A Ranking of All My College Math Teachers

As with most things I rank, I first must put out a disclaimer that this ranking is entirely based on my own experience and opinions. I had classes where I couldn't understand anything the professor was talking about, and the kid next to me was nodding and taking notes the whole time, afterwords commenting how great the lecture was. I completely missed out on a good experience with some teachers just because I didn't understand their subject or teaching style, or because of some other disconnect. Clearly, experiences with these teachers may vary. But these were mine.

What's interesting is how ALL of these people are inarguably good mathematicians. I don't have a single bad thing to say about a single one of them in that regard. They nearly all had PhDs anyhow. I couldn't critique any of these people on their mathematical ability, only their ability to convey information to their students--which are very, very different skills.

Anyways, in an effort to be fair, I included my grades from these classes because as I may or may not have learned from them as teachers, I also may or may not have applied myself nearly enough. I do believe I have to take some responsibility for the classes I didn't learn in. There's definitely a lot of C's, and even a failing grade or two.

Tier 3 -- My Not So Favorite

17. Larry Cannon (Modern Geometry) -- Grade: C

There were two classes that I passed in college that I can confidently say I had no business getting credit for because I didn't learn anything about the subject I took. This very old, well-intentioned man was a professor that I think I can honestly say I didn't learn one single thing from. Some of that was definitely my own fault for not buying into his class and not showing up for the latter half of the semester (if you think I'm gonna keep showing up to a class I'm learning nothing from, you clearly don't know me). But as an educator myself now, I do think teaching a class less conducive to learning than this would be impressive.

I believe I turned in one or two of the weekly homework assignments all semester. Once I realized we were never getting our homework assignments back and there's no way they were being graded ("We'll be getting a grader for this class any day now," he said every week, starting in August and until December), I stopped turning them in. This was also because I figured my time would be better spent doing physics, linear algebra, discrete math, or whatever other elective homework I had this semester, rather than doing homework that was almost certainly just going to end up in the garbage. So it wasn't pure laziness; I'd say it was also an effort to use my time efficiently.

Anyways, this man didn't lecture. He did get up and talk sometimes (about what? I have no idea--hardly about geometry), have us do problems on the board, and have us play around with a few geometry computer programs. But I think that's it. I did okay enough on the final, using mostly common mathematical sense, to scrape a passing grade in this class. I still own the Modern Geometry textbook, which I opened just a few times over 4 years ago. I do wonder the book is any good, but I don't wonder enough to go back and revisit anything about this class.

16. Elena Cherkaev (Applied Math, Game Theory) -- Grade: A, C+

Similar to Dr. Cannon, Elena was very well intentioned and a very kind teacher. It's funny how in high school, the good teachers are just the nice ones who try. But in college, the good teachers are only the ones you can actually learn from.

I don't remember a single thing about Applied Math except solving Ax=b matrices and a few ideas of basic graph theory (this is where I realized graphs can sometimes be represented by matrices--and that was something I learned from the Applied Math book). Outside of that, I have no idea what the subject of "Applied Math" even is at this school besides some matrix work, and I certainly spent more time reading my Applied Math textbook in class than I did listening to the lectures because I wasn't getting much out of them. To be fair, Dr. Chekaev is obviously a brilliant mathematician. But between her accent (Russian, I believe) and my inability to understand the math she presented anyways, my experiences in her class were not very good. 

Although the grades don't show it, I actually had a much better time in her Game Theory class--but that's more because it ended up being my favorite math subject and the theorems tend to make more intuitive sense and be more interesting to me. I did learn a few things in these classes, but it wasn't from anyone but myself and whoever wrote those mediocre textbooks.

15. Robert Brooks (Analysis I) -- Grade: D

Much like most of my bad experiences with math teachers, Dr. Brooks was probably too old to be teaching. It's not that I don't believe an old person can't teach math well--but I've personally never had a good math teacher over age 55 or so, though I can't really say why that is.

But the big difference between Brooks and some of my other older teachers, though, is that Brooks is objectively not that nice of a teacher. I didn't personally have any bad interactions with him, but he didn't take kindly to questions or comments of any sort in his class, let alone making a mistake on your math homework or exam. If he said something or wrote something on the board, he expected you to know it, understand it, and never forget it without asking any questions. Regardless, I showed up almost every day to his class and worked hard, copying down his scribbles of memorized theorems off the board. I was genuinely surprised to not pass his class and ended up needing to retake it--my theory is he had a really strict grading scale and ended up failing a good portion of the class. But I knew when signing up for it again that I'd rather take a chance on a new random professor than take this one from him again. Which, the mystery of an unknown professor can honestly be a pretty big risk in the math department.

14. Firas Rassoul-Agha (Probability) -- Grade: C

This guy had a clear mad scientist vibe, which was probably my favorite thing about him. I wouldn't have been surprised if he showed up to class in a lab coat one day. To his credit, he actually spoke fairly clearly, and what was expected in his class was not hard to understand. But his teaching methods couldn't be more at odds with how I learn. His probability lectures were almost entirely introducing theorems and going really, really deep into them and their derivations/proofs with no grounding in practicality. He never, ever did examples on how to do homework or how to solve problems that would be on exams and quizzes. In classes like Dr. Rassoul-Agha's, it's your job as the student to just apply these difficult theorems to do practical probability problems and it's not his to show you how to do them--his is just to prove the theorems.

This is probably my biggest gripe with most upper level math and science professors I've had. They're so brilliant that they only like to teach very difficult and deep aspects of their subject (difficult to a second or third year math student, I mean). But many of them don't show you just how to solve simple problems or do simple analysis. It's why so often university math lectures were of little use for me. I could show up to hours of class and feel like I didn't learn a single thing that would actually help me in the class.

Tier 2 -- The Passable

13. Jyothsna Sainath (Probability) -- Grade: D

I really didn't think too much on this probability class or professor. She made the class easy enough that when I failed this as a math elective, I figured I'd take it again and pass it the second time. So why did I fail it if it was so easy? Everyone in college has those semesters where things just go downhill--things just randomly feel really difficult, the combination of classes you're taking are just too hard, or you try to work 40 hours a week while going to school, or you're out of town or sick or miss class a lot. That was just one of these semesters for me and the sacrificial lamb ended up being my probability class. Rather than suffer and fail all my classes, I kinda put this one off and made sure I passed the others since there's only so many things you can cram into your brain in a short amount of time and with little sleep.

Dr. Sainath was compassionate and interesting, but her lectures weren't the most clear. I appreciate how easy she made a 5000 level math class on advanced probability and distributions, and my regret here is the circumstances of trying to do too much at once while taking her class.

12. Nghiem Nguyen (Linear Algebra) -- Grade: C+

The number of times this professor half-shouted the words "IS THAT CLEAR??" to the class after explaining something complicated will be forever burned into my mind. To be clear, most of the time when he asked this, things were not clear to me, but I was never gonna be the one to speak for the class and say "no, that's not clear" since in a math class of engineers and math majors, I always felt like one of the dumber kids in there. Maybe to everyone else it was clear. It always seemed like more of a rhetorical question anyways. But the good news is we're definitely getting to the point on this list where lectures are moving up the scale from "useless" to just "mostly useless." I surely learned a thing or two in this class from Dr. Nguyen and I could tell he actually cared about our learning, although strong Asian accents can sometimes make learning math just a little bit harder (not something I'd ever fault a professor for--he can surely speak English more than 1,000x better than I can speak Vietnamese).

In all honesty, Linear Algebra is not a difficult subject. I probably would have done a lot better and gotten more from these lectures if I hadn't just gotten back from a 2.5 year hiatus from school and math alike. So I really can't put too much blame on Dr. Nguyen, but rather probably put some on myself for not staying caught up while gone for so long. At the end of the day, at least he was one of the teachers who actually cared.

11. Graeme Milton (Math Modeling) -- Grade: C

Math Modeling is probably another class I had no business passing, but because Dr. Milton is a kind teacher who recognizes effort and appreciates communication, I ended up with the minimal passing grade.

Dr. Milton is actually a pretty funny guy and has an awesome, strong Australian accent. I wouldn't say I learned much from his lessons because they were pretty complicated and I felt out of my element in his class, but I appreciate his efforts to keep things light in an 8:30 AM class. I also liked that we broke into groups for homework and final math presentations, which was a rarity in my experience as a math major. To be honest, though, I really wasn't very good at math modeling. Some of the group projects I saw were incredibly interesting and ambitious with some very complicated analysis and computer assisted modeling, which made our game theory centered project on competitive pricing look lazy by comparison. We did have some problems with the groups and people getting moved and added to our semester-long groups, so I ended up not getting credit for some of the assignments. I talked to him about it, though, and we worked it out. I'll always appreciate a teacher who doesn't grade strictly and without empathy for the students, even if I didn't find his day to day lectures insightful at all.

10. Tommaso de Fernex (Analysis II) -- Grade: B-

To me, Analysis 2 was just so abstract and difficult conceptually that it probably wouldn't have been a good experience for me without basically a perfect teacher who explains things so slowly and in clear enough terms that the rest of the class would be bored. Well, since Tommaso was not like that at all, my experience with Analysis 2 was not very good. I can't blame the professor entirely for it, though. Even though I struggled with understanding what the course material was even about, I'd say this class was nothing short of typical and probably even representative of what a lot of tough upper level math classes were like for me. Looking back, I do think it's likely that Dr. Fernex is a decent teacher and that it just sucks that I had him for a subject like analysis that I struggle with. 

Experiences like his class just made me come to accept that maybe I'm just not that good at math. Or at least math like analysis. I do wish I had more classes where things were just explained clearly and simply with examples of how to do the homework problems, but that's clearly not how studying math at a university works, so.

9. Jan Gutt (Ordinary Differential Equations) -- Grade: B+

Here's where our list starts to take a turn for the better. Jan was a nice, young, foreign teacher who taught very practically. Although hard to understand at times, he didn't waste all his time with theorem derivations that were irrelevant to actually succeeding in his class. To be fair, math takes a hard left turn when you get to your junior year/3000 level classes because that's where you lose most of the engineering majors who need math purely for its practical purposes--so math after ODE's and Linear Algebra is more abstract, is less 'useful,' and is more often done as a means unto itself. I guess what I'm getting at is while he gets credit for being a better teacher, ODE's wouldn't be the hardest class to teach for someone like me to understand.

8. Stefan Patrikis (History of Math) -- Grade: A

I really, really liked History of Math; the subject was one of my favorites in my college career. Curriculum and subject matter aside, Stefan did often seem a little bit too smart for this class and sometimes had a hard time dumbing it down for us. But he did a great job giving us a well rounded history of the broad subject of 'math' while integrating number theory concepts into the material. The history aspect and the ancient math was really easy with some practice, but the number theory material I felt I was not very well equipped for this early in my education. But it wasn't too heavy, so I can't be too mad.

My one funny anecdote from this class comes from when he assigned the final term paper. I was discussing my topic with one of my classmates, who was writing on the history of the number zero, when I mentioned I was writing my 11 page paper on Fermat's Last Theorem. "You know our teacher studied under Andrew Wiles at Princeton, right?" I did not. I had unknowingly written my history paper about my teacher's old mentor who was one of the most famous modern mathematicians still alive. He definitely showed a lot of interest in reading my essay and had a lot of notes for me when I got it back, including an inaccuracy or exaggeration here or there that he knew from his own personal experience of studying under Sir Andrew Wiles. 

In short, he was a pretty good teacher. And for posterity's sake, it's also worth noting that he also looked just a little bit like Nathan Fillion.

7. Travis Mandel (Analysis I) -- Grade: C

In my mind, I often mix up Stefan Patrikis and Travis Mandel. They were both pretty young, pretty practical, and beyond incredibly smart professors at the University of Utah that I had my Junior year as a math major. The one biggest problem I had with both of them was that they were so intimidatingly smart that just asking them a question about something I didn't understand just made me feel dumb. Which isn't really their faults or anything, but it is relevant to my experiences with them.

Dr. Mandel had the inherent teaching disadvantage of having to teach me analysis, which really isn't a good time for either party. But there's a reason his analysis class was the one I finally passed. He was relatable and genius, though his class was unfortunately tied to an inane analysis textbook that I hated, as every analysis class at the U is. Still though, one of the happiest moments of my college career was logging in to check my grades and finally seeing I had passed Analysis I. I was going to be okay and finish my math degree after all.

6. Christopher Hacon (Number Theory) -- Grade Incomplete

Dr. Hacon's biggest strength was how purely interesting he was. He was expressive, responsive, and had a very European accent. He also won the Breakthrough Prize of Mathematics (which has a $3 million payout) while I was studying math at the U. Although his teaching of Number Theory focused heavily on proofs, these proofs seemed much more well explained and digestible than most of the other classes I had. Still, I found his lectures very, very difficult, but I could at least stay on pace being only slightly behind, unlike a few of the other proof-based lecture classes that I just immediately fell behind and felt lost for most of the semester. I did end up having knee surgery the day of the final, so he was kind enough to give me an Incomplete grade so I could take the final at a later date--though I ended up just retaking the class instead.

Tier 1 -- Great Teachers

5. Gilbert Moss (Number Theory) -- Grade: C+

Finally, we've arrived. These are good teachers. Dr. Moss is one of the most down to earth and relatable math teachers I had. I think it's rare to have a personable math teacher because of how rare it is to be smart enough to get a Math PhD while having the social awareness needed to be a good teacher and read a classroom. Pretty quickly, Gil made it clear that he wasn't just at the university to research and was forced to teach as a byproduct. He's the kind of teacher you could actually talk to: the kind of teacher you'd go get a beer with. He breaks things down into digestible steps, which is easily the most useful thing you can do as a math teacher. It's honestly wild how rare that is at the university level.

4. Tom Alberts (Undergrad Research) -- Grade: A

Although I didn't do too well on the relatively few homework assignments in his class, I remember having a discussion with Dr. Alberts where I basically asked that if my final paper and presentation on Prüfer sequences and directed graphs was good enough if I could still get an A in his class. When he said it was still possible for me to get an A, I went all in on it. I ended up applying myself and learning a ton in the process, as you can see if you read the paper. 

The interesting thing about this class is that there were only about 6 kids in it, so we each did 20-30 minute solo presentations in place of a final. This is so much more preferable than a final exam for a person like me who's less good at math but a little bit better at the social aspect of sharing mathematical knowledge. See, I wasn't that good at advanced math topics, but I was great at breaking down and teaching the complex topics I did understand. As a result, I was also pretty good at writing about mathematics.

One specific meeting I had with Dr. Alberts I still remember several years later. Not really because it was all that special, but because it was so rare that I actually met with my math professors one on one. Even though I say I'm fairly social relative to most people who study math, I didn't like meeting with my professors because of how wholly inadequate meeting with them made me feel. But this experience was a good one--with such a small class, Dr. Alberts was able to get to know me a little bit, make me a research topic recommendation, and give me a book on the topic to read. I do honestly believe he gave me an easier topic based on how I wasn't doing as well in his class. It's a shame it took me so long, but for the last year of my college career, I finally came to understand the value of meeting with and knowing my math professors. This might not have happened if I never sat down to meet with Tom that day.

3. Ken Golden (Calculus 2 & 3, Math and Climate) -- Grade: C, B, A

Ken Golden is one of the most engaging characters in the math department at the University of Utah. He teaches clearly and is probably the most relatable math teacher I've ever had. His study of sea ice in Antarctica was never a dull subject, even though it was a frequent topic in his class and was something I otherwise might not have had too much interest in. He's the only teacher I took a class from three times, and only one of two teachers I took two classes from. The first was Calculus 2, which I found surprisingly difficult, even as someone who had already studied the calc 2 material in high school. I went ahead and took the next calculus class from him as well and had a good experience.

Seven years later, I was looking for a math elective class to finish out my degree and I saw his name attached to a Math and Climate class and jumped for it. It was unfortunate that his class was at 7:30 AM and I was taking an hour long bus ride to get to campus, so if I wanted to attend his class I needed to be up by 5 AM or so (a near impossible feat for me in college). I wish I would have attended more, but I still went all out in writing my final paper and managed to get an A. I may have regrets about bringing politics into my abstract and using wikipedia tables for data, but I was very happy with the research I did and, ultimately, my decision to spend another class with Ken.

2. Sonya Leibman (Calculus) -- Grade: A

Sonya was actually my first math teacher my first semester freshman year and I thought she was absolutely great. She did have the bonus of teaching what was the easiest math class I would take in all of college, but her lectures were so simple and clear that she made it impossible not to learn if you just showed up and payed attention. For some reason, the full-time professors making a decent amount of money (unlike Sonya, a grad student) seemed to either not like to or not be able to break down concepts clearly with an adequate number of examples to the point that math homework was actually easy--not like how Sonya did. She was engaging and clearly she cared, and her efforts weren't lost on me at all. 

What more is there to say? How can you do better as a teacher than teaching a class where you just make the material easy to understand?

1. David Brown (Discrete Math) -- Grade: A

It's still a bit of a mystery to me why I loved Dr. Brown's discrete math class so much. It seemed like the class you either loved or hated--and I loved it. Dr. Brown is eccentric, to be sure, and his class was actually one of the hardest I took at university. It's a little bit hard to quantify and compare how hard a class is because difficulty depends on effort and work ethic (I don't know if it would be THAT hard to get a C in Discrete Math), but I certainly think it was the hardest class I personally worked in and it yielded the highest reward out of any class I've ever taken, math or otherwise. 

I don't even really know how he does it, but if you just agree to buy into his class, him as a character, and the subject of Discrete Math, his class is the most well crafted that you'll experience. He'll be inspiring, he'll tell jokes, he'll give anecdotes and make you think. He'll pitch hypotheticals, throw out moral dilemmas, and all while adding to his cause of helping you be educated in mathematics. He'll give you everything you need to understand the material; he gives you just enough that you don't realize you learned something significant, until you need it on the homework and everything comes together. None of this is to mention how he doesn't require a textbook because he basically wrote his own through volumes of typed notes. That's a ton of sheer effort to handcraft the curriculum and save students some money.

The first impression you get about Dr. Brown on day one in his class is that he's just so real, just like his bulging muscles are (okay, 'bulging' is an understatement). He'll be the first to say that some of the math we learn is a complete joke and some math classes are a waste of time. He'll passionately say that he thinks we should blow up the math curriculum as a whole and rebuild it because it's useless to the point of being unsalvageable--and in fact, he shared this opinion in front of hundreds of people and on camera for thousands to see.

It's not a perfectly crafted Tedx and he definitely lets his goofy side show, but he comes across as sincere with his meaningful critique of math education--which is why I show this talk to my seniors at the beginning of every year. And if you're the kind of person who feels like someone owes them an apology for the poor state of math education and for the turmoil it put you through, look no farther than his Tedx. If you hate math, I really encourage you to watch it and get your apology.

Really, he as a math teacher can be summed up by this review left on Rate My Professors, upvotes and down votes included:

To me, he was everything I want in a college professor (down to earth, relatable, self-aware, knowledgable, teaches clearly) and more. His personality is unlike any person I've ever seen before and I absolutely loved his class for it.