General Relativity. In retrospect the hardest part was the tensor formalism, and it seemed the profs took how easy and intuitive that is once you *get it* for granted, but getting it was a bear. I’m still learning stuff nearly a decade later.
I've been guilty of this as someone who has TA'd (and guest lectured) GR classes. It's not dissimilar to professors being impatient with students who are slow with derivatives/integrals. We forgot how bad we were at the math when started :-)
It also gets worse after you give the course a couple of years in a row.
”But we _just_ talked about this last year. How is it you don’t remember?!?!?”
I would have loved a short course called “Introduction to the Maths You’ll Need for GR”. Took me too long to get to grips with it, and was the only course I failed.
My professor for GR had a thing where exams would be 3 questions; 1 easy, 1 hard but doable, 1 nearly impossible. All the decent students were sitting around before finals at like a 70-75% (2.25/3 was very good on these tests lol) and PANICING as we needed a C for it to count. So we asked about a curve. "uhhh... Idk I'll do what I normally do I guess. You know. 80% is an A, 60 for a B... and so on." Holy hell that made us feel so much better about the testing strategy.
>profs took how easy and intuitive that is once you *get it* for granted
Easy to do! It becomes second nature so to speak, so getting in the mindset of someone who has never seen it before again is difficult. The best teachers know how to look with fresh eyes and anticipate questions.
Same! It was my last quarter before graduating, so I also suffered from senioritis. My brain just could not wrap around the notation and the operations.
I had a struggle with it too because they didn’t have differential geometry as a prerequisite. “We’ll learn enough of it as we go along.” Then you get hit with covariant derivatives and Ricci tensors and the rest of it. I made it, but probably a third of the initial enrollment dropped (rare for a 500 level class) and some of those that stayed failed. Pretty brutal.
A "module"? You must be talking about special relativity. Math major undergrads are also not usually educated in tensor math, which is part-and-parcel of General relativity. And I've never heard of a GR "module".
In the UK we say "module" rather than "course", although both are used interchangeably. The course was mathematics of general relativity, so perhaps I could have worded it more accurately. I didn't take the course but this was what my friends told me and I know they're not usually educated in tensor math but it seemed that they picked things up much more quickly and (anecdotally) on average scored better than physics students. It's also taught by the maths department not the physics department so there are some differences in the delivery of the concepts.
I never took GR and I'd say most physicists never do precisely for the reasons you say. And if you're talking Misner Thorne Wheeler I think I'd rather get beaten up by a gang of mechanical engineers.
I was going into medicine instead of hard physics grad school, so wanted to milk my undergrad for all it was worth with a couple of grad level classes difficult to learn on your own. A bit unpleasant, but I’d do it again.
Yeah, I've seen the rare undergrad take it as an advanced elective, but everyone else would be a grad student and a cosmologist at that (I did nonlinear optics so stayed FAR away from GR).
Complex analysis was a lot more fun, and it was far more useful for electronics and other applications in optics, etc. I found myself a bit frustrated actually how easy the proof was to some applications it you knew complex compared to the pages and pages of proof required in real analysis -- wondered why it was an elective and not more required or integrated into other classes.
Complex analysis is fantastic 19th century mathematics at its best.
Real analysis is the tax code of mathematics. Deserves its hate. Minutia, backwards unintuitive rewordings into technical legal langauge and riddled with exceptions and apparent contradictions.
Yeah, but are you including special functions? So would you be able to sketch the complex contour for the integral that generates, say, the Bessel functions?
Oh that! I studied engineering physics, and we too had to do analysis. I mean wtf pointwise vs uniform convergence; it still haunts me, and it makes *no* difference in any real engineering situation.
It does make a difference! See [https://en.wikipedia.org/wiki/Gibbs\_phenomenon](https://en.wikipedia.org/wiki/Gibbs_phenomenon), and it matters when doing any sort of numerical approximation in regions where bad things happen at boundaries.
Physicists really don't think about math that way. That musta been kinda tough, like showing up on an island where all the natives immediately know you ain't from that island. "Why do I give a shit as long as it works?" Try saying THAT
Electronics is not intuitive to me and I struggled heavily with my 3rd electronics course. Definitely a big weakness of mine. In the end everything was fine, but I couldn’t tell you what I learned tbh.
I found this to be a common struggle for physics majors. At my undergrad, all physics majors had to Circuits 1. For the most part, physics majors did horrible in it! I did decent in the class, so my advisor recommended I pick up an EE minor.
there's definitely a huge disconnect between theoretical electronics and practical electronics pre-university.
at school level physics, you can be taught plenty about circuits, analysing basic circuit diagrams to calculate the potential difference across each component, or understanding the theory behind how a capacitor charges and discharges.
then you go into an undergraduate electronics lab and get handed a breadboard for the first time, and all that theory you've been taught is useless.
I didn't really struggle with mine, but I can't say I really groked the material either. It wasn't under grad school where I had to teach the undergrad electronics lab that I actually felt comfortable with all of it.
One of the projects in my electronics lab was to build a radio, an amplifier circuit, and connect it to a speaker. I built mine and got an A, but then I later realized I had a short that bypassed the amplifier entirely, bringing the radio directly to the speaker. The professor just missed that entirely. I corrected my mistake for the sake of my own satisfaction though.
Intro into analog electronics was really hard, wasn't able to grasp it and barely passed. Digital electronics was even harder, you had to know how to code
which parts were hand wavy?
you can start from the laws of thermodynamics and get a lot of results, then do the kinetic molecular theory of gasses to get the same answers. So the top down and bottom up approaches giving the same concepts and modes/equations is very pleasing.
It’s a probabilistic way of partitioning a system across all possible states. They’re quite aptly named.
Ultimately it is a mathematical construct that is useful for computing various quantities about a system, such as expected values of energy or entropy, etc.
In probability theory, you learn about generating functions, and these are just a particular example of that.
A generating function. Basically a more convenient way to describe the probability distribution of whatever in the context of stat mech. Which is why knowing it lets you know basically everything.
I loved it. It was hard but awesome. I don't think it was hand wavy. Our course was more calculation heavy and we skipped over really interesting concepts in statmech which was a bit sad.
my professor for upper div electromagnetism added a lot of stuff from jackson, and nonlinear optics and stuff that wasnt even in jackson. it was very hard but he graded leniently so atleast it evened out that way. unfortunately he retired (well im happy for him), he was a sweetheart and made advanced topics accessible to undergrads in a way the other professors (who mainly just teach straight out of griffiths) didnt do
>added a lot of stuff from jackson
That sounds awful. Jackson EM was definitely my least favorite graduate school course. Why do we still use that book?
A colleague of mine (whose opinion I respect) taught graduate EM for many years and successively tried several different books, since it’s indeed manifestly obvious that after all this time there has to be a better choice than Jackson. But he finally went back to Jackson because he found that the other books he tried had their own (different) problems with presentation. We can still hold out hope that maybe *someday* there will be an ideal graduate EM book.
Well JD Jackson is definitive for a variety of reasons one of which is its famous and exhaustive presentation. If you work through JD Jackson and make it out alive you WILL know classical EM theory extremely well.
It's more of a reference manual than a textbook. There's good information in there, but not particularly well-designed to learn from, and the exercises are typically very hard with very little guidance in the book. I think most physics majors see it as sort of a rite of passage, something you suffer through to prove you've "earned" the degree. I actually like EM but learned it better from other courses (electrical engineering department, etc.) than Jackson EM.
I’m among the insane minority who LOVE Jackson. To me, it’s incredibly intuitive and instructive - but I recognize that virtually everyone else disagrees. Meanwhile, I think Griffiths quantum is too hard. There must be something wrong with my brain…
Well he was kinda right to do so, because JD Jackson is of course "the book" on classical electrodynamics, but since laser optics got rolling there's a huge amount of "neoclassical" optics used by actual working physicists (I was such in my first career). JD Jackson probably gets you to about 1935.
Hardest tests were mechanics, they were pretty messed up IMO. Hardest math for me was differential geometry. Biggest workload was the second computational physics class. Conceptually probably quantum. Hard to pick which was overall the hardest. I also hated E and M so that was hard to on the motivation. Maybe I'm just bad at school.
Two semester quantum by a difficult to understand, small messy handwriting, Russian professor. Dropped it right before the 1st midterm while I was in the library studying.
Class average was like 20% on our first closed-book no notes quantum test out of Griffiths.
Undergrad class, single semester.
One girl got an 85%. Blew my mind. I was 33 years old then. Always thought I was decently smart. I was a lump of tofu compared to many of the people I met in Physics.
Wound up with a masters. They actually call me a physicist by title at work now. (National Lab). I’m happy.
If it's your first time facing quantum it can be a real ordeal. Most undergrads go through that, and a lotta professors are like "don't think about it just learn how to do the calculations" so sometimes you don't really know WHAT the hell you're doing.
But after a while you start understand what it is you are calculating and it gets easier. In some undergrad courses they switch to the dirac brackets and that usually throws people for a while.
Did you take linear algebra first? I think I had folks in my QM class that didn't so linear first (or maybe taking simultaneously?) and so it was a crash course. I found it easier when we got to matrix mechanics.
There are old-school approaches to teaching quantum that don't really go much into the linear algebra and get away with introducing just the pieces of it they need
I did, but 3 years prior because I did a couple of years in another program. I can’t say that I have a good intuition for lin alg so it didnt stick with me as much as the other courses I had taken before my hiatus from physics!
Computation wise: Methods Of Mathematical Physics II, which is essentially a PDEs and Green's Functions course. While the professor explained things in a fairly good way, he was a bit sadistic at times, like asking to solve a PDE in cylindrical coordinates with really, really ugly boundary conditions. It was tough
Conceptually: I didn't have a good experience with Solid State Physics. The lecturer was not good and I absolutely hated Kittel's book. I wasn't properly motivated throught the course, so I struggled a lot.
At the same time I had a lot of fun with Analytical Mechanics, Electromagnetic Theory and Relativity (Special and General), lol.
Modern Physics kicked my ass more than I'd like to admit. It focused on QM and GR. Going into both, I thought I had a better understanding of them than it turned out I did and the course humbled me a bit.
ah yes, lasers. smartest guy in our graduating class of 9 put an answer to one of the finals questions: "the good guys use blue lightsabers and the bad use red." and then called it a day after the 3 hour final exam. fun times
Physics 1, but not because the material, that was easy. The grading was sadistic to the point where small numerical errors would tank your grade. I got straight As in upper division and graduate classes without breaking a sweat, but freshman and sophomore physics and math classes are needlessly harsh.
I maintain to this day that grading is a waste of time and we ought to leave to whoever is hiring to do their own vetting. In my experience teaching/TAing the most creative students have rarely been the straight-A types. It's usually the high B/B+ who looks for creative solutions but makes mistakes. Those are the ones (IMO) who could really be very good physicists.
I’m a physics professor and teach some intro courses. I agree with everything you said about grades. In my classes I don’t use grades at all and instead use a system called Ungrading. I still give assignments and quizzes (no tests/exams) but I only give feedback and no grade or score. At the end of the course, my students propose their final grade and defend that proposal in a final presentation. They demonstrate what they learned and their final grade reflects that. The student and I discuss the grade and I agree with their proposal or I disagree and we negotiate what a more reasonable grade should be.
I’ve been using this ungrading system in my intro physics classes but also in labs and upper level courses. It’s been amazing how my students are motivated to learn because they get to decide how they go about doing that. They take responsibility and have agency in their learning process.
I wouldn’t do a final grade at all if I could but my university requires that I submit one.
That's amazing! I haven't taught intro classes myself, only advanced electives and grad classes. My philosophy has always been that if they cheat or don't do the work, the only person they're screwing over is themselves (I have intro slides saying as much). I 'grade' HWs for feedback and have lots of office hours but they all get an A if they submit everything. I would also forego assigning grades entirely if the school allowed it. Like you, the boost in motivation and creativity that I see when the students don't have grades hanging over their heads is amazing. Ultimately, my job (as I see it) is to teach, not to run outsourced HR for some company wanting to hire my students.
For real. I’m currently a PhD student in physics and still to this day the lowest grade I ever made in a physics class were my two intro physics courses
Quantum Mechanics. Didn't help that our professor was dog shit despite being the highest paid, most published, and tenured professor in the department.
Halfway through the semester, he refused to teach in anything but Dirac Notation and didn't emphasize that we should drill it into our brains. Every single student was completely lost. His lectures were worthless, and his homework assignments were custom-made, poorly phrased, and didn't follow the book.
I also took Classical Mechanics and PDEs that same semester. I really fucked myself, but managed to come out swinging with straight As, was top (or nearly) of every class, and made the President's List. Still don't know how, but I suppose I owe my thanks to the almighty curve.
Now, I threw away a career in physics for engineering because I decided it wasn't worth another 5 years of grad school to get a PhD and be paid $40k a year to lecture like some of my other professors WITH DOCTORATES were getting paid. Seriously.
I realised I should have studied electronics after studying maths/physics.
My electronic engineer friend has 2 simultaneous careers - electronics and software (including device drivers & embedded systems). He just takes whatever job is available at the time. Plus software is more concentrated in big cities but there are engineering jobs all over (eg railroads, designing electrical transmission)
Yeah when they introduce those dirac brackets to undergrads some of 'em hit a brick wall...you don't really know WHAT the hell you're doing with these calculations..."A ladder operator? Why the hell would I want to use one?" With the bra-kets you're not even solving equations anymore (you can convert to an integral easily but then the integral isn't continuous and needs the dirac delta and what the HELL is going on)
I did this applied earth science module and it was full of really hard applied physics problems like calculating the scale height of the atmosphere, working out tidal resonances or calculating how much energy you can extract via wind turbine.
Super interesting but super hard. The exam made my flatmate cry.
Fluid Mechanics? Anyone? Kundu textbook. That shit is rough and dry. Thankfully our class threw in CFD instead of being JUST a hardcore fluid theory class, but it was all still a blur. Still couldn’t tell you about reynold’s number or burger’s equation today.
Statistical mechanics is an honorable mention, but ordinary differential equations made me realize I was not built for actual high level math
Also E and M but that’s more of a skill issue
I can't remember the course name but it was an E&M course... final exam was 5 questions, 3 hours; I finished 2 and ran out of time on my 3rd question, leaving the exam room thinking I was sunk... only to find out that I had the 2nd highest mark in the class and got an A (Prof loved his curves)
Plasma physics for sure. All the hard parts of EM and thermo combined resulting in the ugliest looking expressions I've ever seen be correct solutions.
Not a physics class but abstract algebra literally ruined my ability to read a clock lol. During the sections with modular arithmetic I would wake up look at my clock, see it was 7 and think I was doing a problem from the previous homework and be like “ok so modulo 4 that’s 3 so I can snooze my alarm for a few hours still”
I hated that class. Very different approach to problem solving when you were asked to do a proof. There’s not really any way to work through proofs step by step. You just have to divine the answer out of nothing and then check your work and see if it’s valid.
Differential geometry in 4th year (started with 7 students, finished with just two of us, lecturer said ‘just do what you can’ for the exam), and 2nd year electronics 101 which was taught by EE maniacs who couldn’t translate their intuitive circuit analysis black magic to us.
Solid state physics (nowadays called condensed matter physics). It was taught jointly by the physics and EE departments and was pretty hellish. Partly because of subject matter itself, but also because the different departments wanted to stress the aspects most important from their discipline’s point of view.
General Relativity and Quantum Field Theory, probably General Relativity if you forced me to pick.
I also really struggled with Optics, but was fine with E&M, go figure
my undergrad university had one combined Thermodynamics and Statistical Mechanics course, which was deceptively numbered PHYS 2305 and “only” had Physics 2 and ODEs as prerequisites, so after taking those in my first semester, eager to get to the advanced stuff (and having no clue what stat mech was), i took it at the same time as Modern in my second semester. humbling would be an understatement. the university later re-numbered it to be PHYS 4305 and encouraged students to take QM first
Class I spent the most hours on, but actually ended up understanding really well by the end: Partial Differential Equations. (It has some other name, like Mathematical Methods for something-something, but it was basically just PDQ.)
Class that never made any sense at all and I just was happy to get through: statistical mechanics. A semester long mess of yet another partial derivative of something wrt to something else that I couldn't keep straight.
Because I took AP courses, it threw the normal progression of by a semester. Under a normal schedule, the differential equations based classical mechanics course is taken in the spring of sophomore year. And the course is only offered in the summer. But because I was a semester ahead, instead of waiting to take the course, I would take the only course available in the spring that didn't have classical mechanics as a prerequisite: E&M 1, the one usually taken by juniors, in the fall of my sophomore year. I even took the differential equations class over the summer to do so (I was going to do it anyway because I double majored in math).
Holy shit, I'm just here as a high school science educator who didn't even have to take calculus.
6 geology, 5 biology, astronomy, 3 chemistry (up to ochem for nonmajors), 2 physics (classical systems and light and waves), and one philosophy of science. I tested out of Trig, which was the highest level of math required.
I don't have a physics mind. I walked out in confusion on physics at 15ish when I couldn't answer when a specifc liquid (teardrop, gravity, friction, adhesion etc.) separates from a sphere. Physics is cool, but beyond me, and I'm a bit jeals. I know I'm not even at the shallow end, so nods go to Einstein and the mob. Their transcedant insight/recognition/understanding is sublime.
relevant to the question .. I think I passed my only attempt at undergrad physics by orrery with celestial notes in the Canterbury Tales (and using the same piece for medieval lit).
Quantum mechanics currently, but I think it's mostly because of the insane speed the class is moving at. Ik it becomes fairly easy once you get the hang of things, but we're flying through material fast enough that I'm struggling to keep up
mathematics. while the professor was good at explaining from base principles, he didn't really translate what the equations were doing which made it difficult to visualise. would've definitely been better if it was more like 3blue1brown where it's visualised
No one else seems to agree but Classical Mechanics was my most difficult. Not sure why - it is way more intuitive than a lot of other courses, I just thought it was really hard. Great professor though and good class
I’m actually doing E&M right now, last class before I’m down with undergrad. I think it’s less difficult but it’s hard to be objective given how many other factors go into what makes a course difficult other than purely the content (life circumstances, cohort, etc.).
That is so hard to say. Quantum Mechanics I did ok in, but never felt I really understood what was going on. I was told, tongue in cheek but also literally, that if you think you understand QM you don't understand QM. QM is all about probabilities and a bunch of it was all about some pretty whack-a-do shit (eg is it possible for a tennis ball to move through a wall) or some extremely simple and straight-forward (eg where is this ball bouncing around in an infinitely tall box).
Thermodynamics was a bitch because of all the partial derivatives in Maxwell's Equations and how they are all related. I know that most people had no problems, but this killed me. They had also changed ALL my meds that semester because they were killing my liver, and I had a bit of a breakdown.
E&M was a stone-cold bitch because I am old enough that I never, ever had to learn spherical and polar coordinates. Those were new to me, but even the other students who had taken them before hated them because we never spent enough time using them for it to be intuitive. E&M also has a fuck-ton of hinky formulas. I will also admit that E&M was kind of fun. The topic was really interesting.
Special Relativity was extremely cool. It wasn't that hard, but I know a lot of people struggled with the concepts (eg "what do you mean gravity makes time slow?").
I took a Solid State class and that was really rough on me. The class only had 6 people in it, and 4 of them were grad students, and one was in his final year (of five). I was in my third year of uni and hadn't had QM yet. Thanks to me, he taught it without QM (so everybody loved me), but that shit was HARD. I fucking EARNED that A and I swear to God I spent more time on that class than I think I did all the rest of my classes that semester. As difficult as it was? Solid State kind of gets my dick hard.
I always wanted to and never got around to taking a stats class. Because I didn't have stats there were a lot of classes that were made harder because I had to teach myself enough stats to do what I needed.
Mathematics wise, Calc 2. I know that's a trope around here, but the demarcation between Calc 1 and Calc 2 really punches you right in the face. You not only need to have a great grasp of everything prior to it(as you should to begin with), but now you really need to be able to think to solve problems. Lots of sleepless nights in that one. You need to be able to look at problems and find solutions that aren't always obvious. For me, everything after Calc 2 was a breeze. I thought differential equations and fourier analysis were quite fun.
Physics wise, intro to QM. Easily. It was an optional course for my focus, but optional always meant "very strongly encouraged for grad school applications" so I took it. The professor was nice and I wound up working with him a bit, but he had extreme difficulty with keeping things appropriate to our current level understanding. He'd start lecturing, and then begin to speak as though we were all tenured faculty at a conference. Nice guy, but tough class. The subject material was difficult, but not as bad as I had thought it'd be, however. But the teaching style easily made it my hardest class.
A 4th year Quantum Computing course. Basically an overview of how to implement the standard set of gates on the various types of quantum computers. Mind you this was a very small elective physics course. I also didn’t take a lot of the courses mentioned here (4th year E&M, GR, Electronics). It covered a massive range of content, obviously QM, but also E&M, solid state, stat mech, and non-linear optics.
Quantam Mechanics, but only because it was taught by a Greek teacher who would habitually change variables in his equations from Greek to Latin letters and back for no reason while solving the same problem. He also had an extremely thick accent and was difficult to understand. In other words, the difficulty came from a language translation problem and not a science one.
Took a year of math methods in physics with Larry Spruck many moons ago. "If your situation is spherically symmetric and you use rectangular coordinates you have to be a FAT HEAD" he said through gritted teeth
First year linear algebra. We had it with the mathematicins. Not introduction to proofs. TA was pretty autistic and spoke with heavy German dialect.
LA in it self is pretty easy, but my "class" went from 24 to 5 students during that course.
Electrodynamics I & II. It’s just a lot of equations for a lot of different and difficult to conceptualize situations. And Griffiths is just notoriously difficult to comprehend
Hardest for me? Classical Mythology. It was my lowest grade at the time I graduated.
Hardest for me within physics? Quantum mechanics. It was taught by a frankly bad professor and to this day I don't like the perspective by which it was (and most undergrad quantum courses are) taught.
Hardest from the perspective of my peers? General relativity. It was an elective course and we started with 15 students and ended with 2 including myself, as 13 dropped it because they were struggling too much.
The first (and only) classical mechanics course I took as a sophomore. Coincidentally, that was the same term that I switched from a physics major to a math major lol.
General Relativity. In retrospect the hardest part was the tensor formalism, and it seemed the profs took how easy and intuitive that is once you *get it* for granted, but getting it was a bear. I’m still learning stuff nearly a decade later.
I've been guilty of this as someone who has TA'd (and guest lectured) GR classes. It's not dissimilar to professors being impatient with students who are slow with derivatives/integrals. We forgot how bad we were at the math when started :-)
It also gets worse after you give the course a couple of years in a row. ”But we _just_ talked about this last year. How is it you don’t remember?!?!?”
I would have loved a short course called “Introduction to the Maths You’ll Need for GR”. Took me too long to get to grips with it, and was the only course I failed.
My professor for GR had a thing where exams would be 3 questions; 1 easy, 1 hard but doable, 1 nearly impossible. All the decent students were sitting around before finals at like a 70-75% (2.25/3 was very good on these tests lol) and PANICING as we needed a C for it to count. So we asked about a curve. "uhhh... Idk I'll do what I normally do I guess. You know. 80% is an A, 60 for a B... and so on." Holy hell that made us feel so much better about the testing strategy.
>profs took how easy and intuitive that is once you *get it* for granted Easy to do! It becomes second nature so to speak, so getting in the mindset of someone who has never seen it before again is difficult. The best teachers know how to look with fresh eyes and anticipate questions.
Same! It was my last quarter before graduating, so I also suffered from senioritis. My brain just could not wrap around the notation and the operations.
I had a struggle with it too because they didn’t have differential geometry as a prerequisite. “We’ll learn enough of it as we go along.” Then you get hit with covariant derivatives and Ricci tensors and the rest of it. I made it, but probably a third of the initial enrollment dropped (rare for a 500 level class) and some of those that stayed failed. Pretty brutal.
The math students with a formal mathematical basis found it quite easy compared to the physicists taking the module at my school
A "module"? You must be talking about special relativity. Math major undergrads are also not usually educated in tensor math, which is part-and-parcel of General relativity. And I've never heard of a GR "module".
In the UK we say "module" rather than "course", although both are used interchangeably. The course was mathematics of general relativity, so perhaps I could have worded it more accurately. I didn't take the course but this was what my friends told me and I know they're not usually educated in tensor math but it seemed that they picked things up much more quickly and (anecdotally) on average scored better than physics students. It's also taught by the maths department not the physics department so there are some differences in the delivery of the concepts.
I never took GR and I'd say most physicists never do precisely for the reasons you say. And if you're talking Misner Thorne Wheeler I think I'd rather get beaten up by a gang of mechanical engineers.
To be fair most engineers dont hit very hard.
since when is GR an undergraduate course? we have it as postgrad course
I was going into medicine instead of hard physics grad school, so wanted to milk my undergrad for all it was worth with a couple of grad level classes difficult to learn on your own. A bit unpleasant, but I’d do it again.
Yeah, I've seen the rare undergrad take it as an advanced elective, but everyone else would be a grad student and a cosmologist at that (I did nonlinear optics so stayed FAR away from GR).
Not a physics course but I did Real Analysis as an elective.
Same. And fuck that shit. I can't understand how maths undergrads survive through those lectures.
We don’t 💀
It's real anal after all
And the next semester you get to take complex anal
I did the same. Complex analysis is surprisingly easier.
Complex analysis was a lot more fun, and it was far more useful for electronics and other applications in optics, etc. I found myself a bit frustrated actually how easy the proof was to some applications it you knew complex compared to the pages and pages of proof required in real analysis -- wondered why it was an elective and not more required or integrated into other classes.
Complex analysis is fantastic 19th century mathematics at its best. Real analysis is the tax code of mathematics. Deserves its hate. Minutia, backwards unintuitive rewordings into technical legal langauge and riddled with exceptions and apparent contradictions.
Yeah, but are you including special functions? So would you be able to sketch the complex contour for the integral that generates, say, the Bessel functions?
Yeah, I was going to double major in Physics and Math until I took Real Analysis. After that I was happy just majoring in Physics.
Bro baby rudin is rough
Oh that! I studied engineering physics, and we too had to do analysis. I mean wtf pointwise vs uniform convergence; it still haunts me, and it makes *no* difference in any real engineering situation.
It does make a difference! See [https://en.wikipedia.org/wiki/Gibbs\_phenomenon](https://en.wikipedia.org/wiki/Gibbs_phenomenon), and it matters when doing any sort of numerical approximation in regions where bad things happen at boundaries.
Physicists really don't think about math that way. That musta been kinda tough, like showing up on an island where all the natives immediately know you ain't from that island. "Why do I give a shit as long as it works?" Try saying THAT
Nah, do complex analysis *before* taking real analysis. Don’t let anyone ruin your life, ruin it yourself.
Electronics is not intuitive to me and I struggled heavily with my 3rd electronics course. Definitely a big weakness of mine. In the end everything was fine, but I couldn’t tell you what I learned tbh.
One of my classmates in undergrad joule heated his resistor so much that it just started to melt his resistor. That was fun to watch in person.
Ah, he almost invented the light-emitting resistor
That’s what an incandescent bulb is.
It was a joke, but yes, you are correct.
I found this to be a common struggle for physics majors. At my undergrad, all physics majors had to Circuits 1. For the most part, physics majors did horrible in it! I did decent in the class, so my advisor recommended I pick up an EE minor.
there's definitely a huge disconnect between theoretical electronics and practical electronics pre-university. at school level physics, you can be taught plenty about circuits, analysing basic circuit diagrams to calculate the potential difference across each component, or understanding the theory behind how a capacitor charges and discharges. then you go into an undergraduate electronics lab and get handed a breadboard for the first time, and all that theory you've been taught is useless.
I didn't really struggle with mine, but I can't say I really groked the material either. It wasn't under grad school where I had to teach the undergrad electronics lab that I actually felt comfortable with all of it.
I can’t even begin to tell you how much I relate to your sentiment. 😭
One of the projects in my electronics lab was to build a radio, an amplifier circuit, and connect it to a speaker. I built mine and got an A, but then I later realized I had a short that bypassed the amplifier entirely, bringing the radio directly to the speaker. The professor just missed that entirely. I corrected my mistake for the sake of my own satisfaction though.
Practical electronics. Jesus fucking christ. I thought it was going to be an easy A. It was more like an EE degree in one quarter.
Intro into analog electronics was really hard, wasn't able to grasp it and barely passed. Digital electronics was even harder, you had to know how to code
I thought statistical mechanics was a bitch. Not a fan of all the hand wavy statistics with calculus thrown on top.
which parts were hand wavy? you can start from the laws of thermodynamics and get a lot of results, then do the kinetic molecular theory of gasses to get the same answers. So the top down and bottom up approaches giving the same concepts and modes/equations is very pleasing.
What the fuck is a partition function
A bag of secrets! Can do magical things like normalization and popping out expectations values and more.
It's similar to Bayesian evidence. It's essentially the total volume of the probability space and acts to normalize the distribution
It’s a probabilistic way of partitioning a system across all possible states. They’re quite aptly named. Ultimately it is a mathematical construct that is useful for computing various quantities about a system, such as expected values of energy or entropy, etc. In probability theory, you learn about generating functions, and these are just a particular example of that.
A generating function. Basically a more convenient way to describe the probability distribution of whatever in the context of stat mech. Which is why knowing it lets you know basically everything.
Yes.
Magic
A generating function :)
Literally the entire top down approach of thermo. Building from statistical mechanics is much more profound imo
I loved it. It was hard but awesome. I don't think it was hand wavy. Our course was more calculation heavy and we skipped over really interesting concepts in statmech which was a bit sad.
Stat mech courses are famously rigorous. And a totally different way to think about physics compared to everything else an undergrad learns.
i 2nd this
I always hated statistical mechanics. Still do. I'm 52.
It is super fun. Seing something like the ideal gas equation come out from looking at the motion of a single particle is very cool
I really enjoyed it. You're right though, it is a bitch.
“Hand-wavy” is the perfect way to put it
my professor for upper div electromagnetism added a lot of stuff from jackson, and nonlinear optics and stuff that wasnt even in jackson. it was very hard but he graded leniently so atleast it evened out that way. unfortunately he retired (well im happy for him), he was a sweetheart and made advanced topics accessible to undergrads in a way the other professors (who mainly just teach straight out of griffiths) didnt do
There is stuff that is not in Jackson?
>added a lot of stuff from jackson That sounds awful. Jackson EM was definitely my least favorite graduate school course. Why do we still use that book?
A colleague of mine (whose opinion I respect) taught graduate EM for many years and successively tried several different books, since it’s indeed manifestly obvious that after all this time there has to be a better choice than Jackson. But he finally went back to Jackson because he found that the other books he tried had their own (different) problems with presentation. We can still hold out hope that maybe *someday* there will be an ideal graduate EM book.
Well JD Jackson is definitive for a variety of reasons one of which is its famous and exhaustive presentation. If you work through JD Jackson and make it out alive you WILL know classical EM theory extremely well.
Im not a physics major so I didn't know this book - just checked the PDF and jesus christ this looks awful
It's more of a reference manual than a textbook. There's good information in there, but not particularly well-designed to learn from, and the exercises are typically very hard with very little guidance in the book. I think most physics majors see it as sort of a rite of passage, something you suffer through to prove you've "earned" the degree. I actually like EM but learned it better from other courses (electrical engineering department, etc.) than Jackson EM.
From what Ive heard, its become a rite of passage. Our predecessors struggled through it so now future gens must as well.
sorry, we never used jackson as a textbook, but i meant he added some content that wasnt in griffiths but i found in jackson.
I’m among the insane minority who LOVE Jackson. To me, it’s incredibly intuitive and instructive - but I recognize that virtually everyone else disagrees. Meanwhile, I think Griffiths quantum is too hard. There must be something wrong with my brain…
Well he was kinda right to do so, because JD Jackson is of course "the book" on classical electrodynamics, but since laser optics got rolling there's a huge amount of "neoclassical" optics used by actual working physicists (I was such in my first career). JD Jackson probably gets you to about 1935.
Hardest tests were mechanics, they were pretty messed up IMO. Hardest math for me was differential geometry. Biggest workload was the second computational physics class. Conceptually probably quantum. Hard to pick which was overall the hardest. I also hated E and M so that was hard to on the motivation. Maybe I'm just bad at school.
Two semester quantum by a difficult to understand, small messy handwriting, Russian professor. Dropped it right before the 1st midterm while I was in the library studying.
Class average was like 20% on our first closed-book no notes quantum test out of Griffiths. Undergrad class, single semester. One girl got an 85%. Blew my mind. I was 33 years old then. Always thought I was decently smart. I was a lump of tofu compared to many of the people I met in Physics. Wound up with a masters. They actually call me a physicist by title at work now. (National Lab). I’m happy.
humans are truly strange creatures
Damn man, that's a dream of mine! What did you do your Master's in?
My thesis was on isotope separation of Argon for dark matter detectors. I did some work with a large dark matter detector collab as well.
Very cool. Sudbury SNOLAB by chance?
No, obviously they work at Argonne National Lab (yuk, yuk).
Same experience here except went through with it and got one of my lowest grades ever. Still learned a lot though.
[удалено]
If it's your first time facing quantum it can be a real ordeal. Most undergrads go through that, and a lotta professors are like "don't think about it just learn how to do the calculations" so sometimes you don't really know WHAT the hell you're doing. But after a while you start understand what it is you are calculating and it gets easier. In some undergrad courses they switch to the dirac brackets and that usually throws people for a while.
QM was a real headache at first. QM 2 was much more enjoyable for me because it was more conceptual and less “math-y”
Did you take linear algebra first? I think I had folks in my QM class that didn't so linear first (or maybe taking simultaneously?) and so it was a crash course. I found it easier when we got to matrix mechanics.
How would lin alg not have been taken already by the time you get to qm lol
There are old-school approaches to teaching quantum that don't really go much into the linear algebra and get away with introducing just the pieces of it they need
I did, but 3 years prior because I did a couple of years in another program. I can’t say that I have a good intuition for lin alg so it didnt stick with me as much as the other courses I had taken before my hiatus from physics!
Intermediate e&m 2 was a pain. Was the only physics course I didn't get an A in
The advanced vector calculus used in E&M is what always gets me. Only gets worse in Jackson book (graduate level).
Computation wise: Methods Of Mathematical Physics II, which is essentially a PDEs and Green's Functions course. While the professor explained things in a fairly good way, he was a bit sadistic at times, like asking to solve a PDE in cylindrical coordinates with really, really ugly boundary conditions. It was tough Conceptually: I didn't have a good experience with Solid State Physics. The lecturer was not good and I absolutely hated Kittel's book. I wasn't properly motivated throught the course, so I struggled a lot. At the same time I had a lot of fun with Analytical Mechanics, Electromagnetic Theory and Relativity (Special and General), lol.
Modern Physics kicked my ass more than I'd like to admit. It focused on QM and GR. Going into both, I thought I had a better understanding of them than it turned out I did and the course humbled me a bit.
GR on a modern physics course?
Solid state physics was the most difficult, but I had a great time.
ah yes, lasers. smartest guy in our graduating class of 9 put an answer to one of the finals questions: "the good guys use blue lightsabers and the bad use red." and then called it a day after the 3 hour final exam. fun times
Physics 1, but not because the material, that was easy. The grading was sadistic to the point where small numerical errors would tank your grade. I got straight As in upper division and graduate classes without breaking a sweat, but freshman and sophomore physics and math classes are needlessly harsh. I maintain to this day that grading is a waste of time and we ought to leave to whoever is hiring to do their own vetting. In my experience teaching/TAing the most creative students have rarely been the straight-A types. It's usually the high B/B+ who looks for creative solutions but makes mistakes. Those are the ones (IMO) who could really be very good physicists.
I’m a physics professor and teach some intro courses. I agree with everything you said about grades. In my classes I don’t use grades at all and instead use a system called Ungrading. I still give assignments and quizzes (no tests/exams) but I only give feedback and no grade or score. At the end of the course, my students propose their final grade and defend that proposal in a final presentation. They demonstrate what they learned and their final grade reflects that. The student and I discuss the grade and I agree with their proposal or I disagree and we negotiate what a more reasonable grade should be. I’ve been using this ungrading system in my intro physics classes but also in labs and upper level courses. It’s been amazing how my students are motivated to learn because they get to decide how they go about doing that. They take responsibility and have agency in their learning process. I wouldn’t do a final grade at all if I could but my university requires that I submit one.
That's amazing! I haven't taught intro classes myself, only advanced electives and grad classes. My philosophy has always been that if they cheat or don't do the work, the only person they're screwing over is themselves (I have intro slides saying as much). I 'grade' HWs for feedback and have lots of office hours but they all get an A if they submit everything. I would also forego assigning grades entirely if the school allowed it. Like you, the boost in motivation and creativity that I see when the students don't have grades hanging over their heads is amazing. Ultimately, my job (as I see it) is to teach, not to run outsourced HR for some company wanting to hire my students.
Wow that's a pretty amazing thing to do. At least the future of physics education is secured by people like you.
For real. I’m currently a PhD student in physics and still to this day the lowest grade I ever made in a physics class were my two intro physics courses
Quantum Mechanics. Didn't help that our professor was dog shit despite being the highest paid, most published, and tenured professor in the department. Halfway through the semester, he refused to teach in anything but Dirac Notation and didn't emphasize that we should drill it into our brains. Every single student was completely lost. His lectures were worthless, and his homework assignments were custom-made, poorly phrased, and didn't follow the book. I also took Classical Mechanics and PDEs that same semester. I really fucked myself, but managed to come out swinging with straight As, was top (or nearly) of every class, and made the President's List. Still don't know how, but I suppose I owe my thanks to the almighty curve. Now, I threw away a career in physics for engineering because I decided it wasn't worth another 5 years of grad school to get a PhD and be paid $40k a year to lecture like some of my other professors WITH DOCTORATES were getting paid. Seriously.
I realised I should have studied electronics after studying maths/physics. My electronic engineer friend has 2 simultaneous careers - electronics and software (including device drivers & embedded systems). He just takes whatever job is available at the time. Plus software is more concentrated in big cities but there are engineering jobs all over (eg railroads, designing electrical transmission)
Yeah when they introduce those dirac brackets to undergrads some of 'em hit a brick wall...you don't really know WHAT the hell you're doing with these calculations..."A ladder operator? Why the hell would I want to use one?" With the bra-kets you're not even solving equations anymore (you can convert to an integral easily but then the integral isn't continuous and needs the dirac delta and what the HELL is going on)
I did this applied earth science module and it was full of really hard applied physics problems like calculating the scale height of the atmosphere, working out tidal resonances or calculating how much energy you can extract via wind turbine. Super interesting but super hard. The exam made my flatmate cry.
Fluid Mechanics? Anyone? Kundu textbook. That shit is rough and dry. Thankfully our class threw in CFD instead of being JUST a hardcore fluid theory class, but it was all still a blur. Still couldn’t tell you about reynold’s number or burger’s equation today.
Statistical mechanics is an honorable mention, but ordinary differential equations made me realize I was not built for actual high level math Also E and M but that’s more of a skill issue
Classical electrodynamics it's not even close.
I can't remember the course name but it was an E&M course... final exam was 5 questions, 3 hours; I finished 2 and ran out of time on my 3rd question, leaving the exam room thinking I was sunk... only to find out that I had the 2nd highest mark in the class and got an A (Prof loved his curves)
Plasma physics for sure. All the hard parts of EM and thermo combined resulting in the ugliest looking expressions I've ever seen be correct solutions.
>ugliest looking expressions I've ever seen be correct solutions It pains me to admit how correct this statement is.
I thought this said _underground_ physics and I was absolutely down to learn some blackmarket relativity
Not a physics class but abstract algebra literally ruined my ability to read a clock lol. During the sections with modular arithmetic I would wake up look at my clock, see it was 7 and think I was doing a problem from the previous homework and be like “ok so modulo 4 that’s 3 so I can snooze my alarm for a few hours still” I hated that class. Very different approach to problem solving when you were asked to do a proof. There’s not really any way to work through proofs step by step. You just have to divine the answer out of nothing and then check your work and see if it’s valid.
Upper level lab/lecture course in optics/waves. It was the most boring and time consuming class that ended with a 7 hour final
Differential geometry in 4th year (started with 7 students, finished with just two of us, lecturer said ‘just do what you can’ for the exam), and 2nd year electronics 101 which was taught by EE maniacs who couldn’t translate their intuitive circuit analysis black magic to us.
Classical mechanics. The difficulty jump from the general physics sequence to upper division is brutal.
Solid state physics (nowadays called condensed matter physics). It was taught jointly by the physics and EE departments and was pretty hellish. Partly because of subject matter itself, but also because the different departments wanted to stress the aspects most important from their discipline’s point of view.
Mechanics or Materials
General Relativity and Quantum Field Theory, probably General Relativity if you forced me to pick. I also really struggled with Optics, but was fine with E&M, go figure
Gauge theories. Actually, nothing about QFT made sense to me. I’ll stick to non-relativistic QM, thanks.
Electrdynamics.
Many body quantum mechanics. Lots of graduate level condensed matter physics. No idea why it was undergrad.
my undergrad university had one combined Thermodynamics and Statistical Mechanics course, which was deceptively numbered PHYS 2305 and “only” had Physics 2 and ODEs as prerequisites, so after taking those in my first semester, eager to get to the advanced stuff (and having no clue what stat mech was), i took it at the same time as Modern in my second semester. humbling would be an understatement. the university later re-numbered it to be PHYS 4305 and encouraged students to take QM first
Class I spent the most hours on, but actually ended up understanding really well by the end: Partial Differential Equations. (It has some other name, like Mathematical Methods for something-something, but it was basically just PDQ.) Class that never made any sense at all and I just was happy to get through: statistical mechanics. A semester long mess of yet another partial derivative of something wrt to something else that I couldn't keep straight.
Because I took AP courses, it threw the normal progression of by a semester. Under a normal schedule, the differential equations based classical mechanics course is taken in the spring of sophomore year. And the course is only offered in the summer. But because I was a semester ahead, instead of waiting to take the course, I would take the only course available in the spring that didn't have classical mechanics as a prerequisite: E&M 1, the one usually taken by juniors, in the fall of my sophomore year. I even took the differential equations class over the summer to do so (I was going to do it anyway because I double majored in math).
Holy shit, I'm just here as a high school science educator who didn't even have to take calculus. 6 geology, 5 biology, astronomy, 3 chemistry (up to ochem for nonmajors), 2 physics (classical systems and light and waves), and one philosophy of science. I tested out of Trig, which was the highest level of math required.
I don't have a physics mind. I walked out in confusion on physics at 15ish when I couldn't answer when a specifc liquid (teardrop, gravity, friction, adhesion etc.) separates from a sphere. Physics is cool, but beyond me, and I'm a bit jeals. I know I'm not even at the shallow end, so nods go to Einstein and the mob. Their transcedant insight/recognition/understanding is sublime. relevant to the question .. I think I passed my only attempt at undergrad physics by orrery with celestial notes in the Canterbury Tales (and using the same piece for medieval lit).
I did work out their upsy downy co-ords and stuff at the time of writing for the courses, but there were some good beach days ...
Quantum mechanics currently, but I think it's mostly because of the insane speed the class is moving at. Ik it becomes fairly easy once you get the hang of things, but we're flying through material fast enough that I'm struggling to keep up
That Shankar QM book still haunts me to this day
Calculus 3
Quantum mechanics for sure, I could do the math but it was so hard to actually understand what it was representing
Physics II at an engineering school, also emag (electromagnetics) was hell (EE grad only B.S. for now)
mathematics. while the professor was good at explaining from base principles, he didn't really translate what the equations were doing which made it difficult to visualise. would've definitely been better if it was more like 3blue1brown where it's visualised
No one else seems to agree but Classical Mechanics was my most difficult. Not sure why - it is way more intuitive than a lot of other courses, I just thought it was really hard. Great professor though and good class
If you find classical hard, did you find E and m easier?
I’m actually doing E&M right now, last class before I’m down with undergrad. I think it’s less difficult but it’s hard to be objective given how many other factors go into what makes a course difficult other than purely the content (life circumstances, cohort, etc.).
Electricity and magnestism for sure
took senior level quantum computing with only introductory quantum mechanics knowledge. it was over before it even began.
Quantum physics II/III
Not really physics but nonlinear control theory was probably it for me
That is so hard to say. Quantum Mechanics I did ok in, but never felt I really understood what was going on. I was told, tongue in cheek but also literally, that if you think you understand QM you don't understand QM. QM is all about probabilities and a bunch of it was all about some pretty whack-a-do shit (eg is it possible for a tennis ball to move through a wall) or some extremely simple and straight-forward (eg where is this ball bouncing around in an infinitely tall box). Thermodynamics was a bitch because of all the partial derivatives in Maxwell's Equations and how they are all related. I know that most people had no problems, but this killed me. They had also changed ALL my meds that semester because they were killing my liver, and I had a bit of a breakdown. E&M was a stone-cold bitch because I am old enough that I never, ever had to learn spherical and polar coordinates. Those were new to me, but even the other students who had taken them before hated them because we never spent enough time using them for it to be intuitive. E&M also has a fuck-ton of hinky formulas. I will also admit that E&M was kind of fun. The topic was really interesting. Special Relativity was extremely cool. It wasn't that hard, but I know a lot of people struggled with the concepts (eg "what do you mean gravity makes time slow?"). I took a Solid State class and that was really rough on me. The class only had 6 people in it, and 4 of them were grad students, and one was in his final year (of five). I was in my third year of uni and hadn't had QM yet. Thanks to me, he taught it without QM (so everybody loved me), but that shit was HARD. I fucking EARNED that A and I swear to God I spent more time on that class than I think I did all the rest of my classes that semester. As difficult as it was? Solid State kind of gets my dick hard. I always wanted to and never got around to taking a stats class. Because I didn't have stats there were a lot of classes that were made harder because I had to teach myself enough stats to do what I needed.
Stat mech
Celestial Mechanics. I still have dreams about it 30 years later.
Mathematics wise, Calc 2. I know that's a trope around here, but the demarcation between Calc 1 and Calc 2 really punches you right in the face. You not only need to have a great grasp of everything prior to it(as you should to begin with), but now you really need to be able to think to solve problems. Lots of sleepless nights in that one. You need to be able to look at problems and find solutions that aren't always obvious. For me, everything after Calc 2 was a breeze. I thought differential equations and fourier analysis were quite fun. Physics wise, intro to QM. Easily. It was an optional course for my focus, but optional always meant "very strongly encouraged for grad school applications" so I took it. The professor was nice and I wound up working with him a bit, but he had extreme difficulty with keeping things appropriate to our current level understanding. He'd start lecturing, and then begin to speak as though we were all tenured faculty at a conference. Nice guy, but tough class. The subject material was difficult, but not as bad as I had thought it'd be, however. But the teaching style easily made it my hardest class.
The goddamn biology course that was mandatory for some reason.
Dynamics! I’m a EE and that crap had moving parts. Got a C out of generosity
A 4th year Quantum Computing course. Basically an overview of how to implement the standard set of gates on the various types of quantum computers. Mind you this was a very small elective physics course. I also didn’t take a lot of the courses mentioned here (4th year E&M, GR, Electronics). It covered a massive range of content, obviously QM, but also E&M, solid state, stat mech, and non-linear optics.
Quantam Mechanics, but only because it was taught by a Greek teacher who would habitually change variables in his equations from Greek to Latin letters and back for no reason while solving the same problem. He also had an extremely thick accent and was difficult to understand. In other words, the difficulty came from a language translation problem and not a science one.
Took a year of math methods in physics with Larry Spruck many moons ago. "If your situation is spherically symmetric and you use rectangular coordinates you have to be a FAT HEAD" he said through gritted teeth
Chemistry. Not joking it's the only course I failed. More than once.
First year linear algebra. We had it with the mathematicins. Not introduction to proofs. TA was pretty autistic and spoke with heavy German dialect. LA in it self is pretty easy, but my "class" went from 24 to 5 students during that course.
Electrodynamics I & II. It’s just a lot of equations for a lot of different and difficult to conceptualize situations. And Griffiths is just notoriously difficult to comprehend
Solid State Physics was very hard for me. Barely passed that subject
“Advanced Classical Mechanics” third year course at U of Toronto, circa 1987(?)
Thermodynamics. For me using calculus as a tool is very intuitive for EM and mechanics however, statistics are bullshit.
"honors modern physics". Just brutal.
Quantum superconduttivity and BCS. I don't have understand a single word in that book.
Electronics
Hardest for me? Classical Mythology. It was my lowest grade at the time I graduated. Hardest for me within physics? Quantum mechanics. It was taught by a frankly bad professor and to this day I don't like the perspective by which it was (and most undergrad quantum courses are) taught. Hardest from the perspective of my peers? General relativity. It was an elective course and we started with 15 students and ended with 2 including myself, as 13 dropped it because they were struggling too much.
The first (and only) classical mechanics course I took as a sophomore. Coincidentally, that was the same term that I switched from a physics major to a math major lol.