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Prof. Short is one of those incredibly smart guys who has never struggled with math, and it shows. He's very comfortable with the material. You can ask him anything and he knows the answer. He awards grades based on how much you know, and not how much you tried.
I spoke with him in office hours a couple times. He knows that students can find the answers to homework from the solutions manuals and online which is why he doesn't give much credit for homework. As a result, almost all of your grade comes from exams (which he writes himself). He definitely tests that you understand the concepts. Just memorizing formulas and algorithms isn't enough to get an A in his class.
He's not the most entertaining professor at UCLA, but he's definitely competent, knowledgeable, nice, and eager to help the students who really want to learn the material.
Math 31B sucks! That's how it works. It's not a fun class, but Professor Short understands that and tries his best to help students with their learning. I took 31B Fall quarter of my freshman year (even though I had yet to take 31A -- UCLA screwed me over with that one) and I ended up getting a D-. Luckily, I was able to retake it. After auditing 31A during the Winter quarter I decided to try 31B for a second time in the Spring. I took the class with Short, and everything I once thought was a foreign language made sense. I'm not sure if it was because of me auditing 31A or if it was Short's teaching ability, but my grade definitely increased. Regardless of the true cause of my grade increase, Short is a very good math teacher. He teaches the material in a much easier format than other professors do (in my experience Tamara Kucherenko). I would recommend taking this class. His tests were pretty damn easy too. He gave out practice tests that were essentially identical to the actual test. Just do the homework - actually do the homework, don't copy or you won't learn anything - and you'll do fine in the class. I ended up earning a B, although I had about an 89%. The one downside to Short is the fact that he does not give out signed grades. It's good if you barely want to skate by with an X- grade, he'll round those up to an X. Just keep in mind X+ don't exist in Short's mind.
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