ\H, it is natural to ask (as we did in the “parabolic” case C/Λ) which elements σ ∈ PSL2(R) = Aut(H) descend to give automorphisms of Y (Γ). The condition we need is clearly that for all z ∈ H and γ ∈ Γ, there exists γ′ ∈ Γ such that σ(γz) = γ′(σz). Of course this holds for all z ⇐⇒ σγ = γ′σ; in other words the condition is that σΓσ−1 = Γ, i.e., that σ ∈ N(Γ). This defin...