As a lecturer, especially in the beginning of the quarter, Professor Chayes was confusing, unclear, and sometimes incoherent. Unless you can learn all the material by yourself, or have a very intelligent, helpful friend, I suggest you find a different teacher for the following reasons:
-He skips certain mathematical steps that made it difficult to follow his thought processes.
-He frequently pauses to loudly pant for several seconds.
-His writing is often small and difficult to read, regardless of how close you are sitting to the board.
-His homework and exam questions are overly theoretical, though he does provide ample extra credit points on the midterms (and I assume on the final as well, though I have yet to take that).

Many students in the class stopped going to lecture, simply because it did not help them with the material at all, and sometimes even confused them on subjects they had previously understood. If you have the poor luck to be enrolled in his class, try to switch out.

I will admit though that his antics can be somewhat amusing, and he doesn't lack for enthusiasm, especially on what he calls the "shark problem." Still not worth it.

If you're somehow left with no other option then Chayes as I was, be ready to look toward other resources for understanding the course material. I recommend using M.I.T. OCW. Watch the videos and then do the assignments. This will help you grasp the concept more then an eternity of office hours with Chayes (I'm exaggerating of course). He's brilliant, I admit. But there are doers and then there are teachers.

His exams aren't hard... tell that to the students who all wrote negative reviews. I'm not gonna lie, he is a smart guy, but he's definitely not the go-to guy when it comes to fulfilling that 1 math requirement for biochem majors or whatever. Do it if you're interesting or find a different prof.

absolutely impossible. his grader literally couldn't do the homework assigned

unfortunately i cant rate this guy below a 1 overall.