That’s it. I can’t go any longer without commenting on this. Since it would be utterly futile to even attempt to candy-wrap my opinions on this particular plaguing issue, I will not bother. The appalling way some mathematics courses, at the third-year level and beyond, are delivered has me lying *face down* on the shores of nausea. I am so utterly sick and tired of having to scribble down notes while an instructor does almost naught more than *rote* recitation from a textbook, bashing out long, dull strings of lifeless equations, or proving trivial (or at least very easy) theorems which just about anyone could figure out in *less time than it takes them to read what you’re writing on the board*. Worst comes to worst, I can always check one of the surely countless number of textbooks that contain this exact same computation. I’m begging you: if you ever catch yourself doing this, *stop*.

I don’t understand why 90% of lecture time is spent doing “follow-your-nose-and-oh-look-what-do-you-know-it-just-falls-out-of-the-definition” proofs while only around 10% is spent actually introducing new concepts or thought-provoking ideas. I don’t understand why students are asked to bash out boring book-keeping results in full detail on assignments. I *know* how to unwind definitions already. It just feels masturbatory now, to the point where I feel like getting a 0 on your assignment so I can have the time to solve *interesting* problems for once. What’s that? You want enlightening examples? Let me show you a trivial proof. What’s that? You think we should talk about alternate ways of viewing things, connections to other concepts, lucid reformulations, fruitful techniques that are ubiquitous in the area? Let me show you a robotic derivation that you could do in your sleep. I’m sorry, but if anyone ever told you that this is what mathematics is about, they lied. How can you defile, with such nonchalance, a subject that spawned from the deepest, most beautiful chasms of our imaginations?

Why are students at this level being treated like first-year calculus students who need to be shown formal, pedantic proofs of everything so they can “get used” to mathematical reasoning and have their notion of rigour properly calibrated? Hello, I’ve only taken like 20+ upper-year pure mathematics courses by now, if not more. I think (or at least by now I sincerely hope) we all *know* what rigour is, and can all *feel* whether a proof is legitimate or not. Otherwise, we would have received our mark of 50 or 60 in PMATH 351 (real analysis), realized this wasn’t for us, and moved on to major in something else.

Try as anyone might, they will never manage to extinguish my interest in mathematics. On the other hand, they are driving me straight to the insane asylum (or rather making me simply pass out cold on my desk during class) with such tedious, technical circle-jerking. People are paying a pretty penny to learn about advanced math, and they’re being taught… [??????] well, I don’t even know what the hell they *are** *being taught.

Someone needs to just put an end to this once and for all. I’ve been resisting making a post like this for probably over a year and a half. I should just stick to graduate courses from now on… but if it was up to me, there would be some serious changes in the way people teach mathematics.

*(I refuse to comment on which course(s) contributed anything to the ultimate authoring of this post. The reason for this is that I do not intend to personally attack or insult any particular instructor. My post is phrased as a general lamentation. However, I am clearly not cowering behind anonymity: I take full responsibility for my opinions, and am very receptive of any criticism or opportunities for further discussion.)*

Would it hurt to replicate these points in a letter to someone in a position of authority e.g. Dean? I can’t tell if the solutions to your problems lie in the prospect of different professors, different curriculum, different mentality, different ‘culture’, or a drastic revision to standard higher mathematical educational academia the world over. I couldn’t even tell you if integrating all the above proposed solutions would be a good solution either. … Honestly, I am wondering if your frustrations are lying in something more singular and/or more discrete but you address it in a generalized fashion.

I’m sure it’s something that should be dealt with or at least continuously critiqued. BUT … will your proposed changes increase revenue for the school? If not, then don’t bother. It’s a business.

I’m not concerned with increasing revenue. I am concerned with understanding how the art of teaching mathematics can be perfected, and becoming a student of that art myself.

I may be overdue for graduation, hence my post is probably biased. Perhaps I am just tired of undergraduate pedantry. Also, I probably should have phrased this post in a less confrontational way, since I am not at all shocked that issues like this (if they are issues) occur: teaching mathematics is an art, as I mentioned, and an extremely difficult one at that. There is no shame in not having completely mastered it (nor is there shame in making arbitrarily large blunders, but I feel this need not be mentioned, given the skilled lecturers in question).

I’m a math professor at UW. I can at least explain what it’s like from the professor’s perspective. As in your case, these are general comments and not necessarily intended to imply anything about any specific courses that I or others have taught.

If I am going slowly in a class, it’s because that is the level of the average student in the class. I’ve never taught any undergraduate class at UW with fewer than ~35 students. With rare exceptions (e.g. advanced sections), any class with that many students is going to have some slower learners. Believe it or not, these students are not actually filtered out by real analysis or whatever, and even if they were, the university would not like it (see below). While classes are not designed for the weakest students, such students nevertheless do bring down the average. For classes which are offered regularly (most are), faculty members have a pretty good idea of what to expect from students, just by looking at past years. The math office even keeps historical records of grade distributions for every year of every course that we offer. We know how good our students are, and we usually get this right.

If we try to make the class interesting anyway, the poorer students end up dropping or getting low grades. The former impacts revenue, and the latter impacts our teaching evaluation scores. The same thing happens if we try to strengthen prerequisites or restrict enrolment. We might attract some good students, but not enough to offset the drop. Math professors are obviously mathematicians and we want to teach interesting and beautiful stuff. But we also pay attention to the incentives that our bosses impose, and those incentives consist of enrolment and evaluations. The evaluations are a direct component of our performance reviews, and there is considerable pressure to maintain enrolment levels; for one thing, low enrolments eventually lead to permanent removal of the course.

A few first-year and second-year courses have solved this problem by offering separate advanced sections. This approach only works when the course has a large enough enrolment to justify a separate advanced section. By the time you get to 3rd and 4th year courses, there is no possibility of advanced sections, but the large mass of average to weaker students are still in school, and it’s hard to control what courses they take. Ivy League schools like Harvard solve the problem by having such a large endowment that tuition revenue is negligible. Absent such a deus ex machina, I sympathize with your predicament but I’m not sure what we can change. Taking grad courses will at least maximize your outcome, even if it doesn’t reform the system.

Thanks a lot for the comment, Professor Jao. The points you made really broadened my understanding of the complexity of the situation, which was initially not so apparent.

Oh, I haven’t read this post before posting my other comment. Oh! And oh, again! To begin with, Mathematics is a solo sport ! Okay? I can’t understand you having such a huge dilemma. The actual fact is that a mathematician would not need a degree from university aside from the point of view of a social status. Yeah, it would probably make a lot of people feel very “mathematicianaly” if they had a degree or if his/her mates called him/her a mathematician.

Where is this desire to restrict your world to what the instructors teach coming from? My world would have been very dark had I have done such a thing until now.

I also do not agree with Mr. David Jao on saying that A is a professor in mathematics therefore A is a mathematician.

In theory, you are probably correct that a professor in mathematics does not necessarily have to be a mathematician. But in practice there are very few, if any, actual counterexamples.

In any case, it’s irrelevant. My point in the original comment was simply that a professor of mathematics, all other factors being equal, is likely to prefer teaching advanced and interesting material. The claim that math professors are mathematicians is sufficient, but not necessary, to establish my point.