The path tracer is impressive, doing it in a month's worth of work is impressive too :) I took a ray tracing course in second grade, and had to leave everything else and write ray tracers during the term.

And, as an item of nostalgia, here is some of my glossy mirror code:

  if(matl->t == M_GLOSSMIRROR){
      double θ0 = acos(cosθ), Δθ = M_PI * matl->rough / 2, lθ, dθ = 2*Δθ/ray->w, dφ = 2*dθ, θ, φ;
      lθ = (θ0 - Δθ) < 0 ? 0 : ((θ0 + Δθ) < M_PI ? (θ0 - Δθ) : (M_PI - 2*Δθ));
      θ = lθ + (p+RAND1)*dθ; φ = -2*Δθ + (q+RAND1)*dφ;
      v4 z = hit->n, x = norv4(subv4(ray->p, scv4(dotv4(ray->p, z), z))), y = crv4(x, z);
      ...