MATH 3250

Before I write this review, I want to give a bit of context. I took Calculus III and ODE with McMillan, so a year of math with him. Both classes followed the same general structure, and the same methods of teaching were applied to both. I say this because if you take a class with him as the instructor, I'd be willing to guess that the same general outline as applied in these previous two classes will be applied.
As an instructor, McMillan is great. Yes, he teaches math, but these classes are so much more than JUST math classes. He mentions physics, astronomy, engineering, circuits, economics, chemistry, philosophy - he is aware that not just math majors are taking his classes, and so he introduces concepts from other fields where this type of math can be applied. He puts a lot of emphasis on physical intuition and understanding where certain ideas are coming from. 30-50% of the exam problems you have will easily be about memorization of definitions and theorems, and the other 50-70% will be about actually solving problems, some being very easy and pulled from the homework and packets, others being more challenging derivations and problems.
The homework's are time consuming, but you will learn a lot. If you go to his office hours, he is more than willing to walk you through how to solve and understand the problems that he has assigned. Normally half of the problems are easy, and the other half are challenging problems. You are not expected to just do math and circle your answer, he is looking for reasoning and logic. You do the math, then write a bit about what you did and why. Then finish solving, then write about what you did and why. You are supposed to provide in depth reasoning about why you did what you did - you could end up having the completely wrong answer but will still get a lot of credit for simply writing out your reasoning. Most people started off with bad homework grades, but by the end of the course were making As or Bs. Don't get freaked out! You can be successful, and you will learn extremely useful things about mathematics and logical reasoning.
Additionally, the grading is very generous. The exam averages are in the 50s and 60s BEFORE the curve. He uses a square root curve so that way most students end up with very high grades on exams. My raw exam grades were typically in the 60s and I would end up with a very high B, or a low to medium A. You also have an opportunity to get extra credit in class participation. Show up to class, attempt problems beforehand, you can easily end up with a 107.5% for your class participation grade, which when I took it, was around 25% of your final grade.
I would go so far as to say that if you participate in class fully, make an average on your homework's between 70-100, and just did the parts of the exam that were memorization based/very easy, you'd end up with a B or B+ EASY. It's a good class, it is challenging, and it is very rewarding.

Professor McMillan is clearly very intelligent, and made an effort to be a good teacher, but unfortunately was not a good teacher.
Every week the professor assigns a 10-15 page packet that you are expected to go through before the lectures of the week. For starters, he generally sent out these packets half a day before our class, which made the expectation of completing them before class highly unfair. However, if you did not go through the entire packet before lecture, you were in trouble - these packets were less a “pre-reading” to prepare you for the content to be taught in class, but rather he seemed to expect us to entirely teach ourselves the content through the packet. This was demonstrated by the fact that he would not reiterate the content in the packets during lectures, and he would expect us to present our answers for questions on the content to the rest of the class (which we also were graded on for accuracy) the same day he introduced the content - essentially we were expected to have already come to class having mastered the content well enough that we could present it to the rest of the class before he even covered it in lecture. As a result, I spent a significant amount of time outside of class attempting to teach myself the content, and my time in class felt absolutely useless since he seemed to barely go over the content.
To make matters worse, the packets he assigned were very, very difficult to understand, and so the majority of what I learnt about ODE this semester came from various online sources and youtube videos rather than through the course that I am paying for. I would like to add that this is the general consensus among many of my peers who also took this class, and isn’t simply because I "lack the comprehension skills."
The TAs for this class were lovely, but prof McMillan did not give them the answers to any homeworks or assignments, and so often they either could not help with homework questions or gave us the wrong answers (they tried their very bests though). McMillan also gave us some practice questions in class (the questions he expected us to complete on our own and then present in front of the class) but did not ever give us complete solutions for these questions, and so at no point did I know if I was ever solving questions correctly as I had no means of checking my solutions - this was very frustrating when attempting to prepare for the exams.
Speaking of the exams, McMillan bragged at one point that the average on his exams were a 40-50%, and I don’t blame him - the exams are tough. They seem to focus very little on actual math and instead seriously emphasise memorisation of definitions and derivations; if you’re looking for a math class that focuses on concepts and proofs then ODE with McMillan is the one for you, but if you’re expecting to do actual math in this class, be prepared to be disappointed.
Overall, McMillan was a nice enough guy - although occasionally a little condescending and unapproachable - and seemed to care about the class. Halfway through the semester he did make an effort to adapt the course structure to accommodate our needs better, which I really appreciated. However, I believe there is something fundamentally wrong with his teaching style, and so I still would not recommend taking this class. If you do, prepare to dedicate a very significant amount of time outside of class teaching yourself the content and completing highly challenging homework questions (which you are expected to work with a group to complete, but even with our 5 minds it took many, many, many hours to complete just a few questions).

Professor McMillan uses a hybrid structure for his classes: he releases packets of the material to be covered in class that week and that week's hw (typically 4-6 questions, 3 easy and 3 hard, that you have the entire week to do), and lectures on the topics in class. He is very smart, so sometimes I had no idea what he was talking about, but it is easy to follow what he is saying if you have read the material before class.
McMillan also uses a generous grading structure; 25% of your grade is based on participation, and the participation grade isn't capped at 100% (capped at 107.5%). The homeworks are difficult, but are graded on your explanation rather than your answer, and if you go to office hours, he will usually tell you the answer expected. The exams are generously curved (usually a square root curve).
McMillan's ODE definitely seems to be on the harder end of classes, but it is one of the most rewarding classes I have taken. He encourages you to think and use math as a logical analysis tool rather than a series of steps to follow, so the learning curve is steep, but I came out of the course feeling like I could read math and was exposed to several new ideas. He is also extremely approachable and genuinely wants his students to do well; he sends out a feedback form mid-semester and changes the course structure based on the responses. Definitely recommend if you have the space for a difficult class in your schedule, and are willing to put the work in.

#tCFS24