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John Dorning is a very classical teacher. His lectures are very straightforward, telling you exactly what you need to be able to do to pass the course. He is not an easy teacher, however he is passionate about the material, and very concerned about whether or not his students understand it. I would recommend him as a lecturer and an overall professor, however his teaching style may not be the best fit for every student.
Dorning teaches right off his notes and most are straight from the book, but he does know his stuff. You'll be learning from the book a lot in his class, he can let the homework get ahead of his lectures. The lectures can be boring but they are informative, and he's a very fair test and quiz giver, he writes his own tests and quizzes so you'll never be blindsided.
Professor Dorning has a very traditional approach to teaching differential equations. He tends to write out theorems on the blackboard and work through all of the more abstract mathematics instead of focusing on examples/application. The lectures are dull and attendance is required. If you use any electronics in class he will kick you out if he catches you. The homework, which is graded both on accuracy and completion, is long and typically goes ahead of what was actually taught in lecture in the last few problems. The TAs grade a few of the same problems on each person's homework, so you may easily lose 0.5 (out of 10) points for a single sign error in your answer on some problems, while not losing anything for having another answer entirely wrong. Professor Dorning is nice, has a deep mastery of the material, and is generally accommodating. If you have any issue with a quiz or exam he will never deduct points, and very often he gives points back if you go talk to him. If you take this class, you will learn differential equations, but it will probably be more difficult to get a high grade with Dorning than with other instructors.
Professor Dorning is a character. He will attempt to pronounce and remember your name while tossing around Spanish words and getting overly giddy over the material.
That being said, he knows the material exceptionally well. He will focus on proofs and derivations, and will always have some sort of proof on his tests. He lectures pretty quickly, yet still manages to get behind on content, to the point where you're doing homework on sections you haven't covered yet.
Overall, with more effort than usual on your part, it is very possible to do well on quizzes, moderately well on tests, and pretty decently in the course. Dorning will amuse you and he honestly wants you to do well in the course.
Professor Dorning is a raving lunatic. HOWEVER this also makes him an effective lecturer because he is completely devoted to the material and goes out of his way to make the lectures interesting. He also likes to see his students do well: the average on both the second and third tests was above a 90. He will occasionally kick someone out for using a cell phone during class, so don't be that guy constantly being asked to leave. You will look like an idiot and it's just not worth it.
As far as the coursework, Diff EQs is the boundary between lower and higher level math. It's more nuanced than Calc I-III, and is really the first class that uses Calc concepts more abstractly. This doesn't mean it's harder; it's just not as straightforward.
Professor Dorning is a goofball, in probably ever sense of the word. But, he knows his stuff and is very enthusiastic about his work. Some students will not like that because with DiffEq, it's very tempting to sit in the back and pass out for an hour - I know. I forced myself to sit in the front row to pay attention (by the way, he'll NEVER remember your name), but it paid off. He says you have to "read, then study" every chapter of the textbook - no you don't. If you pay attention in class, take good notes, and flip through the textbook to help you through tougher HW problems, you'll be okay. The homework problems show up on the tests and quizzes (which were WAY too easy this year - one test had a median of 90...90!!) so just pay attention and you'll get a good grade.
Dorning isn't terrible, he's just...different. He tend to focus on proofs/theories in lecture and insists that you have to read the sections before he talks about him. I found that it's easier to not do that and mostly just teach the material to myself doing the homeworks. Tests aren't too bad, though he always puts a proof at the end. Dorning means well and wants you to succeed, but is overall a little off.
Keys to success:
1) The first day of class, Dorning will tell you to put away your laptop and use a notebook to take your notes. Do exactly what he says and proceed to write down absolutely everything he puts up on the board for the rest of the semester
2) He teaches by worked examples, so your notes will help you with the homework. The homework takes a long time, so start early
3) Use Paul's Online Math Notes to supplement the lectures. They are a nice summary to help study for the quizzes
4) Study the homework and quizzes for tests
And most importantly, do not use your cell phone in class. He will kick your ass out...
Interesting guy. If can just laugh at his quirks, you'll enjoy the class a lot more. He tries to act like a drill sergeant sometimes and then he'll go off on a tangent of some weird joke or metaphor about "Harry Potter magic" that he thinks will make you understand the material better.
Regardless, he's not bad. His tests are fair. He has weekly quizzes but he drops a lot of them (I think three or four). Also weekly homework assignments that sometimes suck, but they grade them pretty easily by only actually looking thoroughly at a couple problems and then just making sure you tried on the rest of them. If you study hard and do all of his practice tests online, you should be in good shape.
Things not to do: use your phone (he'll kick you out), miss class (he takes attendance and will ask to see you after class to find out why you missed), or fall asleep or even look out the window (he'll call you out)
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