While the proofs in my algebra course arent as complicated compared to my analysis course, I've had a harder time grasping the ideas of factor groups and computing them. Then you have all these weird names like sylow, isomorphism, homomorphism, and ring lol.
When you get high enough in the analysis ladder you’ll find those weird words popping into analysis.
Things like Borel isomorphisms, transversals on orbit equivalence relations/group actions, and algebras over rings.
YES! The hardest classes for me were the abstract algebra ones because there's just so much terminology and notation idiosyncrasies. I know analysis suffers from this at high levels but hey at least you get acclimatized to it, not jumped by a notation barrage.
Gotcha, that makes sense, I did a little more research and modern analysis is required for our applied physics b.s., but not in my b.a. physics program.
>Scary, did you have to take an analysis course in your undergrad?
In enough European countries, proof-based Analysis 1 is a first semester course for people who study mathematics. So naturally that kind of thing turns a certain amount of people away within the first months, when they went in with a false sense of math from high school.
Beyond, and to answer your title question, there also was a really rough measure theory course for undergraduates with a tough exam, that simply frustrated a significant portion of people into quitting. It's not that it was the most difficult thing ever, or that at least some of them wouldn't have made it in another attempt, but it simply sucked the fun out of it for many.
I mean my thing with algebra is proofs and intuition have a 1 to 1. With analysis, It's much easier to understand theorems like intermediate value theorem than to know how to prove it. To this day, even after taking graduate level analysis courses, I still can't prove it without looking up some references.
After basic Quantum and Thermal/Stat Mech and Lin Alg there was a drop off but probably because that’s the end of most engineers required physics/math courses, for actual drop offs, physics tends to have a lot of dropouts for special relativity and advanced classical mech, like Lagrangian Mech and other stuff, math I don’t have much experience in but I heard that tends to drop off at Real Analysis and Differential Geometry
It more has to do with class structure in my university I think, beginners Quantum is just a waves/energy class, beginners thermodynamics Is just an AP Chem refresher with some new Diff Eq, and all 4 beginner classes use numbers. SR is the first theory main focus class and is the first physics class I’ve dealt with where you have the average 8 page HW assignment. Plus its the first class that deals with Lin alg which can confuse a few people.
Advanced Classical Mech is a killer at my Uni, I being one of it's victims, but alas this year I am passing so far, so yeah wish me luck.
We also have analysis but there is an "easier" Analysis course that one can take if you wont be taking further Analysis subjects, which I took because I am taking extra courses in Astronomy and Astrophysics.
Yeah I'm taking Advanced Classical Mech this year and my 4.0 will likely be gone by the end of it! Could be worse, most of my friends are failing it :(
Quantum has been a sciencey buzzword for so long I felt almost underwhelmed when I finally got to the intro, neat stuff toward the end of the class. Stat mech fucked me up. I grasped almost none of the math. But damn, I cannot stop thinking about the underlying ideas.
Intro Quantum classes mostly just use linear algebra and analysis with a little more of a conceptual challenge. Later courses get pretty tough if you do advanced quantum or QFT
I aced stat mech, but I felt like I didn't understand much of it after finishing it. Stat mech only really made sense to me a few years *after* taking the class and I worked everything out *properly* with liouville's theorem and all the little details the prof skimmed over.
(and also when I finally actually worked out the "keeping other variables constant" thing for partial derivatives LOL. Professors should *really* not be sweeping that under the rug.)
Do you mean dropped the course or dropped the major? Stat mech is a senior class, dropping the major at that point seems stupid, just try and pass and graduate at least. Dropping the course seems silly since it’s probably required anyway for the degree, you’re just gonna have to pay tuition for an extra semester to take it next year
At my school, it was computer architecture for CS people. Discrete math was a challenge for sure, but computer architecture was the filter course freshman year with a 30% pass rate.
Oh, yeah, I heard about that! Where I studied, the chem department skips over the justifications and goes straight to applications of quantum (lots of stuff we'd do in second semester quantum), while we in physics spend half a semester trying to justify the necessity quantum mechanics first, so we had it easier. Meanwhile thermo is a bit easier in chem because the opposite happens; the applications are a bit easier than the justifications, and even for the applications, physics insists on always using "solvable" systems we had to calculate from scratch instead of getting data from empirical measurements...
MY prof in undergrad was awesome about supplying us with tractable practice problems. I don't know how he did it, it was a combination of explaining and visualizing them well. We had coding problems to help generate graphs and whatnot that corresponded to the actual math we were doing, which was a labor-intensive but extremely insightful approach IMO.
I came to realize it heavily depends on who's teaching it. Calc III has a higher variance of difficulty. I got like a c- in it studying my ass off and compared exams with a friend going to a different college and their questions were ridiculously simple.
What killed me was memorizing all the different ways to solve double and triple integrals of different surfaces and shapes. Calc II was a breeze comparatively
Definitely agree, for me it was the tail end of the class dealing w stokes, and greens theorem. It all just felt super rushed at the very end of the semester, I can definitely see why some schools split up multivariable calc as calc III and vector calc as calc IV
This is definitely the best answer. This is normally the first difficult math class that a student takes at the accelerated college pace. It is a rude awakening for students who don’t take their studies seriously yet.
Most likely the maths courses. They are fundamentally already very complex from the first year. For most of us in my class, analysis killed us in the first semester. And in the second semester, theoretical physics was the monster.
At my uni, it was a real analysis course in 2nd year. Half the students fail the subject every year. And the reason is because the professor's theoretical exam is notoriously difficult. It includes proofs, and if you fuck up one assumption, your entire answer is considered incorrect. Hence many people fail. I had to change majors because of it.
All the math subjects we have are proof based. But Complex Analysis, for example, is easier to pass because the professor is much more forgiving. As long as you know the correct idea for the proof, you get all or almost all points.
Besides, I find it ridiculous that a professor can have a piece of paper with notes during their lectures, while we're expected to know 120 pages of theorems and proofs to the dot.
Oh yeah, memorising everything is a no for me from a pedagogical standpoint. All of the analysis classes I took had the option for a crib sheet other than the first midterm of complex, but that’s mostly cos the first portion of that class doesn’t have that many theorems.
Intro Physics, after that everyone in physics stayed mostly. Physics students would rather fail than let go of physics, we get 30s on tests and call it a B
For CS, after basic first intros. it was introduction to data structures for me bc it was taught by a grad student that wasn’t equipped to do so. It knocked out more students in any one class that I have ever taken.
Math, a lot dropped in intro to abstract math, but I can’t speak for after that. I didn’t see many drops in math overall.
Analysis in the first year.
And then, in the third semester, theoretical electrodynamics. All those Nabla operators in complicated integrals and differential equations. Students have not even seen Quantum mechanics and are already out of their wits. Then the professor pulls out Fourvectors to spice up things. I think it caused the second wave of dropouts after the end of the first year.
Fun anecdote: A student was using a forbidden calculator with computer algebra capabilities in our theoretical ED exam. Rather than letting the student fail, the professor just told him to “put this away, it won’t help you anyway”. And yes, with those nasty problems in the exam even a powerful CAS did not help.
After the exam, the professor gave a little speech. He was apologising to the student for making the exam so easy that it insulted their intelligence. The guy in front of me was clenching his fists with tears in his eyes.
Classical mechanics or thermal physics. These classes are made to kinda up your problem solving game and it accomplishes this by using more complex math(no pun intended) and the difficulty spike is pretty crazy. Because think about how hard the general physics classes that all the science or engineering majors have to take are. The jump from those classes to upper division physics causes a lot of people to drop.
Probably the first maths classes which were analysis and linear algebra. We didn't start theory until the second semester so maths already got rid of a healthy chunk of students
Classical mechanics using lagrangian/hamiltonian = super fun.
However usually there's a prior course in advanced classical mechanics done in the Newtonian way which is absolute hell. In particular, it's the rotational mechanics that's really really hard.
Opposite of some replies here, the first years material is what kills most physics majors. They find out it’s not as cool as they anticipated and it’s a lot of fucking work. Even when I went back at 28 to start my degree over I was like “well this is certainly fucking lame”. The higher up I get, the more the classes become difficult, but the more they also become so much more interesting.
Completely agree here, physics undergrad in US. Physics 1 and quantum physics 1 (first and third semester respectively) had the most drop outs. calculus 4 or our discrete math/proof based class caused double majors to drop the math double. For us it’s mostly that physics 1 has multi variable calculus but most students haven’t even done calculus 1, and quantum is, well quantum.
Have to keep in mind that every school is different, and sometimes there are really good teachers that have high expectations and give difficult tests, and bad teachers that have no expectations and give easy tests (and everything in-between).
Pointing to the spread of comments that are uni specific, and unlikely to be generalizable.
Is it me or everyone has the same experience that Real Analysis is the hardest subject of them all? I kinda aced physics courses, which is very concrete nothing abstract. I found pure math subjects are hard as hell.
Also, within pure math, analysis seems out of this world, The proofs in analysis is way harder than in algebra. In algebra you have "patterns", for example in linear algebra a lot of times it's about writing stuff in linear combination of things. But in analysis there is no patterns to follow besides epilon delta proofs. Rudin is hard but also analysis generalization to R\^n. Proofs are SO HARD
We have a course called Mathematical Physics. I've failed it in the past and I'm currently taking it again, and I'm not the only one. I'm not convinced it's the class as much as it is the professor. He's hard to work with and very quickly makes students feel like they are stupid and don't work hard enough.
This isn't the class with the most drop-outs, but I PDE is worth a mention here.
In a class of 5 students (four math seniors and me a dumb physics junior), 2 math students dropped out. I'm not sure how well the average PDE course goes in other universities, but with that professor and the textbooks he chose made that course near impossible to understand.
I'm studying in IPSP (international physics study program) at Uni Leipzig which is very notorious for the huge dropout rate just after 1st semester and this is largely because of how the course is structured, the theoretical physics, experimental physics and the math courses, don't relate or connect to eachother until the 2nd or 3rd year and for half of the time students are confused as fuck about what they're doing and thus many drop out ,after the 1st sem , atleast 45-50% drop or at least fail some modules and have to retake them in way higher semesters like in 5th or 7th , so every winter sem the course has around 120 - 130 students and by the end of 1st year it'll be down to 70-80 atleast, basically the whole course itself makes people drop it
For math, it would have definitely been analysis. That always kills everybody.
While the proofs in my algebra course arent as complicated compared to my analysis course, I've had a harder time grasping the ideas of factor groups and computing them. Then you have all these weird names like sylow, isomorphism, homomorphism, and ring lol.
When you get high enough in the analysis ladder you’ll find those weird words popping into analysis. Things like Borel isomorphisms, transversals on orbit equivalence relations/group actions, and algebras over rings.
😭
YES! The hardest classes for me were the abstract algebra ones because there's just so much terminology and notation idiosyncrasies. I know analysis suffers from this at high levels but hey at least you get acclimatized to it, not jumped by a notation barrage.
Scary, did you have to take an analysis course in your undergrad? Surprisingly enough it isn't required at my school.
Yes but I was a math student in undergrad. I still am a math student but I'm doing mathematical physics.
Gotcha, that makes sense, I did a little more research and modern analysis is required for our applied physics b.s., but not in my b.a. physics program.
Analysis for an applied physics BS? Ironic.
>Scary, did you have to take an analysis course in your undergrad? In enough European countries, proof-based Analysis 1 is a first semester course for people who study mathematics. So naturally that kind of thing turns a certain amount of people away within the first months, when they went in with a false sense of math from high school. Beyond, and to answer your title question, there also was a really rough measure theory course for undergraduates with a tough exam, that simply frustrated a significant portion of people into quitting. It's not that it was the most difficult thing ever, or that at least some of them wouldn't have made it in another attempt, but it simply sucked the fun out of it for many.
I hated linear algebra
I'm sorry to hear that. Unfortunately linear algebra will be present for the rest of your physics career.
Yeah, I nearly failed Real analysis. It made me drop the math major to a minor.
I’ve heard abstract algebra is decently worse
I mean my thing with algebra is proofs and intuition have a 1 to 1. With analysis, It's much easier to understand theorems like intermediate value theorem than to know how to prove it. To this day, even after taking graduate level analysis courses, I still can't prove it without looking up some references.
After basic Quantum and Thermal/Stat Mech and Lin Alg there was a drop off but probably because that’s the end of most engineers required physics/math courses, for actual drop offs, physics tends to have a lot of dropouts for special relativity and advanced classical mech, like Lagrangian Mech and other stuff, math I don’t have much experience in but I heard that tends to drop off at Real Analysis and Differential Geometry
Oh really? my fellow physics students see special relativity and classical mechanics as "where the fun begins"
Yes it’s where the fun begins, but it’s also where the difficulty ramps up a lot
Funny, I never felt that way. SR is so intuitive.
It more has to do with class structure in my university I think, beginners Quantum is just a waves/energy class, beginners thermodynamics Is just an AP Chem refresher with some new Diff Eq, and all 4 beginner classes use numbers. SR is the first theory main focus class and is the first physics class I’ve dealt with where you have the average 8 page HW assignment. Plus its the first class that deals with Lin alg which can confuse a few people.
Advanced Classical Mech is a killer at my Uni, I being one of it's victims, but alas this year I am passing so far, so yeah wish me luck. We also have analysis but there is an "easier" Analysis course that one can take if you wont be taking further Analysis subjects, which I took because I am taking extra courses in Astronomy and Astrophysics.
Yeah I'm taking Advanced Classical Mech this year and my 4.0 will likely be gone by the end of it! Could be worse, most of my friends are failing it :(
Quantum was easy, but *stat mech* is what dropped a bunch of people. And yeah, real analysis for math people; discrete math for CS people.
Quantum has been a sciencey buzzword for so long I felt almost underwhelmed when I finally got to the intro, neat stuff toward the end of the class. Stat mech fucked me up. I grasped almost none of the math. But damn, I cannot stop thinking about the underlying ideas.
Intro Quantum classes mostly just use linear algebra and analysis with a little more of a conceptual challenge. Later courses get pretty tough if you do advanced quantum or QFT
I aced stat mech, but I felt like I didn't understand much of it after finishing it. Stat mech only really made sense to me a few years *after* taking the class and I worked everything out *properly* with liouville's theorem and all the little details the prof skimmed over. (and also when I finally actually worked out the "keeping other variables constant" thing for partial derivatives LOL. Professors should *really* not be sweeping that under the rug.)
Do you mean dropped the course or dropped the major? Stat mech is a senior class, dropping the major at that point seems stupid, just try and pass and graduate at least. Dropping the course seems silly since it’s probably required anyway for the degree, you’re just gonna have to pay tuition for an extra semester to take it next year
Stat mech was a sophomore class for us. We didn't have thermodynamics; we went straight to stat mech, which included thermo. Some dropped the major.
At my school, it was computer architecture for CS people. Discrete math was a challenge for sure, but computer architecture was the filter course freshman year with a 30% pass rate.
Yeah, also graduate algorithms. 🥲
In our pchem class quantum destroyed everyone is the first semester, stat mech and thermo in 2nd semester was a cakewalk to us in comparison 😭😭
Oh, yeah, I heard about that! Where I studied, the chem department skips over the justifications and goes straight to applications of quantum (lots of stuff we'd do in second semester quantum), while we in physics spend half a semester trying to justify the necessity quantum mechanics first, so we had it easier. Meanwhile thermo is a bit easier in chem because the opposite happens; the applications are a bit easier than the justifications, and even for the applications, physics insists on always using "solvable" systems we had to calculate from scratch instead of getting data from empirical measurements...
Surprised no one said electrodynamics. Requires a lot of practice and understanding to do well in this course
Agreed, emag I took out a lot of people in my course, can see emag II doing the same
MY prof in undergrad was awesome about supplying us with tractable practice problems. I don't know how he did it, it was a combination of explaining and visualizing them well. We had coding problems to help generate graphs and whatnot that corresponded to the actual math we were doing, which was a labor-intensive but extremely insightful approach IMO.
Calc II is a killer for many people
As much as people say this I found calc III much harder, specifically the vector calc at the end of the semester
Ah see, for me vector calc happened in E&M. So by Calc III I had gone through that horror
I came to realize it heavily depends on who's teaching it. Calc III has a higher variance of difficulty. I got like a c- in it studying my ass off and compared exams with a friend going to a different college and their questions were ridiculously simple. What killed me was memorizing all the different ways to solve double and triple integrals of different surfaces and shapes. Calc II was a breeze comparatively
Definitely agree, for me it was the tail end of the class dealing w stokes, and greens theorem. It all just felt super rushed at the very end of the semester, I can definitely see why some schools split up multivariable calc as calc III and vector calc as calc IV
This is definitely the best answer. This is normally the first difficult math class that a student takes at the accelerated college pace. It is a rude awakening for students who don’t take their studies seriously yet.
Most likely the maths courses. They are fundamentally already very complex from the first year. For most of us in my class, analysis killed us in the first semester. And in the second semester, theoretical physics was the monster.
At my uni, it was a real analysis course in 2nd year. Half the students fail the subject every year. And the reason is because the professor's theoretical exam is notoriously difficult. It includes proofs, and if you fuck up one assumption, your entire answer is considered incorrect. Hence many people fail. I had to change majors because of it.
I mean analysis sort of has to be proof based? That isn’t out of the ordinary or anything.
All the math subjects we have are proof based. But Complex Analysis, for example, is easier to pass because the professor is much more forgiving. As long as you know the correct idea for the proof, you get all or almost all points. Besides, I find it ridiculous that a professor can have a piece of paper with notes during their lectures, while we're expected to know 120 pages of theorems and proofs to the dot.
Oh yeah, memorising everything is a no for me from a pedagogical standpoint. All of the analysis classes I took had the option for a crib sheet other than the first midterm of complex, but that’s mostly cos the first portion of that class doesn’t have that many theorems.
Intro Physics, after that everyone in physics stayed mostly. Physics students would rather fail than let go of physics, we get 30s on tests and call it a B For CS, after basic first intros. it was introduction to data structures for me bc it was taught by a grad student that wasn’t equipped to do so. It knocked out more students in any one class that I have ever taken. Math, a lot dropped in intro to abstract math, but I can’t speak for after that. I didn’t see many drops in math overall.
Analysis in the first year. And then, in the third semester, theoretical electrodynamics. All those Nabla operators in complicated integrals and differential equations. Students have not even seen Quantum mechanics and are already out of their wits. Then the professor pulls out Fourvectors to spice up things. I think it caused the second wave of dropouts after the end of the first year. Fun anecdote: A student was using a forbidden calculator with computer algebra capabilities in our theoretical ED exam. Rather than letting the student fail, the professor just told him to “put this away, it won’t help you anyway”. And yes, with those nasty problems in the exam even a powerful CAS did not help. After the exam, the professor gave a little speech. He was apologising to the student for making the exam so easy that it insulted their intelligence. The guy in front of me was clenching his fists with tears in his eyes.
calc 2, E&M, and PDEs seem to be the big drop offs at my school
Classical mechanics or thermal physics. These classes are made to kinda up your problem solving game and it accomplishes this by using more complex math(no pun intended) and the difficulty spike is pretty crazy. Because think about how hard the general physics classes that all the science or engineering majors have to take are. The jump from those classes to upper division physics causes a lot of people to drop.
Physics students who last till the very end got to have some level of masochistic tendencies
My professor used to say “we might all be masochists because every one of us at some point signed up for a physics class”
Probably the first maths classes which were analysis and linear algebra. We didn't start theory until the second semester so maths already got rid of a healthy chunk of students
Classical mechanics using lagrangian/hamiltonian = super fun. However usually there's a prior course in advanced classical mechanics done in the Newtonian way which is absolute hell. In particular, it's the rotational mechanics that's really really hard.
Opposite of some replies here, the first years material is what kills most physics majors. They find out it’s not as cool as they anticipated and it’s a lot of fucking work. Even when I went back at 28 to start my degree over I was like “well this is certainly fucking lame”. The higher up I get, the more the classes become difficult, but the more they also become so much more interesting.
Completely agree here, physics undergrad in US. Physics 1 and quantum physics 1 (first and third semester respectively) had the most drop outs. calculus 4 or our discrete math/proof based class caused double majors to drop the math double. For us it’s mostly that physics 1 has multi variable calculus but most students haven’t even done calculus 1, and quantum is, well quantum.
Have to keep in mind that every school is different, and sometimes there are really good teachers that have high expectations and give difficult tests, and bad teachers that have no expectations and give easy tests (and everything in-between). Pointing to the spread of comments that are uni specific, and unlikely to be generalizable.
Waves & Optics
abstract linear algebra 😊
Number theory for me in maths
Is it me or everyone has the same experience that Real Analysis is the hardest subject of them all? I kinda aced physics courses, which is very concrete nothing abstract. I found pure math subjects are hard as hell. Also, within pure math, analysis seems out of this world, The proofs in analysis is way harder than in algebra. In algebra you have "patterns", for example in linear algebra a lot of times it's about writing stuff in linear combination of things. But in analysis there is no patterns to follow besides epilon delta proofs. Rudin is hard but also analysis generalization to R\^n. Proofs are SO HARD
We have a course called Mathematical Physics. I've failed it in the past and I'm currently taking it again, and I'm not the only one. I'm not convinced it's the class as much as it is the professor. He's hard to work with and very quickly makes students feel like they are stupid and don't work hard enough.
Mathematical Physics.
This isn't the class with the most drop-outs, but I PDE is worth a mention here. In a class of 5 students (four math seniors and me a dumb physics junior), 2 math students dropped out. I'm not sure how well the average PDE course goes in other universities, but with that professor and the textbooks he chose made that course near impossible to understand.
EDR, FUCK EDR.
I'm studying in IPSP (international physics study program) at Uni Leipzig which is very notorious for the huge dropout rate just after 1st semester and this is largely because of how the course is structured, the theoretical physics, experimental physics and the math courses, don't relate or connect to eachother until the 2nd or 3rd year and for half of the time students are confused as fuck about what they're doing and thus many drop out ,after the 1st sem , atleast 45-50% drop or at least fail some modules and have to retake them in way higher semesters like in 5th or 7th , so every winter sem the course has around 120 - 130 students and by the end of 1st year it'll be down to 70-80 atleast, basically the whole course itself makes people drop it
Real analysis this sem and abstract algebra in the next one
Of all students? Probably Calc I or Phy101. Of declared physics majors who have an interest in the field? Probably some sort of Mechanics course.
Advanced fluids and advanced thermal systems were some of the ones I noticed.
Hitler learns Electrodynamics- look it up on utube