Most Difficult Course?

Regular reader Johan Larson sends in a good question about academic physics:

You have written about teaching various courses in modern physics, a subject that has a fearsome reputation among students for skull-busting difficulty. That suggests a broader question: what is the most difficult course at your university? Or even more broadly, how would one determine what course is the most difficult?

This is a good question, but hard to give a single answer to. The most difficult course at the college as a whole would be nearly impossible to determine, because different students find different things difficult. Lots of students who would cower in fear at the mathematics in our sophomore modern physics course will thrive in upper-level literature seminars on critical theory, the very idea of which gives some physics majors cold sweats. And, of course, any given student only takes a tiny fraction of the courses offered, thus most of them will avoid the courses that would be most difficult for them.

So, I don’t think there’s any useful way to define the “most difficult” course for the institution as a whole. The only sensible way to talk about “most difficult” courses is to look at what courses are most difficult for the subset of students who are required to take them. In other words, the question we can actually answer is “What is the most difficult course required for physics majors?”

In which case, there are two courses from the Physics major at Union that are generally regarded as the most difficult, for different reasons. At least as far as I know– I know there are some Union physics grads reading this, who can correct me if I say anything wrong.

The most difficult “ordinary” course is almost certainly Physics 270, “Intermediate Electromagnetism.” This won’t come as a surprise to anybody who’s studied physics, because this is basically the undergrad equivalent of classical electromagnetism out of Jackson’s book, a course which haunts many a physics grad student, often for years after they get their Ph.D..

This course is generally taught out of Griffiths’s book, which is the shiny, friendly version of Jackson. It’s basically a semester course in Maxwell’s Equations (packed into a ten-week trimester, no less), and is highly mathematical. It’s the first time students really have to grapple with the gory details of vector calculus and differential equations– divergence, curl, surface integrals, special functions, Fourier series, etc. We mention Gauss’s Law and the rest in our introductory electromagnetism class, but don’t do a whole lot with it– we use the integral form, and restrict the discussion to systems with a whole lot of symmetry such that the integrals can be done trivially. In Physics 270, the gloves come off a bit, and it’s a real struggle for a lot of students.

The equivalent course is probably right up there on the “most difficult” list for most physics departments. I know that when I took the equivalent at Williams, it was almost certainly the hardest course I took there. (I took it as a tutorial, too– each week, two of us met with the professor for an hour, and took turns working problems from the homework on the board while he made comments and suggestions. Then he assigned another chapter to read, and we went off and beat our heads against the book for a week. Brutal, but effective.)

The other course with a fearsome reputation is Physics 300, Methods of Modern Experimental Physics. This is our required upper-level lab course, and also carries “Writing Across the Curriculum” (WAC) credit, meaning it’s supposed to be a writing-intensive course. Standards for what counts as a WAC vary far more than they really ought to, but historically, at least, this has meant a ton of writing: six full formal lab reports in the course of the ten-week term, each on an advanced experiment that takes a week to do.

That sort of workload and pace is pretty grueling from the faculty side, so it’s no surprise that the students regard it with some fear. It’s also, in my opinion, sub-optimal as a course, because it’s trying to do too many things at once. At some point in the next few years, we’re going to need to substantially rework it. I have some vague thoughts on how to re-work it, but I haven’t had the time or energy to develop them very far yet.

So, those are the two courses that, as far as I know, are regarded as the most difficult of the courses required for the physics major. For a few years, we were perversely offering them in the same term, meaning that some students were enrolled in both of the department’s most difficult courses at the same time. This pushed even some exceptional students very close to the breaking point, so we shuffled the schedule around to put them in different terms (which forced one class of students to take Physics 300 in the spring term of their senior year, which was also not a hugely popular move…).

Again, I suspect that the equivalent course is probably widely regarded as among the most difficult at those departments requiring an advanced lab course. It’s the sort of thing that can easily become a crushing workload for students, particularly when it’s coupled with a significant writing component.

So, that’s my take on the most difficult courses we offer. If you’re in academia (as either student or faculty), what’s the most difficult course at your institution?

33 thoughts on “Most Difficult Course?

  1. Whatever class uses Bird, Steward, Lightfoot as textbook. You know you’ve done well if your book can still inspire nightmares in grad students 50 years after it was written (and still is the standard).

  2. I think that, in relation to what the students have been used to, the hardest course we have is the first semester of calculus-based physics, especially when the student is an incoming freshman taking calculus 1 at the same time (we allow this although I personally advise them to take calculus first).

    The amount of work, and the level of comprehension, that we require of students in this course is far beyond what most of them have experienced in high school. Upper division physics courses are more intellectually complex, but I think the leap from high school into physics + calculus is a shock that students never experience again in quite the same way.

  3. At Duke there were a lot of undergraduates who were “Pre-Med.” To get into medical school, they needed to pass organic chemistry, so this became the gateway course for them — arguably intended to be the most difficult course so it can filter out the contenders from the pretenders.

    I suspect it is similar at other universities that have a large number of students claiming to be “pre-med.” I also suspect there is a similar filter for “pre-law.”

  4. From my own experience, the undergraduate course I took that was the closest equivalent to Physics 270 at Union was definitely the hardest course I took. We didn’t muck about with Griffiths or anything at that level; we went straight into Jackson. There is a reason most physics departments don’t inflict Jackson on undergraduates: they usually aren’t ready for that level of mathematical rigor.

    But as California Condor @3 points out, many universities (especially large schools, both public and private) have courses which are designed to be weed-out courses. Organic chemistry gets its fearsome reputation from the fact that many schools use it as their pre-med weed-out course. Other schools use first-year calculus or physics courses to discourage math-phobic students from majoring in engineering. These universities have to use weed-out courses because the American system generally does not allow universities to put hard enrollment caps on majors (as opposed to specific courses) and resources to teach upper-level courses in STEM disciplines are often limited.

  5. The courses I teach (either Intro to Behavioural Neuroscience or Advanced Behavioral Neuroscience) are routinely described as among the hardest at UA; they’re almost certainly the most challenging offered within Psychology in large part because they’re not really psych classes – mostly bio, some minimal chemistry, and then an overlay of psych. The big conceptual difficulty even for non-psych-expecting folks, though, is the need to integrate multiple levels (i.e. “How does this protein link to this change in neuronal action and then up to the decision to eat that candy?”)

    This semester I’m teaching an Honors version of the intro class, which apparently means that there are no prerequisites; so I have students who cannot tell me what a protein is trying to understand the molecular basis of action potentials. Exam 1 is today; should be fun..

  6. Without a shadow of a doubt, the hardest course on offer at Cornell University is String Theory. It’s intended for third year graduate students in theoretical high energy physics. I (naively) took it in my first year of grad school =S

  7. In our department, definitely QED. The students taking it actually get their own little room to the side where they can work on the problems together.

  8. At Caltech I would claim it was Ph136 – Applications of Classical Physics – all the physics you don’t learn in regular physics classes taught in a one year (three trimester) course.
    Quantum optics, relativistic MHD, advanced solid state.
    Awesome class.

  9. Building on comment #2 from another physics prof…

    When I was at Auburn University, physics majors did not take physics in their first two quarters as freshmen. Instead, they took two other five-credit courses: calculus and a chemistry class for science and engineering majors. The chemistry class was rigorous with plenty of math, but it was mostly algebra-and-logarithms math, as introductory chemistry just doesn’t have the same need for calculus as introductory physics.

    Thus, when the physics majors finally entered physics classes late in their freshman year, they did so with the benefit of college-level instruction in calculus plus experience in a college-level science class. This “delay” wasn’t really a delay, since it allowed the physics to be taught at a more rapid and sophisticated pace, and the earlier quarters were also used to rack up some required English-and-humanities credits.

    A shocking experience from that freshman chemistry class: The professor finished a lecture that was very heavy on logarithms. Immediately after class, a chemical engineering major sitting next to me asked me and another physics major “Guys… what’s a logarithm?”


    We rapidly bundled the guy out into the hallway, sat down on the tile floor, and started teaching him logarithms. He was a very sharp fellow, so he picked it up quite rapidly. In response to our STUNNED questions, he said that he had attended Pittsburg, PA, public schools and had taken every math and science course they offered, but logarithms had never been covered.

  10. Interesting to hear about Methods of Modern Experimental Physics. When I was there, it was spread out over 3 terms.

    Eric Lund – In my experience, weed-out courses are more often myth than fact. Just because a course is difficult, doesn’t mean it’s intended to cut down on majors or to prevent students from getting into med school. Organic chemistry is a tough course where I teach, and has a reputation as a weed-out course, despite the fact that we’re constantly bragging about how many majors we have and about how that number keeps growing. Chem 101, which I teach, also has a reputation as a weed-out course for the nursing major here. It’s true that the nursing program considers that grade (and others), but we don’t make it hard because of the nursing program. We make it as rigorous as we feel it should be.

  11. I should be able to put enough distance between myself and undergrad physics by now . . . but this conversation is giving me cold sweats.

  12. Also…

    My experience with “Methods of Modern Experimental Physics” differs from Chad’s reports here. I took “Advanced Experiments” at the U. of Maryland from Carroll Alley – It had an excellent ratio of high learning to low stress.

    The course required both written and oral presentation of experimental results. Getting tips and practice on good oral presentation of science is something that may get lost in many science-major curricula.

  13. As an EE undergrad student, I think ours had to be the dreaded Junior Lab, for all of the following reasons:

    1) It was as cross-disciplinary as you could reasonably get, meaning that the first semester lecture courses were microelectronics, signals and systems, and power conversion– so the lab would be giving you experiments on all those things. And hopefully you’d get to do the experiment after it had been covered in the corresponding lecture class.

    2) It was a marathon class, all day either Tuesday or Thursday (not both) starting at 8:00 AM and ending at 5:00 PM. Formally. Of course, you have to eat some time in there, and electives were often offered Tues-Thurs at 12:00 to 1:30 PM, too.

    3) You had to actually complete the lab work by 5:00-ish, because you needed them to witness the result and (physically) sign off on it.

    That’s clearly different from the lecture type classes mentioned above. As lecture classes go… looking back, and looking at what I’m doing now, I think it correlates more to the quality of the professor and the interest of the student, than anything else. If you’re bored by the material, it’s likely to be tough. If the professor is horrible, it’s likely to be tough.

  14. In my undergrad physics experience, it was all about how much math you’d had. Our advanced classical mechanics class was widely regarded as the “weed out” course, but my guess is that that’s only because most students took it at the end of their sophomore year, before they’d had anything beyond a basic differential equations class.

    But because I came into college already having had three semesters of calculus and then didn’t take mechanics until I was a junior, I was neck-deep in a two-semester engineering math class and the Griffiths class when I took mechanics, so I thought it was a piece of cake.

    And to Eric Lund @4, I feel like I never would have survived undergrad if they’d given me Jackson that early. That course near about killed me even as a grad student. *shudder*

  15. Out of all of my undergrad classes, the hardest classes were a toss up between 4th semester Classical Greek (dropped it, took up Portuguese, and never looked back), Complex Analysis (I don’t know why I had a difficult time with this one) and 2nd semester Piano (the only class I’ve ever had to take twice and still do miserably. PIANO WHY U SO HARD!??!!)

  16. I tell my Organic class that I would never. Claim that Organic is the hardest class there is (I actually suggest advanced E and M as an example of something harder) I do say that if you integrate difficulty over number of folks that take it, I think Organic comes out ahead. EM may be harder but your nurse at the doctor’s office won’t complain about E and M if tell them you are a physicist. Mention you teach chem and you are 50/50 that the nurse took it and certainly the doctor. Shoot, turf majors take Orgo at our school

    Then again, as an instructor, I think 2nd semester organic is my favorite course to teach. It’s a pretty high level discussion, and you can talk at pretty much a working chemist level. They have most of the basics, and so it’s a lot of application and a lot of the same concepts.

  17. In pointing to Orgo as a weed-out course for pre-meds, California Condor (#3 above) says, “I also suspect there is a similar filter for ‘pre-law.'” Sadly, this is the major differences between the STEM fields and all others. For many reasons, STEM educators have made it their job to push people out. Humanities educators work to keep them in. (Part of this is driven by finances – your department may get paid based on retaining students, not a problem for pre-med faculty with hundreds of enrollees.)

    I also went to Duke, but I was not pre-med and did not major in science. None of my classes were designed to weed out students. I did struggle a little with physics because I was taking it out of interest and not looking to compete for a grade.

    While I had many friends drop the sciences by sophomore year, none of my pre-law friends dropped that path due to a failure to pass a particular course. (Plenty of other good reasons not to be a lawyer, of course…)

  18. I looked at the curriculum before jumping below the break and was pleased that I guessed correctly. But it was easy to guess E+M and advanced lab.

    At the CC where I teach, I had a student hit our local trifecta: Calc 3, Physics 2, and Organic 2 in the same semester with differential equations for desert. However, I think the pre-reqs for those courses are more challenging if you look only at passing rates, and one reason organic can be challenging is that some departments put their worst teachers in that class.

    I’ll add a ditto to comments #2 and #9. The Calc 1 and Physics 1 combo can be deadly if the students are not fluent in both algebra and trig. Typical HS classes, and I include AP calc in that category, or a C in a college pre-calc class leaves students unprepared for the intensity of college math and physics. Chad is, of course, less likely to see this sort of student than I am.

    My undergrad program was quite similar to what is described in #9, with a calc 3 co-req for physics 1 in the spring (in the now extinct quarter system). The attrition rate was still spectacular since there were too many who had “passed” rather than “learned” the calculus.

    Jackson isn’t quite so hard (conceptually) if you learn E+M from the Berkeley volume 2 textbook. It uses cgs units and relativity, and the only slack is that you aren’t expected to be fluent in Calc 3 and PDEs.

    PS – I have a suggestion for your advanced lab redesign that I will send by e-mail.

  19. When I got my physics degree (U of Rochester, 2006) E&M was two semesters, the second of which was taught out of a text that I assume is Jackson-like. It was brutal. It was the second hardest class I took. By far, the worst was stat. mech. That class was a lot of stress, and very little learning.

    On the other hand, my advanced lab class was one of my favorites! I’d say that if this class isn’t one of the best in the curriculum, you’re doing it wrong. We did 3 experiments a semester, and gave an oral presentation to the class at the end. I learned more and had more fun than in any other class.

  20. In undergraduate physics, I’d offer my most difficult experience as being fluid dynamics… taught from Lamb and Batchelor. I have no idea what the thinking was that went into this selection of texts. Jackson was dandy by comparison.

  21. Having taught in science departments at both Princeton and the University of California, I find the suggestion (e.g., in #17 above) that science faculty “have made it their job to push people out” completely antithetical to my experience. The colleagues I have known have all very definitely felt that their job was to help students succeed, though their abilities to rescue woefully underprepared students varied, especially in the enormous and impersonal introductory classes that existed at both institutions (at UC for budget reasons, at Princeton by institutional choice). Many students arrive unprepared for college level mathematics, and even more students arrive without college level study skills. Students without both will be “weeded out” of science pretty quickly.

  22. When I took organic chemistry (at Duke…hmm, pattern) it definitely was a weed-out course, but not, I think, intentionally so on the part of the faculty. The problem was the other students, who were almost all pre-med, and were so competitive with each other that they would pull all sorts of crazy stuff trying to gain advantage. Being followed into the bathroom on the morning of the midterm by someone who wanted to psych me out was a particular low point, but there were others.

    I lasted one semester as a potential chem major before switching to physics, where the coursework was harder but my classmates viewed tests and problem sets, and not each other, as the barriers to be surmounted.

  23. Tercel – When I took the advanced lab class at Union, it was also one of my favorites. I wonder if the change is just taking it from 3 terms to one or if something else has been modified.

    Jason – As a STEM faculty member, I certainly don’t make it my job to push people out. I make my students work hard and I refuse to cave to grade inflation, but my goal is to get every student to understand the material well enough to move on. Giving high grades to students who haven’t grasped the material doesn’t do anyone any favors – it leaves them floundering when they have to build on what they’re supposed to have learned. In my experience, that’s something that separates STEM from humanities. As a freshman English major, I took classes with seniors because there was very little hierarchy in the coursework. There’s no way I could have stepped into a chemistry class with seniors as a freshman.

    Of course, there were prerequisites for some courses, but except for senior seminar, it was generally something like a single survey course. That got frustrating by the time I was a senior and we weren’t doing anything more advanced than I did when I was a a sophomore.

  24. Re: the “weed-out” courses, a couple of thoughts…

    1) I am trying to resist the temptation of questioning the difficulty of a subject if anyone can get through if they put in the time and take the classes. Although my colleagues I think would not be so generous.

    2) Orgo as a weed-out class part a: Actually, at our school, orgo isn’t really our weed-out class. We have a far bigger F/W rate for gen chem, particularly second semester. Students coast through first semester gen chem relying on their high school background, and then hit second semester where it all of a sudden gets new and they are lost. I’m sure if they took everything twice they could do better the second time, but they don’t want to do that, of course. And we generally DON’T dump our worst teachers into organic courses by any means. That would be idiotic, in fact, since they are either our majors or our second largest set of service courses. We can’t afford to treat the depts we serve poorly, or they might seek others to serve them. We work very hard to try to keep the quality as high as we can for our sophomore organic courses. We don’t always succeed, depending on personnel issues, but we surely try. Now, our situation is fairly unique because we offer four separate sophomore organic courses, and most places don’t do that. We can split chem majors from the pre-meds, for example, and even split the chem Es from the chem majors (this is extremely rare). Therefore, the competition issues that Margaret mentions are not quite the same (and shouldn’t be at all anyway, since no one grades on a curve)

    I’ll save part 3 for the next post

  25. 3) Orgo as a weed-out class part b: on the whole, it’s not the instructors who make orgo the weed-out course, it is the curriculum itself, and it is very much an infrastructural problem I think. The problem with orgo is that it is so bloody dramatically different from what most students have previously encountered in their chemistry, and, unfortunately, gen chem is not doing a good job preparing students for organic. That’s not really by design, and in principle, it doesn’t have to be, but it happens in practice.

    Students take gen chem and spend their time learning concentration units and balancing equations and ideal gas laws and then acid/base equilibrium. These are all critical skills to have in chemistry, but, aside from equilibrium, mean little in organic class (and while the students can presumably calculate acid/base equilibrium concentrations in gen chem, they can’t recognize an acid/base reaction for the life of them; ask them why Grignard reagents are sensitive to water and they are flummoxed).

    There are things taught in gen chem that are important introductory topics for organic, such as atomic and molecular structure, bonding, polarity (btw, did you know that the whole “electronegativity differences” for polarity only really applies to the first row? The polarity of a C-I bond is completely unrelated to the difference in EN) formal charges, and intermolecular forces. Unfortunately, while these get taught, they don’t end up being emphasized, and ultimately end up as qualitative topics in a sea of concentration units, gas laws, balancing equations and acid/base equilibria. Moreover, even when structure is taught, way too much time is spent going over unusual stuff, like PCl5 or XeF4. As I always tell my colleagues, why are you drawing PCl5? If you can draw Lewis structures, you can draw the structure of DNA and proteins. Why don’t you do that instead? Make complex organic molecular structure part of the vocabulary in general chemistry; there is no need to wait for organic to do this.

    The reason, however, is because historically gen chem has been staffed by inorganic and p-chemists (look who writes the textbooks – it’s pchemists and inorganic chemists; Silberburg is a rare organic chemist who has written a gen chem book). Therefore, they teach it from the pchem and inorganic perspective. Structure examples are predominantly inorganic complexes. Equilibria examples include the dimerization of NO2. The table of weak acids is mostly main group oxo acids, such as HClO2, H3PO4, HNO2, HF, HOCl, HCN. It might contain organic acids like formic and acetic, but no structures for them, and no indication of what is even the acidic proton. And since these are the ones in the tables, they are the ones that end up being used in the problems. Kinetics examples are generally also inorganic processes. Redox processes are Zn/Cu ribbons. It’s no wonder that when students start organic they feel like they are in a completely different world!

    When I was teaching gen chem, I worked to do it far more in the language of organic chemistry. Our Lewis structures were mostly organic molecules. We had a biochemist teaching second semester and her examples of equilibria and buffers were the same that she used in her biochem course. I didn’t teach it, but if I would have, my kinetics examples would have been biological systems with enzyme catalysis. Because they can do that. We don’t need to use the decomposition of N2O5 –> N2O + O2 as an example of first order kinetics.

    Gen chem could do a lot better job of preparing the students for organic. Orgo doesn’t need to be a weed-out course.

  26. What frustrated me most with teaching organic chemistry was that, despite two semesters of general chemistry, the whole “count the numbers of bonds on your atoms” rule was still not in place. I started with reviewing H 1 bond, C 4 bonds, N 3 (or 5), O 2, followed by a pop quiz next class with nothing but “draw any valid structure for this elemental composition”. One third of the class was unable to do it (nothing sneaky, explicitly stated no ionic structures, only those four elements). And those were science majors…

  27. @28. Absolutely correct. Genchem is dominated by pchemists and inorganikers. Why? Because the organic folks are always busy with organic! Our organic chemists rarely teach genchem. This always turns genchem into baby pchem and baby inorganic courses. They could use many more examples of organic molecules from the book to look at valence and isomerism, but they don’t. Why? Because the textbook doesn’t.

  28. For me it was probably the Berkeley-sequence intro E&M course. I’d had had high school calc, and AP credits, and didn’t want to waste a year, so I jumped right in first quarter. It was worth it, with a lot of effort I caught up just fast enough to get an A. I somehow missed Jackson, somehow I felt I already knew E&M. I think what matters is how well the students math prep (and raw ability), matches what is needed for whatever courses heshe is taking. Some courses are hard in different ways, -my son had a biology course that was just a ton of work (he claimed three and a half hours per day) -they have now split that into two semesters instead of one. In that case, there probably wasn’t anything insurmountable about the material, just the amount of it.

    There are some areas like science, and especially engineering, that a lot of students who are actually math-a-phobic, think they’d like to major in. Encountering a weed-out course as early as possible is a definite benefit to these students, who then have time to redirect their interests.

  29. I have taught organic on and off since 1981 and it is true some students find it hard, other find it easier than they thought. But teaching graduate organic synthesis, not that is a hard course. All the laws and rules you have learned turn out to be more like guidelines. Molecules are like analog computers, you put in the conditions and it calculates the output (product) based on acidity, electron distribution, size, rates, equilibrium and probably a dozen other things you might not consider at first. Every single molecule is an individual. But wrong answers are still easy for the teacher to identify.

  30. My vote is for ALL of them at Caltech (except the economics ones). Not because of the material, but because of the other students. For a person of average intelligence, it was the intellectual equivalent of being beaten up for my lunch money daily.

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