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Disclaimer: I took 32A with Chayes (the 32A option didn't show).
Lincoln Chayes is brilliant. His main fault is that he does not know how to convey that brilliance. I went to every lecture, and very rarely did I come out of knowing more than I knew going in. I was able to manage this class because I was lucky enough to get a great TA (shoutout to Will Rosenbaum. Side note: check out will rosenbaum.com for great review material). I would not have been able to do most of the homework if I hadn't gone to discussion and office hours. Will explained the concepts in an easy-to-understand way that Chayes could never do.
The tests incorporated a couple of homework problems, but more than half of the problems used new language and concepts that had not been covered in lecture. I remember keenly a midterm problem that apeared on a homework set the following week. His tests have extra credit per se, in that there are a max of 120 points, but only 100 possible (235/200 for the final). There is always partial credit, so don't ever leave a problem blank.
If you can take 32A and not take Chayes, you're saving yourself a quarter of extra stress and grief. He does have his entertaining moments, and he's a bit quirky (he jokingly pants during long proofs and wears the same thing every day), but he's too smart to teach a mostly freshman math class.
There is a lot to be said about Lincoln Chayes. There is no doubting he is a brilliant mathematician who understands the material in a manner in which I do not believe most people on Earth could possibly comprehend. However, as a result of his own brilliance and innate understanding of mathematics, he has a great deal of difficultly conveying the subject the material and he cannot help but give his personal opinions on how mathematics should be taught and displayed and substitutes what he values to be significant in place of what your textbook might say. Indeed, a lot of what he tests on cannot be directly found in the Rogawski text. I recommend buying Stewart's multivariable book, as he takes some problems from it.
His class is somewhat hard; the homework sets are very difficult and the exams mirror them. If you can get every homework problem right, then you can get good grades on his exams...maybe. The catch? He writes the homework problems and he refuses to release an answer set to them. A problem I thought I had the correct answer to appeared on the midterm and I lost 3/4 credit. The key to success in this class, most likely, is to work in groups and befriend your TA.
I easily got A's in 21A and 31B taught by Rothschild, but I struggled through the class of the great Lincoln Chayes. I do not think his class is ideal for one who needs to get through math requirements or one who aspires to major in mathematics. I recommend avoiding this professor. He may not wreck your GPA, but he has caused me undue stress and shattered any desire I had of furthering my academic career through math.